Neutron Yield in Thick Targets: Exploring Low
and Intermediate Energies and Validating Model
Codes
Thesis submitted to
University of Calicut in partial fulfilment
for the degree of
Doctor of Philosophy
in
Physics
by
FATHIMA SHIRIN SHANA.A.T
under the guidence of
Dr.ABDUL GAFOOR.A.K
Principal(Rtd)
Government Arts and Science College, Kondotty
Research guide
Department of Physics
Government Arts and Science College,
Calicut
May 2024




”Verily, With Hardship Comes Ease”
Dedicated to My Beloved
Family and Friends
iv
Acknowledgements
Undertaking this PhD has been a truly life-changing experience for me and it
would not have been possible to do without the support and guidance that I received
from many people.
I would like to express my gratitude to my PhD Supervisor, Dr.Abdul Gafoor.A.K,
and Co-Guide Dr.Binitha.M.P for their support, guidance, and valuable insights
throughout the entire research work.
I am unable to begin this thesis without expressing my sincere gratitude to Dr
Sugathan.P, Scientist, IUAC, NewDelhi, I am incredibly grateful to him for all the
support and encouragement he given, during my doctoral period. Undoubtedly he is
a gods hand to me. He is such an exceptional academic expertise, coupled with his
commitment to support early career researchers truly make him a role model in the
often competitive world of academia. Without his guidance and constant feedback
this PhD would not have been achievable.
I extend my heartfelt appreciation to my work mentor Dr. M.M.Musthafa,
Senior Professor, Department of Physics, University of Calicut for his guidance and
suggestions during my research period.
The experiment work described in this thesis is carried out at IUAC, NewDelhi,
and I would like to express my sincere gratitude to research scientists Golda,K.S.,
Saneesh and Divya for their great support in NAND facility. Also I am very much
thankful to Dr.Ambar Chatterjee for his help in data acquisition.
I am also very much grateful to all my respected seniors, colleague and friends
starting with my birthday partner Gokul Das,K Hajara, Shaima Akber, Swapna
Balakrishnan, Anjali, Akhil ramesh, Nived, Aneena, Parvathi, Dinto, Vishnu, Anju,
Ummukulsu, Vafiyya, Midhun, Farhana thesni, Bhagyasree, Rajesh KK, Abdul Ka-
reem, Mohamed Aslam, Shafna, Nithu Ashok, Jisna rahman, Madhu.N , Ihsana,
Reena.V.N, Jasna Nizam, my IUAC friends Chandra, Mayur, Ritu, and Allan all of
them encouraged and helped me at every stage of my personal and academic life and
longed to see this achievement come true. A special thanks to my friend Vidhya.L
who brought me and guided me to the path of PhD.
v
Acknowledgement vi
I want to express my deepest gratitude to my family members. My father, Kun-
himoideen master and mother Rajila Moideen, for their tireless work and unwavering
commitment provided for me, while always discussing the value of education have
made a significant influence on my career path. And I hope they are proud of the
significant role they have played in shaping my path. Also words cannot express the
cheerful support from my sweet littles, My sister Dr. Aysha Leena Liyana, brother
Muhammed Shammas and sister in law Razana during my research journey. Not
least many kisses to my grandparents, A.T.Saidalavi, Fathima and Rukhiyya, my
uncles and aunts, Faisal Ali, Noushad Ali, Shamna, Zainul Abid, Shameema and
Haseena for all their dedication and Prayers which inspired to achieve my goal.
And of course a huge hugs to my in laws: Father and Mother Abdul Khader
and Safiya, sister and brothers: Noushad, Rasheeda, Shahid, Jamsheed, Rashid,
Rubeena, Najeeba, Aneesha, Sofiya, Raheeb, Rashid for their constant support and
prayers throughout my PhD journey.
Over all, No words to my all in all, my soulmate husband my (ikku) Dr.
Shameed, Thank you for always being my rock, accompanying me through the highs
and lows of this academic journey. His support and belief in me have been a source
of strength and motivation.
Words Never enough for my kindred spirits, my lovely sister Rohini Anantha
Padmanabhan, Achan and Amma(Mr. Venkiteswaran K and Mrs.Seethammal.K.S)
how they treated me as a daughter during my Pre-PhD days, I am very much
indebted for them.
Finally, As the well-known proverb tells “It takes a village to raise a child” I
strongly believe that this is the time which my native place waited for, each of them
directly and indirectly helped and prayed for me through out this journey and I
wholeheartedly thank them all. A verymuch thankful to all my neighbours, family
and natives of Jubilee road, especially, A very big awes to Mr.Musthafa kaku and
Saji thatha my family friends who gifted me laptop at its most needed time in which
I completed my whole PhD work.
Above all I owe to Allah Almighty for granting me the wisdom, health and
strength to undertake this research task and enabling me take it to its completion.
Contents
Acknowledgements v
List of Figures xi
List of Tables xv
Abbreviations xvii
List of Publications xviii
Preface xx
1 Introduction 1
1.1 Background and Motivation of the study . . . . . . . . . . . . . . . . 3
1.2 Overview of the thesis structure . . . . . . . . . . . . . . . . . . . . . 4
2 Literature Review 7
2.1 Nuclear reactions and its importance . . . . . . . . . . . . . . . . . . 7
2.2 Thick target reactions and their relevance . . . . . . . . . . . . . . . 8
2.3 Gaps in the literature and need of this work . . . . . . . . . . . . . . 13
3 Basic Theory and Model Codes 15
3.1 Reaction mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Direct Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Compound nucleus mechanism . . . . . . . . . . . . . . . . . . . . . . 18
3.3.1 Weisskopf-Ewing theory . . . . . . . . . . . . . . . . . . . . . 18
3.3.2 Hauser-Feshbach theory . . . . . . . . . . . . . . . . . . . . . 20
3.4 Pre-equilibrium Reaction . . . . . . . . . . . . . . . . . . . . . . . . . 21
vii
Contents viii
3.4.1 Exciton model . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.4.2 Hybrid model . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.4.3 Multi-step Direct (M.S.D) and Multi-step Compound (M.S.C)
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.5 Optical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.6 Nuclear level densities . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.6.1 Composite Gilbert-Cameron model . . . . . . . . . . . . . . . 29
3.6.2 The Back-shifted Fermi Gas Model . . . . . . . . . . . . . . . 30
3.6.3 The Generalized Superfluid Model . . . . . . . . . . . . . . . . 31
3.6.4 The Enhanced Generalized Superfluid Model . . . . . . . . . . 31
3.6.5 Microscopic level densities . . . . . . . . . . . . . . . . . . . . 32
3.7 Nuclear Reaction Codes and Tools . . . . . . . . . . . . . . . . . . . 32
3.7.1 EMPIRE-3.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.7.2 TALYS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.7.3 NeuCBOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.7.4 Directory Structure . . . . . . . . . . . . . . . . . . . . . . . . 36
3.7.5 PACE 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.7.6 SRIM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4 Thick target neutron yield-Low energy 41
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 Neutron energy spectra deduced for some elements . . . . . . . . . . 43
4.2.1 Alpha bombarded on Silicon . . . . . . . . . . . . . . . . . . . 43
4.2.2 Alpha bombarded on Aluminium . . . . . . . . . . . . . . . . 47
4.2.3 Alpha bombarded on Magnesium . . . . . . . . . . . . . . . . 50
4.3 Thick target neutron yield for Am-Be source. . . . . . . . . . . . . . . 56
4.3.1 Theoretical formalism using NeuCBOT . . . . . . . . . . . . . 58
4.3.2 Theoretical formalism using EMPIRE-3.2 code . . . . . . . . . 59
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5 Measurement of neutron energy from Am-Be 67
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.2 Facility Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.3 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.3.1 Am-Be source . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.3.2 BC501A neutron detector . . . . . . . . . . . . . . . . . . . . 70
5.3.3 BaF2 Gamma detector . . . . . . . . . . . . . . . . . . . . . . 71
5.3.4 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.3.5 Time of Flight method . . . . . . . . . . . . . . . . . . . . . . 73
5.4 Electronics setup and data acquisition system (DAQ) . . . . . . . . . 74
5.5 TOF energy spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.6 Comparison of experimental results with theoretical predictions . . . 82
Contents ix
5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6 Thick target neutron yield-Intermediate energy 85
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.2 Study of intermediate energy neutron yield . . . . . . . . . . . . . . . 87
6.2.1 12C on 27Al . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.2.2 12C on natTi . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.2.3 12C on 56Fe . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
7 Summary and Conclusion 97
7.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
8 Recommendation 103
Bibliography 105
List of Figures
3.1 Nuclear reaction mechanisms . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 Nuclear reaction cross section with separation of the three reaction
mechanisms depending on the emission energy . . . . . . . . . . . . . 17
3.3 Schematic diagram of behaviour of particle and holes in exciton model. 23
4.1 The angle integrated neutron energy spectra for thick targets of Sili-
con at four different α-particle energies, determined from time of flight
measurements(black line), The red line represents the result obtained
from NeuCBOT. From top to bottom of the figure: 5.5MeV, 5MeV,
4.5MeV,4MeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2 The angle integrated neutron energy spectra for thick targets of Alu-
minium at four different α-particle energies, determined from time
of flight measurements(black line), The red line represents the result
obtained from NeuCBOT. From top to bottom of the figure: 5.5MeV,
5MeV, 4.5MeV,4MeV . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.3 The angle integrated neutron energy spectra for thick targets of Mag-
nesium at four different α-particle energies, determined from time of
flight measurements(black line), The red line represents the result ob-
tained from NeuCBOT.From top to bottom of the figure: 5.5MeV,
5MeV, 4.5MeV,4MeV . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.4 The angle integrated neutron energy spectra for thick target of Boron
Nitrate at α-particle energy 5.5 MeV determined from time of flight
measurements(black line), The red line represents the result obtained
from NeuCBOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.5 The angle integrated neutron energy spectra for thick target of Cal-
cium fluoride at α-particle energy 5.5 MeV determined from time of
flight measurements(black line), The red line represents the result
obtained from NeuCBOT . . . . . . . . . . . . . . . . . . . . . . . . 54
4.6 Neutron yield for various elements is calculated by code NeuCBOT in
comparison with measurements. Neutron yield is given as the number
of neutrons per 107 alphas. . . . . . . . . . . . . . . . . . . . . . . . . 55
4.7 Energy level diagram of 12C . . . . . . . . . . . . . . . . . . . . . . . 57
4.8 Neutron energy spectrum predicted by NeuCBOT . . . . . . . . . . . 59
4.9 Neutron energy spectra at 900 . . . . . . . . . . . . . . . . . . . . . . 60
xi
List of Figures xii
4.10 Observed Neutron spectra,including the straggling corresponds to en-
ergy 3.6 MeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.11 Integrated neutron energy spectrum . . . . . . . . . . . . . . . . . . . 62
4.12 Neutron energy spectrum calculated using EMPIRE-3.2 with straggling 63
4.13 Resultant spectra from EMPIRE-3.2(red line),Geiger spectra(dotted
green line) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.1 NAND facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2 The encapsulated Am-Be source . . . . . . . . . . . . . . . . . . . . . 70
5.3 5 in (diameter) x 5 in ( height) BC501A liquid scintillator cell mounted
on a 5 in diameter PMT . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.4 The schematic diagram of the experimental setup (not to scale) . . . 73
5.5 Block diagram of the electronics setup used for signal processing and
data acquisition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.6 Zero-cross distribution showing distinct separation of neutrons and
γ-rays interacting inside BC501A detector . . . . . . . . . . . . . . . 76
5.7 Two dimensional histograms of zero-cross time vs. light output for
untagged and gamma-tagged conditions. . . . . . . . . . . . . . . . . 78
5.8 Two dimensional histogram of zero-cross time vs. time-of-flight. . . . 79
5.9 Simulated intrinsic efficiency of 5 in. x 5 in. single cell BC501A
detector as a function of neutron energy. . . . . . . . . . . . . . . . . 80
5.10 The Am-Be neutron energy spectrum from present measurement (solid
line), compared with ISO 8529-2 reference spectrum[66] (red dashed
line) and spectrum obtained by Scherzinger (2015) (blue dash-dotted
line). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.11 The neutron energy spectrum of Am-Be source measured compared
with EMPIRE-3.2 calculated . . . . . . . . . . . . . . . . . . . . . . . 82
5.12 The neutron energy spectrum of Am-Be source compared with mea-
sured TOF and calculated NeuCBOT . . . . . . . . . . . . . . . . . . 83
6.1 Comparison of Neutron yield data of 12C on 27Al at 00 reported by V.
Suman et al[67],with theoretical data from EMPIRE-3.2 and PACE 4. 87
6.2 Comparison of Neutron yield data of 12C on 27Al at 300 reported by V.
Suman et al[67],with theoretical data from EMPIRE-3.2 and PACE 4. 88
6.3 Comparison of Neutron yield data of 12C on 27Al at 600 reported by V.
Suman et al[67] with theoretical data from EMPIRE-3.2 and PACE 4. 89
6.4 Comparison of Neutron yield data of 12C on 27Al at 900 reported by V.
Suman et al[67],with theoretical data from EMPIRE-3.2 and PACE 4. 90
6.5 Comparison of Neutron yield data of 12C on 27Al reported by V.
Suman et al[67],with theoretical data from EMPIRE-3.2 with pre-
equilibrium(wp) and without pre-equilibrium(wop) and PACE 4. . . . 91
6.6 Comparison of neutron yield data reported by[24] with EMPIRE-3.2
and PACE 4 for 12C on Ti at 144 MeV . . . . . . . . . . . . . . . . . 92
List of Figures xiii
6.7 Comparison of Calculated neutron yield data from HIC-1 code data
reported by H.W.Bertini[68] with those obtained from model calcu-
lations EMPIRE-3.2 and PACE 4 for 12C on 56Fe reaction at 00 and
300 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.8 Comparison of Calculated neutron yield data from HIC-1 code data
reported by H.W.Bertini[68] with those obtained from model calcu-
lations EMPIRE-3.2 and PACE 4 for 12C on 56Fe reaction at 600 and
900. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
List of Tables
2.1 Neutron yield of some (α, n) sources[10] . . . . . . . . . . . . . . . . 8
2.2 The activity, neutron emission in n/s for Am-Be . . . . . . . . . . . . 9
2.3 Thick target(α,n) neutron yields per 107 α-particles reported in the
literature[21], The results of Liskien and Paulsen[13][14] were ob-
tained from calculation, the values presented by Bair and Gomez del
campo[18][15] are also from calculation and by West[20] are from mea-
surement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.1 The angle integrated neutron energy spectra for thick targets of silicon
at four different α-particle energies[21] . . . . . . . . . . . . . . . . . 45
4.2 The integral n/α values for thick targets of silicon at four differ-
ent α-particle energies obtained from literature and from the code
NeuCBOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3 The angle integrated neutron energy spectra for thick targets of Alu-
minium at four different α-particle energies[21] . . . . . . . . . . . . . 48
4.4 The integral n/α values for thick targets of aluminium at four dif-
ferent α-particle energies obtained from literature and from the code
NeuCBOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.5 The angle integrated neutron energy spectra for thick targets of Mag-
nesium at four different α-particle energies[21] . . . . . . . . . . . . . 51
4.6 The integral n/α values for thick targets of magnesium at four dif-
ferent α-particle energies obtained from literature and from the code
NeuCBOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.7 Representation of 9Be (α,n)12C reaction Q-value . . . . . . . . . . . . 58
xv
Abbreviations
PEQ Pre-equilibrium
MSD Multistep Direct
MSC Multistep compound
EGSM Enhanced Generalized Superfluid Model
NAND National Array of Neutron Detectors
TOF Time of Flight
ADC Analog to Digital Convertor
CFD Constant fraction Discriminator
PSD Pulse Shape Discrimination
DAQ Data Acquisition
xvii
List of Publications
Publications
1. Energy measurement of 241Am-9Be neutrons by tagged neutron time-of-flight,
F.S. Shana, K.S. Golda , N. Saneesh , D. Arora and P. Sugathan. Applied
Radiation and Isotopes,193(2023) 110655,
2. Secondary neutron production from 56Fe bombarded by 12C,A.T. Fathima
Shirin Shana, M.M. Musthafa, A.K. Abdul Gafoor, M.P. Binitha Oncology
and Radiotherapy,16 (8)(2022)5-8,
Publications Co-authored
1. Entrance channel dependence of quasi fission in reactions leading to 206Po
compound nucleus. Hajara, K, M.M. Musthafa, Fathima Shirin Shana et
al.,Nuclear Physics A. 1042. (2023).122789.
2. Evaporation residue cross section measurements for the Si 30 + Yb 176 reac-
tion. Hajara, K, M.M. Musthafa, F.S.Shana et al.,Physical Review C. 105.
(2022)
Conference Proceedings
1. Gamma gated neutron spectrum from Am-Be source, A.T.Fathima Shirin
Shana, M.M.Musthafa, A.K.Abdul Gafoor, C .V. Midhun, Divya Arora, N.
Saneesh, K.S Golda, P. Sugathan and S.Ganesan,Proceedings of the DAE
Symp. on Nucl. Phys. 64 (2019)
xviii
Publications xix
2. Measurement of neutron energy spectrum from 241 Am-Be source using CR-
39 track detector, A.T.Fathima Shirin Shana, M.M.Musthafa,C.V.Midhun,
Gokul Das.H, Arun.P.V,Proceedings of the DAE Symp. on Nucl. Phys. 66 (2022)
3. Probing Pre-equilibrium Neutron Emission in heavy ion reactions at large pro-
jectile energies, A.T.Fathima Shirin Shana, M.M.Musthafa,C.V.Midhun
,Proceedings of the DAE Symp. on Nucl. Phys. 67 (2024)
4. A study of alpha-induced pre-equilibrium neutron emission in natural Tita-
nium, Gokul Haridas, C V, Midhun, Musthafa, F.S.Shana et al.,,Advanced
Reactor Physics Conference(2022)
5. Lifetime measurement of 19/2 isomer in 175Re, Ritu Rani, Anu Rathi, N.
Bansal, F. S. Shana et al.,,Proceedings of the DAE Symp. on Nucl. Phys.
66 (2022)
List of Conference/Workshop attended
1. DST-PURSE supported Satellite Symposia on Physical Sciences, held at Bharathiar
University, Coimbatore, Tamil Nadu during September 13-15, 2022.
2. DAE-BRNS Workshop on “Nuclear Reaction data and its compilation for EX-
FOR database” to be held at Department of Physics, Bharathiar University,
Coimbatore, Tamilnadu, India during November 14-18, 2023.
3. DAE Symposium on Nuclear Physics held at Indian Institute of Technology
Indore, Madhya Pradesh during December 09-13, 2023.
4. Workshop on Geant4 for Applied Nuclear Physics held at University of Calicut,
Kerala during February 19-21, 2024.


Preface
The nucleus and it’s characteristics were a mysterious thing to humankind
for a long time. Many inventions have resulted from the constant attempt of
mankind to explain the complete structure of the nucleus. The foundations
of ”Nuclear Physics” was set by Dalton’s theory of the atomic structure of
matter, J.J. Thomson’s discovery of the electron, Henry Becquerel’s discovery
of radioactivity, Rutherford’s discovery of the atomic nucleus and the nuclear
constituent particles and Chadwick’s discovery of the neutron. The study of
the nucleus is considered to be started with the discovery of radioactivity by
Henry Becquerel in 1896. A nuclear reaction is a tool to study the characteris-
tics of the nucleus and the nature of the force between the nucleons. A nuclear
reaction occurs when a projectile nucleus is bombarded with a target nucleus,
leading to the emission of particles and/or radiation leaving behind the residual
nucleus. The residual nucleus will generally be at an excited energy level. One
has the information of the system before the reaction and the system after the
reaction but does not have the information of what exactly happening inside a
nucleus during the reaction process. This information is drawn from the reac-
tion outcomes. Thus to explain the reaction mechanism, Niels Bohr proposes
a satisfactory model for the nuclear reaction. According to this model, the
incident particle fuses with the target forming a compound nucleus system by
sharing its energy and angular momentum with all the nucleons in the target.
The compound nucleus then decays by emitting particles and/or gamma rays.
This decay is independent of the mode of formation. This is known as Bohr’s
compound nuclear mechanism or independent hypothesis. Analysing nuclear
reaction in relatively larger energy, it is observed that the compound nuclear
reaction theory is valid at relatively lower excitation energies. On the other
hand, at very high excitation energies, the direct reaction mechanism will pre-
vail. However, the emission of a particle from the nucleus before attaining
Preface xxi
the equilibrium state can be observed in many nuclear reactions induced by
fast projectiles and the process is referred to as the Pre-equilibrium Emission.
At moderate excitation energies, Pre-equilibrium (PEQ) emission process has
been identified as the prominent reaction mechanism. In PEQ mechanism,
the projectile may share its energy among a small number of nucleons which
may further, interact with other nucleons and during this cascade of nucleon-
nucleon interaction through which the projectile energy is progressively shared
among the target nucleons and there is a reasonable chance that the particles
are emitted long before the attainment of statistical equilibrium.
In order to test the validity of nuclear reaction models and predict the
behaviour of unknown system, it is essential to have a large number of data on
nuclear reactions covering a large number of nuclei in the periodic table over a
wide range of excitation energy. Nuclear reaction data is also important in the
fields like Nuclear engineering and Energy production, Medical and Industrial
Applications, Astrophysics and Cosmology, Materials Science and Radiation
Shielding, etc.
In Nuclear Engineering, data informs reactor design by influencing parame-
ters such as power levels, neutron flux distributions and fuel cycle management.
Accurate predictions of neutron yield aid in optimizing reactor efficiency and
safety measures. Further data is vital for predicting fuel depletion and burn-up
in nuclear reactors. These calculations guide fuel management strategies and
ensure efficient reactor operation.
Data is critical for Medical isotope production for radiography, cancer
treatment and other medical applications. The data are also employed in non-
destructive testing of materials. Neutron yield data aids in designing efficient
neutron sources for material analysis, defect detection and quality control.
Further data plays an important role in Stellar Evolution and Nucleosyn-
thesis, Accurate neutron yield data is essential for modeling stellar evolution
and understanding nucleosynthesis process.
Preface xxii
From the above findings it is well understood the facts that a wide range of
studies have been done with nucleon and heavy ion induced reaction regimes.
The studies at low and intermediate energies holds immense significance in
the areas of both theoretical nuclear physics and practical applications. Hence
this thesis aims to solve the complexities of thick target reaction in the low to
intermediate energy range.
In the present work a theoretical estimate of neutron yield from thick
targets for low and intermediate energy projectile system for different ener-
gies has been carried out. The nuclear model codes were used as a tool to
compare the results. These nuclear models were used to predict the neutron
emission results at various selected incident energies. The models are based
on an agreement with the nuclear data available in experimental data library
EXFOR. The theoretical code EMPIRE-3.2, NeuCBOT(TALYS+SRIM) and
PACE 4 is used in the present work for the code validation.
The present work focuses on two distinct case studies, both involving neu-
tron emission in thick targets and the validation of nuclear reaction model
codes. In the first case study, the focus is on low-energy neutron emission
from thick targets. This involves a comprehensive comparison of neutron
yield predictions obtained from two nuclear reaction model codes,EMPIRE-
3.2 and NeuCBOT, with experimental results. The experimental data is de-
rived from α bombardment of several light elements, including boron, carbon,
oxygen, fluorine, magnesium, aluminium and silicon at four distinct monoen-
ergetic α-particle energies (4.0, 4.5, 5.0 and 5.5MeV). Furthermore, to gen-
erate neutron energy spectra theoretically, a special case of Am-Be source
is explored, The neutron yield from Am-Be is evaluated as it is a case of
(α,n) reaction. The spectra generated by NeuCBOT, calculates the neutron
Preface xxiii
yield using TALYS, The mass stopping power are read from a library gener-
ated by SRIM. In EMPIRE-3.2 total neutron yield was achieved by integrat-
ing the neutron spectra over the range 0-9.37MeV. We computed the strag-
gling and energy loss for alpha particle in Am-Be using SRIM code. It shows
the peak corresponding to ground(0MeV), first(4.4MeV) and second-excited
states(7.65MeV)respectively. To test the code validation the resultant spec-
trum from EMPIRE-3.2 code is compared with spectrum generated by Geiger.
The code predicted a good spectrum with peaks of n0 colony around 8MeV
and 9MeV. Prominent peaks around 1.9MeV, 2.2MeV and 4.8MeV contribute
n1 colony and the spikes formed from thermal to 1.5MeV results the n2 colony
respectively. This work will be helpful in calibration facilities, in laboratories,
shielding and the radiation protection protocols etc.
Furthermore, Inorder to validate these predictions and ensure their ac-
curacy, an experimental validation of model code was also performed using
Am-Be source. α-particles from 241Am fuses with 9Be at an incident α en-
ergy of 5.48MeV is measured using TOF method. experiment was performed
using one of the BC501A neutron detector from NAND facility, IUAC, New
Delhi. The neutron yield obtained from present TOF measurement shows the
neutron yield distribution from 0.3 to ∼ 6.5MeV. The experimental data have
been compared with the standard neutron reference spectrum as well as earlier
measured data. In the overlapping energy region of 0.3 - 6.5MeV, our data
agrees well with the ISO 8529-2 reference neutron radiation spectrum. As
compared to earlier measurements, we have extended the neutron yield mea-
surements down to 0.3MeV and applied neutron detection efficiency correction
to the data. With respect to earlier measured data, we observed significant
improvement within the energy interval from 0.3 to 3MeV. The technique
provides a simple means for characterization of the neutron sources used in
calibrating and optimizing the performance of BC501A based neutron ToF fa-
cility. The measured data is also compared with EMPIRE-3.2 and NeuCBOT
Preface xxiv
code, agreement between measured data and EMPIRE-3.2 evaluated spectrum
is found to be good between 2.5MeV to 6MeV, the two prominent peaks at
2.8MeV and 4.6MeV are estimated. The comparison with NeuCBOT with
TOF spectra is also made. It is found a discrepancy around 2MeV to 5MeV,
the way in which Am-Be source are made seems to have an influence on the
neutron emission rate in these energy ranges, as the NeuCBOT code works
with material composition .
So far we studied on compound reactions within the area of low-energy
scenarios. However, as we move into higher energy regimes, we observed a
different phase of nuclear reactions, where mechanisms like pre-equilibrium
emissions dominates. Here we use the nuclear reaction model code EMPIRE-
3.2 as it can account pre-equilibrium contribution. Inorder to study the pre-
equilibrium emission, the neutron emission in intermediate energy range has
been estimated for different target-projectile systems 12C on 56Fe, 27Al,natTi.
The chosen targets are important because these are prominent accelerator
structural materials. This study results to understand the effect of PEQ con-
tribution in intermediate energy range. Here we have used the code EMPIRE-
3.2 and PACE 4 for estimating neutron yields. We investigated the effect of
pre-equilibrium, various level densities and optical potentials in this study.
The comparison of the estimated neutron yield from both the reaction model
codes EMPIRE-3.2 and PACE 4 with available experimental data has been
made. In 12C on 27Al and 12C on natTi, available experimental data were
compared with EMPIRE-3.2 and PACE 4 code, the data is found to be in
good agreement with theoretical results made using level density model-3 of
code EMPIRE-3.2. It has been also observed that the PEQ parameters of
the code EMPIRE-3.2 satisfactorily reproduces the result, whereas, the code
PACE 4 calculations falls of faster than the EMPIRE-3.2 code because PACE
4 do not have the PEQ model included. For the system 12C on 56Fe available
calculated data is compared with the codes with same optimized parameters
Preface xxv
of above systems. This comparison allows us to evaluate the reliability of our
calculations by expecting experimental data to fall within the same region as
our computational results.
Above findings concluded that in low energy neutron emission studies
NeuCBOT code gives a better results as it can calculate energy loss in case of
thick targets, while in intermediate data neutron emission EMPIRE-3.2 code
gives better prediction and simulation as it can calculate for high energy ion
projectiles. Also it is understood that at intermediate energy range approx
7 A MeV, the PEQ neutron emission is prefered and PEQ emission increases
with increase in energy range. These model calculation would be useful to
improve theoretical codes which are based on different models, potentials and
phenomenological parameters. These model calculation of neutron emission
studies for different structural materials are important for evaluation of nu-
clear data which are having application in accelerator environment and nuclear
energy programmes.
Chapter 1
Introduction
The nucleus and it’s characteristics were a mysterious thing to humankind
for a long time. Many inventions have resulted from the constant attempt of
mankind to explain the complete structure of the nucleus. The foundations
of ”Nuclear Physics” was set by Dalton’s theory of the atomic structure of
matter, J.J. Thomson’s discovery of the electron, Henry Becquerel’s discovery
of radioactivity, Rutherford’s discovery of the atomic nucleus and the nuclear
constituent particles and Chadwick’s discovery of the neutron. The study of
the nucleus is considered to be started with the discovery of radioactivity by
Henry Becquerel in 1896[1]. A nuclear reaction is a tool to study the charac-
teristics of the nucleus and the nature of the force between the nucleons. A
nuclear reaction takes place when a projectile nucleus hits a target nucleus,
leading to the emission of particles or radiation leaving behind the residual
nucleus. The residual nucleus will generally be at an excited energy level. One
has the information of the system before the reaction and the system after the
reaction but does not have the information of what exactly happening inside a
nucleus during the reaction process. This information is drawn from the reac-
tion outcomes. Niels Bohr[2] proposed a model, which satisfactorily explains
1
Chapter 1. Introduction 2
the reaction mechanism. According to this model, the incident particle fuses
with the target forming a compound nucleus system by sharing its energy and
angular momentum with all the nucleons in the target. The compound nucleus
then decays by emitting particles and/or gamma rays. This decay is indepen-
dent of the mode of formation. This is known as Bohr’s compound nuclear
mechanism or independent hypothesis[2]. By analyzing nuclear reactions, it
is observed that the compound nuclear reaction theory found to be valid at
relatively lower excitation energies only and at higher excitation energies it is
found to be not valid. On the other hand, at very high excitation energies,
the direct reaction mechanism will prevail[3]. However, the emission of a par-
ticle from the nucleus before attaining the equilibrium state can be observed
in many nuclear reactions induced by fast projectiles and the process is re-
ferred to as the Pre-equilibrium Emission[4]. At moderate excitation energies,
Pre-equilibrium (PEQ) emission process has been identified as the prominent
reaction mechanism. In PEQ mechanism, the projectile distributes its energy
among a limited number of nucleons which then interact with other nucleons
and during this nucleon-nucleon distribution the projectile energy is gradually
distributed among the target nucleons and there is a reasonable chance that
the particles are emitted long before the attainment of statistical equilibrium.
In order to test the validity of nuclear reaction models and predict the
behaviour of unknown system, it is essential to have a large number of data on
nuclear reactions covering a large number of nuclei in the periodic table over a
wide range of excitation energy. Nuclear reaction data is also important in the
fields like Nuclear engineering and Energy production, Medical and Industrial
Applications, Astrophysics and Cosmology, Materials Science and Radiation
Shielding, etc.
Chapter 1. Introduction 3
In Nuclear Engineering, data informs reactor design by influencing parame-
ters such as power levels, neutron flux distributions and fuel cycle management.
Accurate predictions of neutron yield aid in optimizing reactor efficiency and
safety measures. Further data is vital for predicting fuel depletion and burn-up
in nuclear reactors. These calculations guide fuel management strategies and
ensure efficient reactor operation.
Data is critical for Medical isotope production for radiography, cancer
treatment and other medical applications. The data are also employed in non-
destructive testing of materials. Neutron yield data aids in designing efficient
neutron sources for material analysis, defect detection and quality control.
From the above findings it is well understood that a wide range of studies
have been done with nucleon and heavy ion induced reaction regimes. The
studies at low and intermediate energies holds immense significance in the
areas of both theoretical nuclear physics and practical applications. Hence
this thesis aims to solve the complexities of thick target reaction in the low to
intermediate energy range, employing model codes for validation, thus bridging
the gap between theory and experiment.
1.1 Background and Motivation of the study
Nuclear reactions at low and intermediate energies exhibit compound nucleus
formation, direct reactions and particle emissions[5, 6, 7, 8]. Nuclear reaction
data in thick targets subjected to such interactions provide an understanding
on dynamics of these processes. The primary objective of this research are
two case studies of neutron emission in low and intermediate energy in thick
target scenarios and to develop a comprehensive validation framework for the
Chapter 1. Introduction 4
nuclear reaction model codes. The central theme of this thesis revolves around
three key pillars:
1.Theoretical framework of neutron yield:
An extensive discussion of the theoretical framework governing nuclear
reactions in the low to intermediate energy regime with essential concepts and
to develop mathematical foundations.
2.Experimental data collection:
A systematic study of (α, n) reactions in thick targets, particularly focusing
on the case of Am-Be as the target nucleus and an incident alpha energy of 5.48
MeV. Experimental data will provide a benchmark for model code validation.
3.Model Code Comparison and Validation:
A critical examination of established nuclear reaction model codes, in-
cluding NeuCBOT, EMPIRE and others, with a detailed comparison of their
predictions against the experimental data.
1.2 Overview of the thesis structure
The chapters of this thesis are organized as:
Chapter 2: Literature Review:
This chapter gives a thorough review of existing literature covering thick
target neutron yield, nuclear reaction models and validation methodologies.
Chapter 3: Nuclear models and Codes:
This chapter covers an extensive discussion of the theoretical framework
governing nuclear reactions in the low to intermediate energy regime, along
with an overview of nuclear reaction model codes EMPIRE-3.2, PACE 4,
Chapter 1. Introduction 5
TALYS and NeuCBOT. This chapter equips with essential concepts and math-
ematical foundations.
Chapter 4: Thick target neutron yield-Low energy:
This chapter critically evaluates the codes performance. A comprehensive
comparison made of the experimental data with predictions from nuclear re-
action model codes.
Chapter 5: Measurement of neutron energy from Am-Be:
In this chapter a detailed explanation of the Time Of Flight experimental
setup and measurement techniques employed to collect the neutron yield data
necessary for validation.
Chapter 6:Thick target neutron yield-Intermediate energy:
In this chapter, a theoretical examination of neutron yield in thick target
materials in the intermediate energy range is conducted. The primary focus
has been on estimating the contribution of pre-equilibrium (PEQ) emissions
of neutron yields.
Chapter 7: Summary and Future works:
This chapter summarizes the research findings, accomplishments and new
possibilities for research in the areas of thick target neutron yield measurements
and nuclear reaction model codes.
Chapter 2
Literature Review
2.1 Nuclear reactions and its importance
A nuclear reaction is found to occur when two nuclei interact with each other.
This interactions might be elastic or inelastic. Experimentally it is achieved
by bombarding projectiles like proton, neutron,α-particle, γ-ray, photon or a
heavy nucleus on a target nucleus[9]. In order to overcome the Coulomb re-
pulsive force between the two nuclei, the projectile should have enough kinetic
energy to approach the target nucleus. If the incident energy is below Coulomb
barrier, a nuclear reaction will not take place. The interaction occurs within
an inter nuclear distance of 10−14m. The energy and angular momentum ex-
change may take place between the nuclei during the interaction stage and a
compound nucleus is formed. This nucleus de-excite by the emission of one or
more nucleons leaving behind the residual nucleus or emit radiation.
7
Chapter 2. Literature Review 8
2.2 Thick target reactions and their relevance
The primary objective of this research is to evaluate the (α, n) reactions in
thick target scenarios to study the low energy range and to study the neu-
tron emissions in intermediate energy range to understand the pre-equilibrium
emission and develop a comprehensive validation framework for the nuclear
reaction model codes.
A comprehensive literature survey on the 9Be(α, n) reaction was made.
Normally Be is chosen to get maximum neutron yield. Here the neutron is
produced through the reaction;
4α +9 Be −→13 C −→12 C +1 n (2.1)
Other light elements like Li, B and F can be used otherthan Be, while Be yields
the greatest neutron output per α-particle Table. 2.1 [10] shows the Neutron
yield of some (α, n) sources
Table 2.1: Neutron yield of some (α, n) sources[10]
α-emitter Target Reaction Q-Value Neutron yield per α
241Am B 10B(α, n) +1.07 MeV 1.3x10−5
241Am F 19F(α, n) -1.93 MeV 4.1x10−6
241Am Be 9Be(α, n) +5.71 MeV 7.0x10−5
238Pu C 13C(α, n) +2.2 MeV 1.1x10−5
210Po Li 7Li(α, n) -2.79 MeV 1.0x10−6
Chapter 2. Literature Review 9
Table 2.2: The activity, neutron emission in n/s for Am-Be
Activity Emission neutron n/s
1mCi 2.2x103
10mCi 2.2x104
100mCi 2.2x105
1Ci 2.2x106
10Ci 2.2x107
Am-Be source is the most popular amongst various (α,n) sources due to
its low γ-dose rate and long half life(458 y). Also it is widely employed as a
calibration source for neutron instrumentation. The activity, emission neutron
n/s and dimension is given in Table. 2.2
Neutron energy spectrum of an Am-Be source using gamma gated NTOF
technique was measured in 1998,in that study the neutron groups populated
the 2+ states and higher states were identified[11]. Furthermore the neutron
energy spectra observed using time of flight technique agrees qualitatively with
calculated energy spectra by Geiger and Van Der Zwan in 1975[12].
When α particles of energy Eα bombarded on thick targets, the resulting
neutron yields Y(Eα) is evaluated from available (α,n) cross sections σ(Eα)
with linear stopping powers dEα/dx(Eα),of the α particles in the target mate-
rial by the equation:
∫ 0 1
Y (Eα) = ρ. σ(Eα) .dEα (2.2)
E dEα/dx(Eα α)
where ρ is the atomic density.
Chapter 2. Literature Review 10
Liskien and Paulsen [13][14] presented findings derived from computations
involving elements such as Lithium, Beryllium, Boron, Carbon, Nitrogen, Oxy-
gen, Fluorine, Neon, Magnesium, Aluminium and Silicon. They also examined
Uranium compounds, including UC, UO2 and UF6, across alpha-particle en-
ergy levels spanning from the threshold to 7 MeV. The outcomes indicated an
average uncertainty of approximately 30%, inferred from variations in linear
stopping powers and cross-sectional data.
Thick target (α,n) yields were experimentally measured using 4π flat re-
sponse moderator dètectors, where the target is placed at the center of the
moderator and the Van de Graaff accelerators produced the α-particles. Bair
and Gomez del Campo [15] measured thick targets of 6Li, 7Li , Li, Be, 10B,
11B, B, ZnF2, PbF2, Mg, Al, Si and
28SiO2 for α-particle energies in the range
from 3 to 9 MeV with a typical uncertainty of 5%. They measured with eight
SF3 counters were embedded close to the surface of a 1.5 m diameter spherical
graphite moderator[16]. They also reported calculated yields for the com-
pounds UO2 and UC. Macklin and Gibbons[17]and Bair [18] measured thick
target neutron yields for carbon. The yields were measured with the same
detector as used by Bair and Gomez del Campo.
West and Sherwood [19][20] measured α on thick targets of Be, BeO, BN,
C, Mg, Al, Si, Fe, Zr, UC, UO2 and stainless steel for α-particle energies 3.6 to
10 MeV with a typical uncertainty of 1.5%. They performed experiment with
a cylindrical polythene moderator (diameter 1.0 m, length 1.0 m) with nine
3He counters at a particular known distances from the axis. A systematical
uncertainty in the yield data occurs due to lack of information about neutron
energy spectra. This is pointed out by Bair and Gomez del Campo[15].
Chapter 2. Literature Review 11
Data for thick target (α,n) yields obtained from the above mentioned cal-
culations and experiments, which are comparable with results presented in this
thesis, are shown in Table. 2.3
Table 2.3: Thick target(α,n) neutron yields per 107 α-particles reported in
the literature[21], The results of Liskien and Paulsen[13][14] were obtained from
calculation, the values presented by Bair and Gomez del campo[18][15] are also
from calculation and by West[20] are from measurement
Eα(MeV ) B C O F Mg Al Si BN UO2 References
4.0 100 0.37 0.13 7.9 1.0 0.19 0.10 – 0.040
4.5 170 0.42 0.24 19.0 2.7 0.87 0.31 – 0.072 [13]
5.0 240 0.53 0.36 39.0 5.8 2.9 – – 0.11 [14]
5.5 – 1.1 0.51 – – 7.4 – – 0.15
4.0 62 0.42 – 8.8 0.77 0.169 – – 0.050
4.5 106 0.48 – 21.6 2.63 0.802 0.16 – 0.107 [18]
5.0 156 0.63 – 43.9 6.44 2.64 0.52 – 0.164 [15]
5.5 206 1.08 – 77.5 12.6 6.97 1.14 – 0.236
4.0 – 0.43 – – 0.83 0.166 0.040 28.8 0.049
4.5 – 0.50 – – 2.93 0.812 0.156 42.3 0.103 [20]
5.0 – 0.65 – – 7.04 2.81 0.565 62.6 0.157
5.5 – 1.12 – – 13.7 7.56 1.24 90 0.221
More over the neutron yield from thick target heavy ion interaction is also
considered. The data is important for neutron dosimetry, shielding design
of accelerators and medical applications. Modern carbon ion therapy uses
high energy 12C beam for medical therapy and the design and operation of
Chapter 2. Literature Review 12
such accelerator facility require accurate knowledge on neutron shielding due
to background neutrons produced by beam hitting on surfaces. The present
work discusses about the neutron yield from thick targets of 56Fe,27Al and
natTi when bombarded by 12C. Since these targets are widely used in building
accelerators and cavities.
However, it is understood that at high beam energy, the pre-equilibrium
neutron emission is preferred and pre-equilibrium neutron emission was ob-
served even at 7.2 A MeV for the reaction 16O on 181Ta thick target by Nandy
et.al[22]. Energy distributions of emitted neutrons were measured at 00, 300
and 600 with respect to the beam direction using the proton recoil scintillation
technique. The results from equilibrium and Pre-equilibrium (PEQ) nuclear
reaction models compared provided the emission of PEQ neutrons at this pro-
jectile energy. This model also shows that PEQ emissions occurs only before
any scattering between target and projectile nucleons start.
C.Sunil et.al[23] measured energy distributions of emitted neutrons for 110
MeV 19F ions bombarding thick 27Al target. He made the measurements at
00, 300 , 600 , 900 and 1200 employing time-of-flight technique using scintil-
lation detector. The data compared with calculated results from equilibrium
nuclear reaction model codes like PACE 2 and EMPIRE-3.2 using various level
density options. In another work, the angle-integrated energy distribution of
neutron dose was calculated for 12C incident on Ag and Ti targets at 12 A
MeV[24]. It was observed that for both the reactions the calculated dose un-
der predicted the measured values below 22 MeV neutron energy. At higher
energies, the agreement is good for Ti target, but for Ag target experimental
data are slightly over predicted by the calculations. J.Acharya et.al[25] mea-
sured emission spectra at beam energies of 130, 140, 145, and 150 MeV for
Chapter 2. Literature Review 13
19F-induced reactions on 181Ta, 89Y and 51V. Measurements were performed
with liquid scintillator detectors kept at eight angles ranges from 25-143 de-
grees using time-of-flight and pulse-shape discrimination. He made compari-
son with ALICE 2014 and PACE 4 calculations to study the role of breakup
and pre-equilibrium effects. Predictions with ALICE 2014 without adjusting
the parameters gives a good agreement with the measured data. Comparison
with PACE 4 brings out the contributions arising from pre-equilibrium effects.
Neutron multiplicity distribution at high energy heavy ion collision have been
measured by Holub[26] and Hilsher et.al[27]. The neutron detector array at
IUAC have also been extensively used for neutron multiplicity from fission
induced by heavy ions[28][29][30]
A comparison between different codes to calculate neutron yields and spec-
tra and experimental data has been given in several papers[31][32][33][34].
2.3 Gaps in the literature and need of this
work
There are many works reported in literature on thick target (α,n) energies
[22][23][24][25]. The available data are still inadequate to provide additional
inputs to test the accuracy and validity of the reaction models used in most
popular reaction codes. More over the neutron yield from thick target ion
induced data in intermediate energy range are very few to generate a systematic
and consistent description of the dynamics of pre-equilibrium reactions and its
dependence on projectile energy. There are very less comparison with model
codes that brings out the contributions arising from pre-equilibrium effects.
Chapter 2. Literature Review 14
In the light of these findings from national and international researchers,
we studied the thick target (α,n) yield and pre-equilibrium contribution in
neutron emission in ion induced reactions at intermediate beam energies and
analysed data based on nuclear reaction models.
Chapter 3
Basic Theory and Model Codes
A set of well-designed nuclear reaction models is necessary to theoretically
explain experimental results. Various researchers have used them as a founda-
tion. The international nuclear community has used them as a foundation and
developed many nuclear codes that can predict nuclear data using computer
programming. However, it is also essential to validate the codes by compar-
ing the experimental data with the data predicted by the codes. The nuclear
modular codes NeuCBOT, TALYS, EMPIRE-3.2, PACE 4, codes have been
used in the present study. The following sections provide a brief discussion of
the various reaction models.
3.1 Reaction mechanism
On the basis of the energy range of the incident particles, there are three com-
mon nuclear reaction mechanisms:(1) Compound nuclear reaction mechanism,
(2)Direct reaction mechanism and (3) Pre-equilibrium reaction mechanisms.
This are shown in Fig. 3.1. Fig. 3.2 shows how these reaction processes work
as reaction products in relation to projectile energy.
15
Chapter 3. Basic Theory and Model Codes 16
A brief description of the compound nuclear reaction theory and some
of the compound nuclear mechanism and pre-equilibrium mechanisms which
were actually used in the statistical theoretical model codes are explained in
the following sections.
Figure 3.1: Nuclear reaction mechanisms
a+ A −→ A∗ −→ b+B (3.1)
3.2 Direct Reaction
The direct reaction occurs the lowest time, 10−22 s, which is nearly the same
as a particle passing through a nucleus. An incident particle takes one or more
nucleon from the target nucleus or it may lose its constituent particles in the
Chapter 3. Basic Theory and Model Codes 17
Figure 3.2: Nuclear reaction cross section with separation of the three reaction
mechanisms depending on the emission energy
target. The former reaction is known as pick up, whereas the latter is known as
stripping.In inelastic scattering, a particle just interacts, gets or loses energy
and then ejects a particle. The reaction is likely to occur if the particle’s
energy (>10 MeV). The associated angular distributions in the direct reaction
mechanism exhibit a significant peak in the forward direction. One useful
method for understanding the direct reaction process is the couple channelled
approach or Distorted Wave Born Approximation (DWBA). Here are some
examples of direct reactions:
Stripping reaction: A(d, n)B, A(d, p)C, etc.
Pick up reaction: X(n, d)Y or X(n, t)Z, etc.
Inelastic scattering: A(n, n’)A.
Chapter 3. Basic Theory and Model Codes 18
3.3 Compound nucleus mechanism
Bohr (1936)[1] provided an explanation of this reaction mechanism. A low
energy particle or nucleon that hits and penetrates a target nucleus shares all
of its kinetic energy among all of the target nucleons. As a result, the nucleus,
which was previously in the ground state, is currently excited due to an excess
of energy. The mean lifetime of this equilibrium state is extremely short,
approximately 10−16 s. After that, it decomposes, releasing a residue and an
ejectile. Suppose a nucleon ”a” hits a target ”A,” and before it produces
the products ”b” and ”B,” the compound nucleus ”A*” has formed. The
Weisskopf-Ewing and Hauser-Feshbach models both incorporate the compound
nucleus mechanism[35, 36]. The reaction mechanism can be categorized into 2
steps; The first stage involves the formation of the compound nucleus and the
second stage involves its decay. The compound nucleus, which is in the excited
state, is formed by the energy lost by the projectile in the target nucleus. The
second stage involves the release of more energy by the ejection of particles or
electromagnetic radiation.
3.3.1 Weisskopf-Ewing theory
Breit-Wigner theory describes how compound nuclear states are excited at low
energy by resonance through individual states. [37] for the process’s absorp-
tion cross section α → β at the resonance energy Er, having corresponding
total width, partial width of formation and decay Γ, Γα, Γβ respectively. The
statistical factor g, accounts the spin of particles forming the resonance and
Chapter 3. Basic Theory and Model Codes 19
the total angular momentum J.
Π gΓβΓα
σαβ(E) = (3.2)
k2 (E − 2Er)2 + Γ4
(2J + 1)
g = (3.3)
(2Sα + 1)(2Sβ + 1)
One can write:
σαβ ∼
Γβ
σCN(C) (3.4)
∑ Γ
Γ = Γα (3.5)
α
Γα ∝ gαk 2α σCN (3.6)
So finally the cross-section can be written as:
∑g k2β βσCN(β)σαβ = σCN(C) (3.7)2
α gαkασCN(α)
If the ejectile’s energy falls between Eβ to Eβ + dEβ keeping the residual
system in the energy range of Uβ to Uβ + dUβ , then Uβ = ECN -Bβ-Eβ. Since,
k2 = 2µE,
∑ (2∫Iβ + 1)µβEβσCN(β)ω(Uβ)dUβσαβ(Eβ)dEβ = σCN(C) (3.8)
c (2Iα + 1)µαEασCN(α)ω(Uα)dUα
Where, µβ is the ejectile’s reduced mass. This is the angle integrated cross-
section in Weisskopf-Ewing form.
Chapter 3. Basic Theory and Model Codes 20
3.3.2 Hauser-Feshbach theory
Reaction cross sections with large number of complex nuclear states are de-
scribed by Hauser-Feshbach theory. The cross section is expressed as the prod-
uct of two factors, the cross section σa for the compound nucleus formation
and the probability Pb for the decay into channel b:
σab = σaPb (3.9)
At a given orbital angular moment l, the compound nucleus formation
cross section is given by
σa = πλ
2
a(2l + 1)T a (3.10)
Where λa is the reduced wavelength in the incident channel, Ta is the
transmission coefficient
T 2a = 1− |Saa| (3.11)
Where Saa is the average S-matrix. Decay probability can be expressed in
terms of transmission coefficient as
Pb = ∑Tb (3.12)
c Tc
Thus obtained,
σ = πλ2
TaTb
ab a(2l + 1)∑ (3.13)
c Tc
Where Ta and Tb are the transmission coefficient of incident and exit
channel and Tc is the collective transmission coefficient for all exit channels.
Considering the interacting particle with spin, the spin of the projectile and
the spin of the target combined to form the spin of channel ’s’, which in turn
Chapter 3. Basic Theory and Model Codes 21
combine with orbital angular momentum l to form the total nucleus angular
momentum J. In the case of the outgoing channel, the probability of getting
particular ’s’ is given by,
(2s+ 1)
Ps = (3.14)
(2i+ 1)(2I + 1)
Similarly, the probability of s combining with l to give J is
(2J + 1)
PJ = (3.15)
(2s+ 1)(2l + 1)
Weighting the partial waves by (2l+1) the crossection becomes
∑
2 (2J + 1) ∑TaTbσab = πλa (3.16)(2s+ 1)(2l + 1) Tc
Jπ c
Where π is the parity of compound state, The transmission coefficient depends
on angular momenta l,s and J.
3.4 Pre-equilibrium Reaction
In the process of compound nucleus, a nucleus enters a transient equilibrium
stage before decaying, whereas there is no equilibrium in the direct response
mechanism. The pre-equilibrium process is the stage of the process where
the nucleus decays into reaction products before achieving complete statistical
equilibrium. The experimental observations that unable to properly explained
by the compound nucleus or direct reaction mechanism discovered in the 1950s.
These data were in the moderate energy range. It implies that a third mecha-
nism, the pre-equilibrium, could exist somewhere in between these two. This
Chapter 3. Basic Theory and Model Codes 22
process is significant between 10 MeV to 200 MeV. According to the mech-
anism, the nucleus enters a series of excited states and generates a complex
energy structure, but before it reaches a statistically stable stage with a spe-
cific angular momentum, it decays. Two semi-classical models from Griffin
(1966) and Kalbach (1973), called the exciton model and the hybrid model,
respectively, can be used to describe this mechanism[38, 39]. The quantum
mechanical explanations are given by Feshbach, Kerman and Koonin by devel-
oping the Multi-step direct reaction (MSD) and Multi-step compound (MSC)
reaction mechanism.
3.4.1 Exciton model
This model expects that the projectile by interacting with the target, gives rise
to a simple arrangement distinguished by a few number of excitons (n=p+h),
which are excited particles and holes. The basic exciton model[38] is shown in
Fig. 3.3. For a nucleus with excitation energy Ec , the partial level density at
exciton number n can be expressed as follows:
gnEn−1
ρn(E) = (3.17)
p!h!(p+ h− 1)!
where, g is the single particle level density and p and h are the number of
excited particles and holes respectively. It is seen that for small value of n, the
level density function increases quickly and hence the rate of transition ∆n = 2
is larger than the ∆n =−2. As n increases the particle level density moderately
levels off. At n =n̄, the exciton number becomes constant and there are as
many ∆n = 2 transitions as ∆n = −2 until equilibrium is finally established.
Then the energy differential pre-equilibrium cross-section σPEQ(E), is the sum
Chapter 3. Basic Theory and Model Codes 23
Figure 3.3: Schematic diagram of behaviour of particle and holes in exciton
model.
of the cross-sections from each exciton state:
∑n̄
σPEQ(E) = σabs Dn, Pn(E) (3.18)
n=n0
∆n=2
where, σabs is the projectiles absorption cross-section by the target. Dn refers
the probability of reaching the n exciton state (the depletion factor). Pn(E)
refers the ejectiles emission probability with energy E from the n exciton state.
If the projectile is a nucleon the summation begins from the initial exciton
number n0 which is 3 . In the case of cluster projectiles n0 is commonly
assumed to be equivalent to the number of nucleons in the projectile plus 2 (1
excited particle + 1 hole)
The depletion factor Dn is given by [109],
[ ∫ ]
D nn = Π ′ 1− dEPn′ (E) (3.19)n =n0
∆n=2
Chapter 3. Basic Theory and Model Codes 24
The emission probability, Pn(E), is defined as the ratio of the emission rate
with energy E from exciton state n to the rates of all transitions (collision +
emission) from n at all energies. If λcn (E) is the emission rate from n exciton
state to definite channel c with energy E and the emission from n = +2, -2 and
0 transitions are λn+ , λ
n
− and λ
n
0 respectively. Then the emission probability
can be defined as:
λn
P (E) = c
(E)
n ∫ (3.20)
λn + λn+ − + λ
n n
0 + dEλc (E)
Hence, to obtain Pn(E) the emission rates are summed over all E in the de-
nominator. The general expression for the emission rate is:
ρ
λn(E) = n
′ (U) (2s+ 1)mϵσinv(ϵ)
c (3.21)ρ 2 3n(Ec) π ℏ
′
where, n is the exciton number following the ejectiles emission with ν nucleons:
′
n = n − ν, U is the excitation energy of residue given by U = Ec− B− ϵ with
B the ejectile separation energy, s and m are the intrinsic spin and the reduced
mass of the ejectile and σinv(ϵ) is the inverse cross-section, i.e., the cross-section
of the time-reversed process of ejectiles absorption by the residual nucleus.
3.4.2 Hybrid model
The hybrid model calculates PEQ energy-differential cross- section σPEQ (a;
x, ϵ) of a nucleon x (x: proton or neutron) as sum of energy-differential cross-
sections from each exciton state n:
∑n̄ ∑n̄
σPEQ(a : x, ϵ) = σ
x
abs(a) DnPn (ϵ) = Dnσn(a : x, ϵ) (3.22)
n=n0 n=n0
∆n=2 ∆n=2
Chapter 3. Basic Theory and Model Codes 25
Pxn(ϵ) is the probability of emission of x-type ejectile from n-exciton state with
energy ϵ. Pxn(ϵ) can be written as,[ ]
P x(ϵ) = fx.P (x, ϵ) P nn n n c (x, ϵ) (3.23)
Where fxn denots the number of x type of exciton in the n exciton state, P
x
n is
the probability of x having energy ϵ in the n-exciton state. This can now write
as: [ ]
ρn(U,E)
σn(a : x, ϵ) = σabs(a) f
x P nn c (x, ϵ) (3.24)ρn(Ec)
The ratio ρn(U,E)/ρn(Ec) gives the probability of the number of excitons in a
particular state. The emission probability Pnc (x,ϵ) is,
n
P n
λc (x, ϵ)
c (x, ϵ) = (3.25)λnc (x, ϵ) + λ
n
t (ϵ)
Substituting this in above equation the hybrid model expression becomes
∑ [ ]n̄ ρn(U,E) λn(x, ϵ)
σPEQ(a : x, ϵ) = σ (a) D f
x c
abs n n (3.26)
n=n ρn(E ) λ
n
c c (x, ϵ) + λ
n
t (ϵ)0
∆n=2
The emission rate can be expressed as,
n 2mϵσinv(ϵ)λc (x, ϵ) = (3.27)gπ2ℏ3
Also,
[ ]
λnt (x, ϵ) = 1.4x10
21(ϵ+ S )− 6x1018 2 −1 −1x (ϵ+ Sx) k sec (3.28)
Chapter 3. Basic Theory and Model Codes 26
3.4.3 Multi-step Direct (M.S.D) and Multi-step Com-
pound (M.S.C) Model
Feshbach, Kerman and Koonin (FKK) proposed the break-up of the pre-
equilibrium emission spectra into Multi-step direct (MSD) and Multi-step
compound (MSC) components in their quantum mechanical theory of pre-
equilibrium reactions. The Multi-step Direct (M.S.D) model based on the
theory that at every excitation there should be a minimum of one particle in
the continuum and so there is a finite probability of particle emission per stage.
Obviously, the M.S.D model works only in the first few interactions only when
the particle just enters the nucleus. The particle momentum is in the direction
of the projectile and hence it is peaked in the forward direction.
After a few number of two-body interactions it shares complete energy
and momentum, the energy per particle is small, while the excited number of
particles will be higher. Also, at this stage there is no particle in the con-
tinuum, but the statistical fluctuation in energy will provide a particle in the
continuum. Hence the direction of emission will be either isotropic or symmet-
ric about 90. This corresponds to the Multi-step Compound (M.S.C) nucleus
formation, where there is an equilibrium in energy sharing has taken place but
the energy per particle in each state is less. In this way this theory of pre-
equilibrium explained the energy sharing process through two non interacting
chains called P-chain (At least one particle is in the continuum) and Q-chain
(All the particles are in the bound state). The MSD and MSC components
can be evaluated separately since the P-chain and the Q-chain do not interfere
with one another. Their sum is the overall pre-equilibrium cross-section:
σPEQ(ϵ) = σMSD(ϵ) + σMSC(ϵ) (3.29)
Chapter 3. Basic Theory and Model Codes 27
In the FKK theory, σMSD(ϵ) and σMSC(ϵ) are calculated quantum mechan-
ically. σMSD(ϵ) is evaluated by partitioning the partial level densities into
bound and unbound states of densities. The exciton model calculates σPEQ(ϵ)
and after evaluating σMSD(ϵ) the σMSC(ϵ) component is obtained by subtract-
ing σMSD(ϵ) from σPEQ(ϵ).
In calculating σPEQ(ϵ) Dn is defined as the probability of reaching the
n-exciton state without any prior particle emission. However, different com-
binations of excited particles and holes may result in the same n. Therefore
Su(p, h) is employed instead of Dn which is the probability of reaching a (p,h)
configuration with at least one excited particle in the unbound state. Dn is
given by,Dn= Su (p, h) + Sb(p, h) where Sb (p, h)represent the probability of
all the particle in the bound state, which doesn’t lead to emissions.
Now the equation for σPEQ can be written as:
∑p̄
σ = σ S (p, h)T (p, h)λuPEQ abs u u c (p, h, ϵ) (3.30)
p=p0
The quantities Su(p,h), Tu(p,h) have been calculated quantum mechanically
by Kalbach[40].
3.5 Optical Model
A significant amount of ”projectile-target” reaction data has been successfully
interpreted by the nuclear optical model in terms of the complex interaction
potential. During a nuclear reaction, the two nuclei interact, and all of the
other nucleons in the system combine to produce a single nucleon. If a system
has N nucleons, then subsequently N Schrödinger’s equations are needed to
describe the system. Inorder to solve the equations, It is necessary to have
Chapter 3. Basic Theory and Model Codes 28
the suitable form of potential. This potential is considered complex in the
optical model,which is having real part and an imaginary part. It is considered
that the incident particle’s interaction with the nucleus constitutes an optical
phenomenon. Any obstacles in the path of an electromagnetic wave cause
it to be diffracted or refracted when it moves from one medium to another.
The nucleus also diffracts the incident particle wave in the similar way. As a
result, the total potential V(r) has a real portion that represents the diffraction
phenomena and an imaginary part that represents the refraction part. The
potential is represented by the following equation, with real part U(r) and
imaginary part W(r)
V (r) = U(r) + jW (r) (3.31)
The model was proposed by Bethe(1937)[41], which was explored by Fesh-
bach (1954)[36] in order to apply to neutron-induced nuclear processes. Optical
model is effective and reliable in explanation for most of the experimental data.
This model has been modified as per the requirements from time to time.
3.6 Nuclear level densities
According to quantum mechanics, energy is quantized, resulting in energy
states. Nuclear level density refers to the energy states per unit energy interval.
This parameter plays significant role in the nuclear reaction mechanism. Bethe
has done significant work in the field of nuclear level density in 1936. The space
between energy levels becomes smaller as density increases. If it is infinite, the
state should be a continuum. This parameter has played a significant role
in the development of nuclear modular codes. Various level density models
are provided in the EMPIRE-3.2 code[42]. The validity of these model code
Chapter 3. Basic Theory and Model Codes 29
has been evaluated and described in Chapters 5 of the present study. Each
model for level density is described briefly here. Five models are featured in
the most recent version of EMPIRE-3.2. Bethe provided the basic formula for
level density which is given below.
∆Eex
1
= (3.32)
ρ(Eex)
Where, ∆Eex represents the energy interval and ρ(Eex) denotes the level
density.
According to this, a nucleus can be considered as a gas of nucleons, with
each nucleon occupying a distinct energy level based on the nucleus’ temper-
ature. Thus, the nuclear level density can be written as
√
ρ(Eex) = ce2 aE
ex
(3.33)
Where c indicates proportionality constant, a is the level density parameter
and Eex represents the excitation energy of the compound nucleus. In order
to make the calculated data match with the experimental data, the parameter
a is adjusted. This model is also regarded as a constant temperature model as
well. This basic idea is used to modify the other level density models.
3.6.1 Composite Gilbert-Cameron model
In 1965 Gilbert Cameron[43] modified the constant temperature level density
formula as,
1 E −∆− E0
ρT (E) = exp[ ] (3.34)
T T
Chapter 3. Basic Theory and Model Codes 30
Where T denotes temperature, E denotes excitation energy, δ is the pairing
energy and E0 is an adjustable energy shift and the Fermi gas formula is used
when the excitation energy E exceeds the matching point energy Ux.
√
exp(2 aU)
ρf (U) = √ 1 5 (3.35)
12 2σ2(U)a 4U 4
Where, σ2 is spin cut of parameter, the level density parameter a is given
by ( )
1− exp(−γU)
ã(U) = a 1 + δW (3.36)
U
Where, ã is the asymptotic level density parameter, W is the shell correction
energy and δW is the damping parameter. The parameter for asymptotic level
density is given by
2
ã = αA+ βA 3 (3.37)
Where A is the mass number, α and β are the global parameters.
3.6.2 The Back-shifted Fermi Gas Model
In this theoretical model, the pairing energy is regarded as an adjustable
parameter[44]. Up to 0 MeV, the fermi gas expression is applied. The overall
density is: √ √
ρ tot √ 1 π exp(2 aU)F (Ex) = (3.38)
2πσ 12
1 5
a 4U 4
And the level density is,
[ ] √ √
1 2 (J + 1)2
ρF (Ex, J, π) = √
J + 1 2 π exp(2 aU)exp 1 5 (3.39)2 2 2πσ3 2σ2 12 a 4U 4
Chapter 3. Basic Theory and Model Codes 31
3.6.3 The Generalized Superfluid Model
The generalised superfluid model (GSM) is based on the superconducting na-
ture theory of Bardeen-Cooper-Schrieffer. The phenomenological model ex-
hibits a low-energy superfluid phase transition[45, 46], where the pairing energy
term has a significant effect on the level density. There are two distinct energy
regions in the GSM model: low and high. An additional shift of the excitation
energy δshift is given in the GSM to enhance the level density parameter[46].
U = EX +N∆0 + δshift (3.40)
Where ∆ = √120 and n = 0, 1 and 2 for even-even, odd-even and odd-oddA
nuclei, respectively.
{ (
f(U∗
)
)
a(U,Z,A) = ã(A) 1 + δE0 ∗ , U > Ucr(3.41)U 1
Where Ucr denotes the condensation energy subtracted from the effective ex-
citation energy.
3.6.4 The Enhanced Generalized Superfluid Model
The Enhanced Generalized Superfluid Model (EGSM) make use of the super-
fluid model below the excitation energy. It has the enhancement of spin distri-
bution contribution in Fermi gas model which is different from the GSM[47].The
non-adiabatic form of nuclear rotation is used to improve the level density for
evaluation. As a result, it takes the geometry of the nucleus in a dynamical
condition. This deformation is included into level density formulations via mo-
ments of inertia and the level density parameter, which increases as the surface
Chapter 3. Basic Theory and Model Codes 32
of the nucleus increases. The role of the nuclear surface component and linear
dependence on asymptotic have vanished in the parameterization of EGSM,
which covers collective enhancement. EGSM global systematics does not take
discrete levels into consideration.
3.6.5 Microscopic level densities
Several microscopic methods are available to evaluate the level densities. In
the microscopic super fluid model, the GSM approach was employed to com-
pute the level density and other parameters of the excited nucleus. It considers
realistic single particle level schemes [48]. In the collective model, the codes
use this method to generate the level density for the reaction data prediction.
In the development of the codes, two basic microscopic level density models are
employed. S. Goriely estimated the level densities for the RIPL data library
using Hartree-Fock calculations [48] for excitation energies up to 150 MeV and
spin values up to I = 30. Hilaire and Goriely suggested this novel energy, spin
and parity dependent nuclear level densities based on the microscopic combi-
natorial model[49]. This model is having intrinsic state density and collective
enhancement. The calculations make use of nuclear structure properties deter-
mined within the deformed Skyrme-Hartree-Fock-Bogolyubov framework[50].
Recent versions of the codes also include temperature-dependent Hartree-Fock-
Bogolyubov calculations utilising the Gogny force.
3.7 Nuclear Reaction Codes and Tools
Statistical nuclear reaction models are developed in order to validate the data
and evaluate the predictive power of the nuclear theories. Computer codes
Chapter 3. Basic Theory and Model Codes 33
are developed in accordance with particular models. To evaluate nuclear reac-
tion data and nuclear data analysis, the nuclear reaction computer code with
specific nuclear reaction models are employed. In the present work, statisti-
cal nuclear reaction computer codes EMPIRE-3.2[42] and TALYS-1.8[51] and
NeuCBOT[52] are employed for theoretical analysis.
3.7.1 EMPIRE-3.2
The nuclear model code EMPIRE takes account compound, direct and pre-
equilibrium nuclear reactions. EMPIRE-3.2 reads as much data from the RIPL
input directory and the local input parameter library as feasible. Only the
input parameters that the code does not know, such as incident energy, pro-
jectile, target and the number of emitted particles, must be given by the user
for the following ejectiles: neutrons, protons, deuterons, tritons and light ions.
EMPIRE input consists of two parts. Mandatory Input and Optional input
Mandatory input contains basic data necessary to specify the case and the
structure is given below:
The first line indicates the incident energy in the laboratory system (in
MeV). The second and third represents the mass and atomic numbers of a
target and a projectile. The next seven lines define the number of emissions
Chapter 3. Basic Theory and Model Codes 34
to be followed for each ejectile. The code automatically sums over all possible
decay sequences to reach the given residual nucleus. The mandatory input is
followed by optional input, which allows modifications to the default model
parameters.
Optional input comprises of an arbitrary number of records, entered in
any order and closed with the GO record, which specifies the end of the in-
put. EMPIRE-3.2 [42] is a modular system of nuclear reaction codes that may
be used to calculate over a wide range of energies and incident particles. It
consists of several nuclear models. A projectile can be a neutron, proton, any
ion (including heavy-ions) or a photon. The energy range extends from the
unresolved resonance region for neutron-induced reactions ( keV) and goes up
to several hundred MeV for heavy-ion induced reactions. The code calculates
the major nuclear reaction mechanisms, including direct, pre-equilibrium and
compound nucleus ones. Direct reactions are described by a generalized opti-
cal model (ECIS03) or by the simplified coupled-channels approach (CCFUS).
The pre-equilibrium mechanism can be employed by a deformation depen-
dent Multi-step direct (ORION + TRISTAN) model. Finally, the compound
nucleus decay is described by the full featured Hauser-Feshbach model with γ-
cascade and width-fluctuations. A comprehensive library of input parameters
covers nuclear masses, optical model parameters, ground state deformations,
discrete levels and decay schemes, level densities, fission barriers, moments of
inertia and γ-ray strength functions[53].
In this work the theoretical estimation was done by EMPIRE-3.2 code.
System of codes for modelling the reaction and an extensive parameter library.
Which is mainly helpful here to retrieve the data points which obtained as the
output file.
Chapter 3. Basic Theory and Model Codes 35
3.7.2 TALYS
TALYS is a software that evaluates nuclear reactions within the energy range
of 1 keV to 200 MeV of several particles neutrons, gamma rays, protons,
deuterons, tritons, helions and alpha particles. The program gives detailed
and exact information on reaction cross sections based on several reaction
mechanisms, including direct reactions, pre-equilibrium emission and com-
pound nucleus processes. The code calculates the cross sections for all the
reaction channels for a given incident energy. The key elements of a TALYS
input file are projectile, element, mass and energy. The input can be run
with default parameters or with multiple options and parameters provided in
the TALYS manual[51]. The code involves different nuclear models for each
mechanism such as statistical theory of Hauser-Feshbach for the compound
nuclear, exciton model using PCROSS code for pre-equilibrium contribution
and the ECIS06 code for calculating the transmission coefficient and direct
reaction contributions using suitable optical model potential. In the output,
one can get all possible reaction channel nuclear data such as reaction cross-
sections, angular distribution, the cross section from different excitation levels,
etc. There are a total of six level density models (ldmodel 1–6) defined in the
TALYS code:[51]
ldmodel-1 is described as Constant temperature and Fermi gas model (CTFM)
ldmodel-2 is Back-Shifted Fermi gas model (BSFG)
ldmodel-3 is Generalized Superfluid model (GSM)
ldmodel-4 as Microscopic level densities (Skyrme force) from Gori- ely’s tables.
ldmodel-5 as Microscopic level densities (Skyrme force) from Hilaire’s combi-
natorial tables.
ldmodel-6 as Microscopic level densities (temperature dependent HFB, Gogny
Chapter 3. Basic Theory and Model Codes 36
force) from Hilaire’s combinatorial tables.
3.7.3 NeuCBOT
NeuCBOT is a nuclear reaction tool used to evaluate the (α, n) yield of ma-
terials to a given set of α particle energies or α-emitting nuclei, it compiles
output from code TALYS [51] with nuclear decay information from the ENSDF
database[54] and stopping power calculations from code SRIM [55].
NeuCBOT allows the user to provide a material composition in order to
calculate (α , n) yields for any arbitrary material. This can be done by speci-
fying the elemental composition of the material and the mass fraction of each
element[52]. A list of α particle energies and branching ratios is obtained for
each isotope from the ENSDF database. NeuCBOT evaluates the neutron
yield and energy spectrum for each α particle as it slows down in a material
and interacts with each isotope present[52].
The basis of the calculations with this tool is the nuclear reaction database
produced by TALYS and SRIM code which is explained below:
3.7.4 Directory Structure
Here the databases are stored in the ./Data directory. inside this directory
there are sub directories, which are given below[52]:
• ./Data/StopingPowers/ : Here we get the stopping powers generated by
SRIM for each element
• ./Data/Decays/ : This directory contains the ENSDF files with alpha
decay data for given isotopes
Chapter 3. Basic Theory and Model Codes 37
• ./Data/abundances.dat : This contains the natural abundances of every
isotope[56]
• ./Data/Isotopes/ : This directory is having the TALYS-generated (al-
pha,n) reaction data library.
There is a directory called NSpectra/ within an isotope’s directory, which
contains outgoing neutron energy spectra for alpha particles of a given energy
undergoing the (alpha,n) reaction on this isotope. The TalysOut/ directory is
having the output from TALYS, from each generated alpha particle at a given
energy on the isotope. Files in this directory is having cross sections for the
different alpha-induced nuclear reactions, including the (alpha,n) reaction, as
well as cross sections for producing various excited nuclei and gammas at vari-
ous energies[52]. Inorder to run NeuCBOT, provided a material description(-m
material file name) and an alpha energy list (-l alpha list name) also supply a
list of contaminants in the decay chain of interest (-c contaminants list name).
The other list of arguments used by NeuCBOT is given below, followed by
parameters required by that option (written in square brackets) and the de-
scription of what that option does is written in parenthesis[52].
• -l [alpha list file name] (file with a list of alpha energies to be used)
• -c [decay chain file name] (file with a list of alpha-emitting contaminants)
• -m [material composition file name] (file with a description of the material
composition)
• -s [alpha step size in MeV] (the step size to be used when integrating
over the alpha energy, minimum of 0.01)
Chapter 3. Basic Theory and Model Codes 38
• -t [no arguments] (tells NeuCBOT to run TALYS for reactions not in
libraries)
• -d [no arguments] (if an element is missing from the (alpha,n) database,
automatically run the download element.sh script to download the ele-
ment’s database)
• -o [output file name] (name of text file to store output to)
The NeuCBOT files have been taken in a right way during the calculations
inorder to obtain a better result.
3.7.5 PACE 4
PACE 4, works with Hauser-Feshbach formalism which follows the angular
momentum coupling at each stage of de-excitation of an excited nucleus[57].
For light ions, optical model calculations are used whereas, for heavy projectiles
bass model is used for fusion cross section and initial spin distribution[58]. The
Gilbert-Cameron level density is used in the calculation, with level density
parameter, a=A/10, where A is mass number of compound nucleus.
3.7.6 SRIM
SRIM is a set of programs which calculate the stopping and range of ions (10 eV
- 2 GeV /amu) into matter. In this code the user can choose ion type, energy
and direction to evaluate target damage. In this work SRIM 2008 code has
been used to calculate SRIM stopping power, range and energy straggling[55].
These model codes have been used in the present study to calculate neutron
yield. So to estimate the emission spectrum from a system the code need to
Chapter 3. Basic Theory and Model Codes 39
run with different nuclear models. A brief description of this estimation is
discussed in the following section.
Chapter 4
Thick target neutron yield-Low
energy
4.1 Introduction
In this chapter, the nuclear model codes introduced in Chapter 3 are applied to
predict neutron spectra resulting from thick target interactions. In the context
of nuclear reaction applications, thick target neutron energy spectra resulting
from the bombardment of various light elements by α- particles are of great
significance. The computations of these spectra are conducted for elements
such as Boron, Fluorine, Magnesium, Aluminium and Silicon at four differ-
ent monoenergetic α-particle energies 4.0, 4.5, 5.0 and 5.5 MeV, employing
the NeuCBOT code. Here the primary objective is to study alpha-induced
neutron yield in thick targets. The integral of the angle-integrated spectrum
is compared with the angle integrated neutron energy spectra (and their in-
tegrals; n/α-values), from time-of-flight measurement by G.J.H. Jacobs et.al.
41
Chapter 4. Thick target neutron yield-Low energy 42
[21]. Furthermore, to generate neutron energy spectra theoretically, a special
case of Am-Be source is explored
The yield Yi (Eα, En) of neutrons at energy En produced by an α particle
of energy Eα travelling a distance dx is given by
Y (Eα, En) = ηiσi(Eα, En)dx (4.1)
where σi (Eα, En) is the cross section for this particular interaction. The
mass stopping power is given by,
−1 dE
S(E) = (4.2)
ρ dx
Where ρ is the total density of the material, integrating over Eα as the α
particle slows down gives
∫ Eα |
α ηi σi(Eα, En)Yi =
|
| dEα (4.3)ρ 0 S(Eα)
∫
N Eα
|
ACi σi(Eα, En)
= | dE
|
α (4.4)Ai 0 S(Eα)
where NA is Avogadro’s number, Y
α
i (En) indicates the thick-target yield of
neutrons of energy En from a given α particle, Ci is the mass fraction of isotope
in the material and Ai is the target isotope’s mass number, The net yield of a
material is then calculated by adding the yields of each target isotope.
Chapter 4. Thick target neutron yield-Low energy 43
∑
Y α(En) = Y
α
i (En) (4.5)
i
If Pα to be the probability of an α particle appearing in a decay of the
decay chain. The total neutron yield of energy En is then defined as
∑
Y (E αn) = PαY (En) (4.6)
α
The total number of neutrons obtained at any energy is the integral of
Y(En) over the entire neutron energy spectrum [52].
4.2 Neutron energy spectra deduced for some
elements
NeuCBOT is used to calculate (α, n) yields, here (α, n) yields for several
materials using NeuCBOT is calculated and compared with the calculations
performed using measured yields.
4.2.1 Alpha bombarded on Silicon
The experimental work reported by G.J.H. Jacobs [21] contains three stable
isotopes of Natural Silicon; 28Si , 29Si and 30Si. The ground state of the residual
nucleus has Q-values of -8.1 MeV, -1.5 MeV, and -3.5 MeV for the (α,n)
reactions. 29Si(α,n)32S and 30Si (α,n)33S are the only energetically allowed
(α,n)reactions. It may be possible for both residual nuclei to remain in the first
Chapter 4. Thick target neutron yield-Low energy 44
excited states and the ground states. The maximum possible neutron energy
produced by 5.5 MeV α-particles is 3.7 MeV and 1.7 MeV, respectively. In this
work on1y the neutrons from the 29Si (α,n) reaction contribute above 1.7, 1.2,
0.7 and 0.2 MeV neutron energy for the range of alpha energies 5.5, 5.0, 4.5 and
4.0 MeV. Below these energies both reactions, 29Si(α,n) and 30Si (α,n)equally
contribute. This is due to its isotope abundances and cross sections have the
same order of magnitude. The four angle-integrated spectra are presented
numerically in Table. 4.1
Calculations of angle-integrated cross sections using the model code NeuCBOT
were made for Silicon. These cross sections, together with linear stopping pow-
ers were used to construct angle-integrated spectrum. This is compared with
the experimentally obtained result. Systematically, the calculated spectra are
too low. However, they agree on their shapes in a reasonable way. The cal-
culated four angle-integrated spectra along with the spectra obtained from
time-of-flight measurements are presented graphically in Fig. 4.1.
The integral n/α - values are shown in Table. 4.2. All n/α - values from
the literature are included for comparison and are consistant with the current
NeuCBOT results.
Chapter 4. Thick target neutron yield-Low energy 45
Table 4.1: The angle integrated neutron energy spectra for thick targets of
silicon at four different α-particle energies[21]
En(MeV ) 5.5 MeV ϕ(En) 5 MeV ϕ(En) 4.5 MeV ϕ(En) 4 MeV ϕ(En)
0.1 42.4 35.3 9.52 1.92
0.2 43 34.1 9.58 1.9
0.3 42.3 32.1 9.95 2.02
0.4 45.3 35.4 8.93 1.95
0.5 59.4 48.9 6 1.09
0.6 74.8 58.3 5.56 0.51
0.7 79.5 51.5 2.05 0.51
0.8 81.3 39.9 1.03 0.62
0.9 78.8 27.9 1.07 0.54
1 71.9 17.7 1.34 0.55
1.1 63 8.84 1.51 0.11
1.2 44.5 2.96 1.98 0.86
1.3 32.4 1.5 2.42 0.98
1.4 24.5 1.81 2.95 1.52
1.5 18.5 2.99 4.21 2.67
1.6 13.1 4.52 5.82 3.94
1.7 9.5 5.99 6.87 3.84
1.8 8.4 7.6 7.23 3.27
1.9 9.5 9.66 8.05 3.34
2 10.4 11.2 8.34 3.69
2.1 12.4 12.3 7.57 2.78
2.2 14.7 14.9 6.63 1.2
2.3 17 18.2 5.8 0.24
2.4 18.3 18 4.87 0.01
2.5 18.8 15.5 4.27
2.6 20.6 12.8 3.12
2.7 22.6 10.5 1.44
2.8 23.8 9.19 0.3
2.9 23.3 9.15 0.02
3 21.5 9.73
3.1 19.1 1.76
3.2 14.7 3.61
3.3 11.7 0.86
3.4 10.4
3.5 9.3
3.6 7.8
3.7 5.5
3.8 2.3
Chapter 4. Thick target neutron yield-Low energy 46
Figure 4.1: The angle integrated neutron energy spectra for thick targets of
Silicon at four different α-particle energies, determined from time of flight mea-
surements(black line), The red line represents the result obtained from NeuCBOT.
From top to bottom of the figure: 5.5MeV, 5MeV, 4.5MeV,4MeV
Chapter 4. Thick target neutron yield-Low energy 47
Table 4.2: The integral n/α values for thick targets of silicon at four different
α-particle energies obtained from literature and from the code NeuCBOT
Eα(MeV ) 5.5 5.0 4.5 4 References
– – 3.7 1 [Lis 77[13]]
In unit of 11.4 5.2 1.6 – [Bai 79[15]]
10−8 n/α 12.4 5.65 1.56 0.40 [Wes 82[20]]
11.3 5.81 1.38 0.41 [Jacob et al[21]]
15 6.2 1.88 0.37 [NeuCBOT]
4.2.2 Alpha bombarded on Aluminium
According to the work reported by G.J.H. Jacobs [21] the maximum possible
neutron energy produced by 5.5 MeV α-particles is 2.6 MeV. The four angle-
integrated experimental spectra along with the calculated spectra obtained
from NeuCBOT are presented graphically in Fig. 4.2
The calculated spectra are again symmetrically high as compared with
experimental but the shape is well reproduced. the angle-integrated spectra
presented in Table. 4.3.
The integral n/α - values are presented in Table. 4.4. For comparison, all
n/α - values obtained from the literature are given and are matches clearly
with the recent NeuCBOT results.
Chapter 4. Thick target neutron yield-Low energy 48
Table 4.3: The angle integrated neutron energy spectra for thick targets of
Aluminium at four different α-particle energies[21]
En(MeV ) 5.5 MeV ϕ(En) 5 MeV ϕ(En) 4.5 MeV ϕ(En) 4 MeV ϕ(En)
0.1 34.8 12 2.53 1.7
0.2 34.2 13.3 3.21 0.8
0.3 31.7 12.1 4 0.79
0.4 26.9 6.8 5.55 1.01
0.5 32.4 8.9 7.27 2.1
0.6 34.5 13.1 7.63 3.09
0.7 34.1 16 7.35 3.4
0.8 32.6 17.3 6.18 2.15
0.9 31.8 11.8 8.84 1.96
1 31.6 11.5 9.95 1.19
1.1 35.7 18.2 9.1 0.46
1.2 34.2 17.5 6.4 0.07
1.3 33.6 15.6 3.94
1.4 35.8 16.6 2.26
1.5 37.1 16.3 1.27
1.6 38.2 14.8 0.29
1.7 37.1 11.3
1.8 31.4 7.5
1.9 27.3 4.5
2 25.9 2.1
2.1 24.3 0.3
2.2 22
2.3 18.5
2.4 13.4
2.5 6
2.6 1.5
Chapter 4. Thick target neutron yield-Low energy 49
Figure 4.2: The angle integrated neutron energy spectra for thick targets of Alu-
minium at four different α-particle energies, determined from time of flight mea-
surements(black line), The red line represents the result obtained from NeuCBOT.
From top to bottom of the figure: 5.5MeV, 5MeV, 4.5MeV,4MeV
Chapter 4. Thick target neutron yield-Low energy 50
Table 4.4: The integral n/α values for thick targets of aluminium at four different
α-particle energies obtained from literature and from the code NeuCBOT
Eα(MeV ) 5.5 5.0 4.5 4 References
7.4 2.9 0.87 0.19 [Lis 77[13]]
In unit of 6.97 2.64 0.802 0.169 [Bai 79[15]]
10−7 n/α 7.55 2.81 0.812 0.166 [Wes 82[20]]
7.47 2.60 0.87 0.19 [Jacob et al[21]]
9.08 3.52 0.916 0.172 [NeuCBOT]
4.2.3 Alpha bombarded on Magnesium
From the work of G.J.H. Jacobs[21] the four angle-integrated spectra are pre-
sented graphically in Fig. 4.3. Only neutrons from the 25Mg (α,n) reaction
contribute above 5.4, 4.9, 4.4 and 3.9 MeV neutron energy for the α energies
5.5. 5.0. 4.5 and 4.0 MeV spectrum respectively. The integral n/α values
are given in Table. 4.5. The figure clearly shows a relatively good match with
NeuCBOT estimates, the yields are found to be significantly higher than the
corresponding experimental observations.
The integral n/α - values are presented in Table. 4.6. For comparison, all
n/α - values obtained from literature are given and are well matches with the
present NeuCBOT results.
Chapter 4. Thick target neutron yield-Low energy 51
Table 4.5: The angle integrated neutron energy spectra for thick targets of
Magnesium at four different α-particle energies[21]
En(MeV ) 5.5 MeV ϕ(En) 5 MeV ϕ(En) 4.5 MeV ϕ(En) 4 MeV ϕ(En)
0.1 18.4 7.4 2.04 0.5
0.2 16.4 6.3 1.99 0.5
0.3 16.5 6.1 2.05 0.52
0.4 17.3 6.6 1.99 0.55
0.5 17.1 7.6 2.08 0.57
0.6 17.6 8.5 2.96 0.8
0.7 18.7 9.5 3.83 0.98
0.8 18.4 9.8 4.06 1.45
0.9 18 10.1 4.35 1.81
1 18.1 10.5 4.69 1.91
1.1 18.7 10.8 5.33 2
1.2 19.6 12 6.2 2.22
1.3 19.9 13.7 7.01 2.06
1.4 21.9 15.9 8.05 1.89
1.5 25.1 19.1 9.25 1.61
1.6 29.2 21.8 9.4 1.66
1.7 29.6 21.1 8.89 1.56
1.8 31.9 21.7 7.95 1.47
1.9 37 22.7 7.11 1.34
2 38 21.9 6.85 1.37
2.1 40.5 21.6 7.12 1.34
2.2 39.9 20.2 6.54 1.21
2.3 37.5 17.6 5.32 1.09
2.4 36.4 16.2 5 1.01
2.5 35.7 16 4.82 0.85
2.6 34.6 15.3 4.7 0.82
2.7 34.4 14.5 4.71 1.08
2.8 34.5 13.4 4.59 1.38
2.9 34.1 12.8 4.21 1.47
3 30 11.6 3.61 1.44
3.1 25.8 10.2 3.27 1.43
3.2 20.4 8.8 3.33 1.48
3.3 16.6 7.9 3.75 1.6
3.4 16.6 8.9 4.51 1.73
3.5 17.5 9.7 4.86 1.91
3.6 17.9 9.4 4.96 2.05
3.7 18 9.3 4.9 1.94
3.8 18 9.7 5.18 1.86
3.9 18 10.4 5.46 1.79
4 18.1 11.2 5.61 1.69
4.1 18 11.6 5.63 1.69
4.2 18.6 12.2 5.68 1.51
4.3 18.9 12.3 5.17 1.4
4.4 18.2 11.6 4.22 1.29
4.5 17.4 10.2 3.62 1.16
4.6 16.8 9.2 3.27 1.06
4.7 17.1 8.8 3 0.88
4.8 17.2 8.3 2.67 0.62
4.9 16.8 7.3 2.35 0.5
5 15.8 6.1 2.7 0.48
5.1 15.4 5.3 1.77 0.51
5.2 14.9 4.8 1.51 0.56
5.3 13.9 4.3 1.32 0.61
5.4 12 3.9 1.25 0.6
5.5 10.4 3.5 1.25 0.6
5.6 9.1 2.9 1.26 0.56
5.7 8.1 2.4 1.27 0.52
5.8 7.3 2 1.27 0.48
5.9 6.3 1.7 1.25 0.43
6 5.6 1.7 1.18 0.38
6.1 5.1 1.7 1.04 0.33
6.2 4.5 1.7 0.95 0.3
6.3 3.9 1.7 0.85 0.27
6.4 3.6 1.6 0.73 0.2
6.5 3.4 1.4 0.64 0.16
6.6 3.4 1.3 0.55 0.11
6.7 3.1 1.2 0.45
6.8 3 1 0.39
6.9 2.7 1 0.32
7 2.5 0.9 0.23
7.1 2.4 0.8 0.14
7.2 2.1 0.7
7.3 2.1 0.6
7.4 2 0.5
7.5 2 0.4
7.6 2 0.2
7.7 2
7.8 2.1
7.9 1.8
8 1.6
8.1 0.4
Chapter 4. Thick target neutron yield-Low energy 52
Figure 4.3: The angle integrated neutron energy spectra for thick targets
of Magnesium at four different α-particle energies, determined from time of
flight measurements(black line), The red line represents the result obtained from
NeuCBOT.From top to bottom of the figure: 5.5MeV, 5MeV, 4.5MeV,4MeV
Chapter 4. Thick target neutron yield-Low energy 53
Table 4.6: The integral n/α values for thick targets of magnesium at four dif-
ferent α-particle energies obtained from literature and from the code NeuCBOT
Eα(MeV ) 5.5 5.0 4.5 4 References
– 5.8 2.7 1.0 [Lis 77[13]]
In unit of 12.6 6.4 2.63 0.77 [Bai 79[15]]
10−7 n/α 13.7 7.04 2.93 0.83 [Wes 82[20]]
13.3 6.65 2.60 0.73 [Jacobs[21]]
14.7 7.39 3.09 0.991 [NeuCBOT]
Figure 4.4: The angle integrated neutron energy spectra for thick target of
Boron Nitrate at α-particle energy 5.5 MeV determined from time of flight mea-
surements(black line), The red line represents the result obtained from NeuCBOT
Chapter 4. Thick target neutron yield-Low energy 54
Inorder to check the code validation, The spectra for Boron and Fluorine
were calculated out of the compounds Boron Nitride and Calcium Fluoride
respectively. The corresponding spectra is compared with the experimental
spectra obtained from G.J.H. Jacobs [21]. Natural Boron contains only 19.8%
10B compared with 11B 80.2% . This explains the predominant contribution
of neutrons produces by the 1ater reaction in the neutron energy spectra. The
spectra together with calculated spectra for Boron Nitrate are shown in Fig.
4.4 and the spectra for Calcium Fluoride is shown in Fig. 4.5
Figure 4.5: The angle integrated neutron energy spectra for thick target of Cal-
cium fluoride at α-particle energy 5.5 MeV determined from time of flight mea-
surements(black line), The red line represents the result obtained from NeuCBOT
Chapter 4. Thick target neutron yield-Low energy 55
The two spectra are in good agreement for producing the shape, however
in both cases NeuCBOT yield shows systematcally higher yield.
NeuCBOT in comparison with experimental data are presented in Fig. 4.6,
which shows the neutron yield for various elements calculated by code. The
neutron yield is given as the number of neutrons per 107 alphas, which is
compared with the works of[19][15]. A fair agreement between NeuCBOT and
experimental data is seen for most elements.
Figure 4.6: Neutron yield for various elements is calculated by code NeuCBOT
in comparison with measurements. Neutron yield is given as the number of neu-
trons per 107 alphas.
Chapter 4. Thick target neutron yield-Low energy 56
In general the angle-integrated n/α values , which calculated from the
NeuCBOT nearly reproduces the shape of spectra which obtained experimen-
tally, However in all the cases the values from the NeuCBOT are consistent
with experimental1y determined results published by wes et al.[20]. It is found
that the calculated values are generally larger than the experimentally deter-
mined values in all the cases.
The neutron spectra are also calculated theoretically at various combina-
tion of energies using EMPIRE-3.2 nuclear reaction code as EMPIRE-3.2 code
is a comprehensive code that can handle a broad range of nuclear reactions, in-
cluding neutron-induced reactions, proton-induced reactions, ion-induced reac-
tions and more. The subsequent section provides a comprehensive explanation
of these calculation.
4.3 Thick target neutron yield for Am-Be source.
To generate the neutron energy spectrum using the NeuCBOT and EMPIRE-
3.2 code, specifically focusing on low-energy alpha particles the Am-Be system
is selected as a special case study. Am-Be source is the most popular amongst
various (α,n) sources due to its low γ-dose rate and long half life(458 y). Also
it is widely employed as a calibration source for neutron instrumentation. The
5.48MeV α particle from the 241Am source undergo fusion with 9Be to form
the compound nucleus of 13C at an excitation energy of around 14.4 MeV.
Depending on the thickness of Be the excitation energy of 13C may vary from
10.6 MeV to 14.4 MeV. Neutron from such resonance populate various states
of 12C depending on the structure of states.The expected neutron spectrum
from Am-Be is simulated using NeuCBOT (Neutron Calculator Based On
TALYS)[52]. Alpha straggling and tunneling affected to spectrum is also taken
Chapter 4. Thick target neutron yield-Low energy 57
in to cosideration. Due to the source composition matrix effects in alpha
energy loss and multiple scattering of neutrons inside the source, the emitted
neutrons are having a continuous energy. To understand the exact nature of
neutron spectrum, the individual neutron colonies corresponding to residual
energy states of 12C has to be correlated through the level scheme of 12C. An
approximate idea of neutron energies obtained from energy levels of 12C of the
reaction 9Be (α,n)12C is given in Fig. 4.7.
Figure 4.7: Energy level diagram of 12C
The following Table. 4.7 presents the reaction Q-values.
Chapter 4. Thick target neutron yield-Low energy 58
Table 4.7: Representation of 9Be (α,n)12C reaction Q-value
State Q-Value
Ground state 5.70 MeV
4.4 MeV 1.27 MeV
7.65 MeV -1.95 MeV
4.3.1 Theoretical formalism using NeuCBOT
NeuCBOT is having a material composition to calculate (α, n) yields for Am-
Be material. Here the material is described as AmO2Be 80%Be 20% AmO2 by
mass. There are two ways to specify the list of α particle energies and relative
intensities. Either the user can directly give these values, or NeuCBOT provide
a list of α-emitting isotopes and their relative probabilities.
As NeuCBOT runs, it outputs the alpha energy every 10 keV (with the
-d option) and it automatically acquires (alpha,n) data. Otherwise, if TALYS
is already installed, use the -t option. The output gives the overall neutron
production, which is computed by integrating all of the (alpha,n) cross sections
along the alphas’ trajectories as they slow down, the derivation used for this
is well discussed in chapter 2. The number of neutrons produced per decay
of the entire decay chain or list of alpha energies being simulated is given in
Chapter 4. Thick target neutron yield-Low energy 59
units. Therefore, the integral over the entire cross sections provides the total
yields output of NeuCBOT. The neutron energy spectrum of Am-Be given by
NeuCBOT is shown in Fig. 4.8
 1400
neucbot
 1200
 1000
 800
 600
 400
 200
 0
 0  2  4  6  8  10  12
En(MeV)
Figure 4.8: Neutron energy spectrum predicted by NeuCBOT
4.3.2 Theoretical formalism using EMPIRE-3.2 code
The neutron energy spectra for various combination of angles are calculated.
Fig. 4.9 shows the neutron energy spectra at 900 for 5 MeV. Due to the reaction
9Be(α,n)12C which forms the compound nucleus 13C results the formation of
neutron with energies above 0.5 MeV.
Yield
Chapter 4. Thick target neutron yield-Low energy 60
 1400
En-5MeV
 1200
 1000
 800
 600
 400
 200
 0
 0  2  4  6  8  10
En(MeV)
Figure 4.9: Neutron energy spectra at 900
The peaks n0 , n1 , n2 are the neutron energy distributions from the
9Be(α,n)12C reaction, leaving the 12C in the ground(0 MeV), first(4.4) and
second-excited states(7.65 MeV), respectively. They were calculated by set-
ting the Q-values Q1 = 5.70 MeV, Q2 = 1.27 MeV, and Q3 = -1.95 MeV,
respectively. The spectra at other energies are also investigated. The calcu-
lation is based on an excitation curve for neutrons in the n0 , n1 , n2 group.
It is reasonable, to consider an α-particle passing through the target, slowing
down and eventually stopping. As the α-particle enters the beryllium target,
with energy 5.5 MeV, it produces neutrons in the n0 group corresponding to
Intensity
Chapter 4. Thick target neutron yield-Low energy 61
an energy E(n0 ) near 9.37 MeV.
Straggling and energy loss for alpha particles are also evaluated for Am-Be
source. The value for incident particle using the SRIM code is computed for
each energy, the corresponding longitudinal and lateral straggling is acquired,
taking the square roots for each value gives the ∆x, this results in the energy
loss straggling corresponding to each energy. As seen in Fig. 4.10
Figure 4.10: Observed Neutron spectra,including the straggling corresponds to
energy 3.6 MeV
Integrating the neutron spectra over energy range(0-9.37MeV), the total
neutron yield of the reaction can be determined . The corresponding plot in
histogram is shown in Fig. 4.11
Chapter 4. Thick target neutron yield-Low energy 62
The spread in energy represented mathematically by guassian, the detailed
expression was discussed above in equation. The range can be obtained by
integrating the energy loss rate along the path. Hence the final spectrum.
which is shown in Fig. 4.12
 1400
EMPIRE-integrated spectrum
 1200
 1000
 800
 600
 400
 200
 0
 0  2  4  6  8  10
En(MeV)
Figure 4.11: Integrated neutron energy spectrum
Intensity
Chapter 4. Thick target neutron yield-Low energy 63
 1400
EMPIRE-3.2
 1200
 1000
 800
 600
 400
 200
 0
 0  2  4  6  8  10
En(MeV)
Figure 4.12: Neutron energy spectrum calculated using EMPIRE-3.2 with strag-
gling
For various energies, energy straggling for alpha-particles of up to 10 MeV
is determined. The straggling width is seen to decrease with particle energy
increases. The observed neutron spectra can be interpreted as follows , As
the α beam enters the beryllium target, with energy 5.54 MeV, it produces
neutrons in the n0 group corresponding to an energy En near 9.37 MeV. Furthur
population of states around 13.5 MeV of 13C causes neutron channels of energy
8.5 MeV. The energy loss due to straggling, scattering, with in the sample
thickness, cause spreading and shifting of neutron energy resulting in n0 colony
with peaks around 9 MeV and 8 MeV respectively, after scattering, straggling
and attenuation. Population of 4.439 MeV state of 12C from 13C produces
Yield
Chapter 4. Thick target neutron yield-Low energy 64
an energy range around 6.5MeV is also included in this colony. Similarly,
the prominent peak observed at neutron energy 3.6 MeV is due to the level
excitation of 12C supported by neutron channels of 13C giving energies around
1.9 MeV, 2.2 MeV and 4.8 MeV respectively contribute to the formation of n1
colony. The resonances in 9Be crossection at lower alpha energies contribute to
the various spikes formed from thermal to 1.5 MeV. This results the formation
of n2 colony.
 1400
EMPIRE-3.2
Geiger
 1200
 1000
 800
 600
 400
 200
 0
 0  2  4  6  8  10  12
En(MeV)
Figure 4.13: Resultant spectra from EMPIRE-3.2(red line),Geiger spec-
tra(dotted green line)
Fig. 4.13 shows the resultant spectrum compared with the spectrum gen-
erated by Geiger[12]. In the case of Geiger the reported spectra is averaged
Yield
Chapter 4. Thick target neutron yield-Low energy 65
distribution without accounting straggling and internal scattering, initial res-
onance of n2 colony is also lost here. The stopping power, energy straggling
and alpha tunneling evaluation made a better precision for the present work
over the previous publications.
4.4 Conclusion
The calculation is performed to generate neutron energy spectra using two
different nuclear reaction modeling codes: NeuCBOT and EMPIRE-3.2. the
angle integrated neutron energy spectra for thick targets of Magnesium, Sili-
con, Aluminium at four different α-particle energies 4.0, 4.5, 5.0 and 5.5 MeV
are determined. In all these cases the values from the NeuCBOT are consis-
tent with experimental1y determined results. These findings concluded that
in low energy neutron emission studies NeuCBOT code gives a better results
as it can calculate energy loss in case of thick targets. To generate neutron
energy spectra theoretically, a special case of Am-Be source is explored and
it is noted that the spectra obtained both from NeuCBOT and EMPIRE-3.2
gave promising results. This suggests that these codes are performing well in
simulating neutron energy spectra for the study.
Chapter 5
Measurement of neutron energy
from Am-Be
5.1 Introduction
Based on the insights gained from the preceding chapter, the codes EMPIRE
and NeuCBOT have provided good results, it’s crucial to validate these pre-
dictions using experimental data. So an experiment is planned to conduct
using Am-Be system to measure the neutron energy spectra taking it as a case
study. The experimental results will serve as a benchmark to confirm the ac-
curacy of the model predictions. It is specifically selected the Am-Be system
for experimental measurement of neutron energy spectra as it is focusing on
low-energy alpha particles. The main objective here is to validate the EM-
PIRE and NeuCBOT model codes by measuring the gamma-tagged neutron
spectrum resulting from low-energy alpha interactions.
67
Chapter 5. Measurement of neutron energy from Am-Be 68
5.2 Facility Overview
The National Array of Neutron Detectors (NAND) experimental facility set up
at IUAC, New Delhi was used to perform the experiment, which contains large
array of neutron detectors. There are 100 liquid scintillators in the detector
array, the structure is cylindrical size in which each cell having 5”x5” and type
is BC501A ( Saint Gobain) coupled to a 5” photomultiplier tube. All detectors
are mounted at a fixed distance of 175 cm from the target position. The struc-
ture of these detectors are semi-spherical dome ( geodesic). Here the target is
placed inside a 100 cm diameter spherical scattering chamber with thin walls.
Also the target chamber provides space for charged particle detectors, such
as silicon detectors and large area position-sensitive multiwire proportional
counters (MWPC) to detect neutron emitting sources (heavy ions and fission
fragments) and other light charged particles in coincidence with neutrons. The
whole array setup will enable the measurement of the neutrons’ energy and
angular distribution that are produced during nucleus-nucleus collision[59], the
lab layout is shown in Fig. 5.1.
5.3 Materials and Methods
5.3.1 Am-Be source
The Am-Be radioactive source used in this study was supplied in a double-
encapsulated stainless steel capsule of dimension 17.4 mm in diameter and 19.2
mm in height (shown in Fig. 5.2). The nominal activity of the source is 3.7
GBq (100 mCi) with approximate 2.1x105 neutron emission per sec. The source
contain a homogeneous mixture of 241Am and beryllium metal powder. 241Am
Chapter 5. Measurement of neutron energy from Am-Be 69
Figure 5.1: NAND facility
Chapter 5. Measurement of neutron energy from Am-Be 70
decays by emission of α -particles of 5 different energies (∼ 5.5MeV weighted-
mean energy). When these α particles are captured by 9Be, fast neutrons
and recoiling 12C are produced via reaction 9Be(α,n) 12C*. Depending upon
the neutron decay channel of 13C and the excited states of the recoiling 12C
nucleus, the neutron energy spectrum can have peak structures and continuous
distribution up to a maximum energy of 11 MeV. If the recoiling 12C nucleus is
left in its first-excited state, the emitted neutron is accompanied by a prompt
time-correlated 4.44 MeV de-excitation γ-ray with a branching ratio ∼80%[60].
By detecting the prompt γ-rays in coincidence with neutrons in a TOF setup,
the kinetic energy distribution of the tagged neutrons is determined.
Figure 5.2: The encapsulated Am-Be source
5.3.2 BC501A neutron detector
BC501A liquid scintillator cell of NAND facility[61] was used in this measure-
ment. A single detector (shown in Fig. 5.3) is made up of 5 in x 5 in cylindrical
cell filled with organic liquid scintillator of type BC501A (M/s Saint Gobain)
Chapter 5. Measurement of neutron energy from Am-Be 71
and coupled to a 5 in diameter Hamamatsu Type R4144 µ-metal shielded
photomultiplier tube (PMT). The PMT base consist of a home made volt-
age divider network and a preamplifier circuit. The operating voltage was
set to -1800V and the energy calibration was determined using standard γ-
ray sources. The performance characteristics of the detector has been already
reported[61].
BC501A detector is one of the most commonly employed fast neutron de-
tector for neutron TOF spectrometers. It is well known for its fast timing and
pulse shape discrimination (PSD) capabilities[60]. In this work, the standard
zero-cross (Z/C) timing technique is employed[62] to discriminate the neutrons
from γrays. This technique exploits the properties of the time dependence of
the scintillation pulse on type of interacting radiation. The anode signal after
passing through a shaping network generates a bipolar signal whose Z/C time
interval with respect to the leading edge depends on the shape and rise time
of the scintillation pulse. Measure of this time interval is used to differenti-
ate the neutrons and γ-rays. The electronics circuit for this technique was
incorporated into a custom built PSD module developed at IUAC[63].
5.3.3 BaF2 Gamma detector
The γ detector used in this measurement is a BaF2 detector from Saint Gob-
ain Crystals. It is a tapered geometry scintillator of 30 mm (length) and
25.4/38.1 mm (diameter) coupled to a 2 in Hamamatsu Type R2059 fast PMT
surrounded by µ-metal shield. An integrated passive voltage divider is used to
apply the high voltage and to read out light output signal. The full assembly
is housed in an aluminum enclosure. BaF2 is a standard detector used for fast
timing measurements with sub nanosecond time resolution. This detector was
Chapter 5. Measurement of neutron energy from Am-Be 72
Figure 5.3: 5 in (diameter) x 5 in ( height) BC501A liquid scintillator cell
mounted on a 5 in diameter PMT
used to trigger on the energy deposited by 4.44 MeV γ-rays and provide the
fast timing reference for the TOF.
5.3.4 Measurement
The experiment was performed using one of the BC501A liquid scintillator
mounted at NAND facility of IUAC. The Am-Be source was placed at the cen-
tre of 4 mm thick and 100 cm diameter scattering chamber with its cylindrical
symmetry axis aligned to the vertical direction in the lab. The BaF2 detector
was kept close to the source at same height with its crystal front face approx-
imately 3 cm from the source enclosure. A BC501A detector mounted on the
array at same height with the source and at a radial distance of 175 cm from
the centre of target chamber was selected for the measurement. A schematic
diagram of the experimental setup is shown in the Fig. 5.4. The BC501A trig-
gered on both 4.44 MeV γ-rays and fast neutrons from the source where as
the BaF2 triggered mostly on the energy deposited by 4.44 MeV γ-rays only.
Chapter 5. Measurement of neutron energy from Am-Be 73
Figure 5.4: The schematic diagram of the experimental setup (not to scale)
5.3.5 Time of Flight method
The energy of outgoing neutrons is obtained from the time interval needed
for a neutron to reach a neutron detector (time of flight). This method uses
the detector’s fast timing capability. The pulse from BaF2 gamma detector
produce start signal and the signals from BC501A neutron detector were pro-
vide the stop signal . The time difference between start and stop signals is
defined as the relative flight time and is used to extract the energy of neutrons.
In order to convert the TOF spectrum to the neutron energy spectrum, the
following expression of the kinetic energy is used
( )2
1 L
En = mn (5.1)
2 TOF
where En is the kinetic energy of neutron, mn mass of neutron and L is
the flight path.
Chapter 5. Measurement of neutron energy from Am-Be 74
5.4 Electronics setup and data acquisition sys-
tem (DAQ)
A block diagram of electronics setup is shown in the Fig. 5.5 . The setup was
configured to record the γ-ray energy deposited in BaF2 detector, light output
and the zero-cross timing of the BC501A detector signals for PSD and the
ToF information by means of time difference between the signals of BaF2 and
BC501A detector. The anode and dynode signals from the BC501A detector
were sent to a custom-built dual channel NIM based PSD module which con-
tains electronics for processing the signals from BC501A detectors[63]. The
PSD module generated a constant fraction discriminator (CFD) output which
provided the ’stop’ signal for the time to digital converter (TDC) of the ToF
setup. Another analogue output corresponding to Z/C time with respect to
leading edge of the signal was sent directly to analogue to digital converter
(ADC). The dynode signal (light output) after pre-amplification(PA) was fed
to a shaping amplifier (SA) circuit inside the PSD module. The semi-Gaussian
shaped light output signal was fed to ADC. The timing signal from BaF2 de-
tector was put into a CFD followed by a gate and delay generator (GDG) to
produce the ’start’signal for the TDC. The same signal was also used as the
’master trigger’ for the data acquisition (DAQ) system. The BaF2 dynode
(light output) signal was fed to a pre-amplifier followed by a shaping amplifier
whose output was fed to another channel of ADC. These signals were digitized,
acquired on an event-by-event basis and stored on the disk-file using a VME
based DAQ running on a LINUX PC. Data were also collected without im-
posing the gamma detector trigger condition in which the master trigger was
generated from the CFD output of the PSD module to record the light output
for all neutrons emitted from the Am-Be source. For offline data analysis, the
Chapter 5. Measurement of neutron energy from Am-Be 75
raw data were converted into ROOT [64] format. The TDC used in the ToF
was calibrated with Ortec Model 462 time calibrator.
Figure 5.5: Block diagram of the electronics setup used for signal processing
and data acquisition.
5.5 TOF energy spectrum
The zero-cross distribution obtained from the custom built PSD module was
used to discriminate the neutron events from that of γ-rays detected by the
BC501A detector. The BC501A detection threshold was kept at ∼ 40 keVee
which is equivalent to the light output from ∼ 0.3 MeV neutron. Fig. 5.6 shows
a typical Z/C time distribution obtained in this measurement. As seen in the
figure, good neutron-γ discrimination is achieved by Z/C method. Two di-
mensional histogram of zero-cross time versus light output (light output signal
Chapter 5. Measurement of neutron energy from Am-Be 76
2800
γ − rays
2100
1400
700 neutrons
800 1200 1600 2000
Z/C time (channels)
Figure 5.6: Zero-cross distribution showing distinct separation of neutrons and
γ-rays interacting inside BC501A detector
is proportional to the energy deposited by the impinging radiation in the de-
tector medium) provides a better separation of neutron and gamma events. A
comparison of the zero-cross versus light output plots of the BC501A detector
corresponding to the self triggered and BaF2 triggered conditions are shown
in Fig. 5.7. In the figure, the upper and lower bands of each panel correspond
to neutrons and γ-rays respectively. For same number of collected triggers,
untagged condition (upper panel) shows substantial neutron events having
higher values of light output recorded in comparison to the tagged condition
(lower panel). The significant difference in the neutron light output spectra
qualitatively shows the effect of 4.44 MeV gamma-tagging which restricts the
measured neutron energy spectrum below 7 MeV. The Compton edge (480
Counts
Chapter 5. Measurement of neutron energy from Am-Be 77
keV) for 662 keV gamma ray from 137 Cs corresponds to approximately 750
channels on the horizontal light output axis.
Nevertheless, a more definite separation of neutrons and γ-rays was ob-
tained from a time correlated 2D plot of Z/C distribution. Fig. 5.8 shows a
2D histogram of the Z/C time from BC501A detector plotted as a function
of ToF between BaF2 and BC501A detector signals. Two distinct bands are
seen which can be clearly identified as neutron and γ ray bands. The upper
band (higher Z/C time) corresponding to neutron events are well separated
from the γ-ray events (lower band). A clear separation between γ-ray and
neutron events shows the excellent quality of PSD for light outputs even with
detection threshold as low as ∼40 keVee. A software gate around this neu-
tron band was applied to generate only neutron events. For further analysis
to convert ToF into energy histogram for gamma tagged events, an additional
gating condition was imposed by applying software gate on 4.44 MeV gamma
rays from the energy spectrum recorded by the BaF2 detector. In order to
verify the true ToF peak corresponding to gamma-rays, the time correlation
measurement was done in the same setup by replacing the Am-Be source by
a reasonably strong 60Co γ-ray source. Considering the prompt γ-ray peak
position in the ToF spectrum as reference time, the neutron ToF events were
converted event-by-event into energy histogram using the expression of TOF.
The neutron yield distribution was further corrected for detection efficiency
of the BC501A scintillator. The neutron detection efficiency of a single 5
in. x 5 in. cell used in NAND array has been measured and compared with
Monte-Carlo simulation[61]. Fig. 5.9 shows the simulation result for variation
of neutron detection efficiency of a single cell as a function of neutron energies
up to 10 MeV keeping the detection threshold at ∼0.3 MeV.
Chapter 5. Measurement of neutron energy from Am-Be 78
30
2500
25
untagged neutrons
2000
20
1500 15
10
1000
(a)
5
500
30
2500
25
γ- tagged neutrons
2000
20
1500
15
1000 10
(b)
5
500
1000 2000 3000 4000
Light output (channels)
Figure 5.7: Two dimensional histograms of zero-cross time vs. light output for
untagged and gamma-tagged conditions.
Z/C time (channels) Z/C time (channels)
Chapter 5. Measurement of neutron energy from Am-Be 79
30
2500
neutrons
25
2000
20
1500 15
10
1000
5
500
1000 2000 3000 4000
Time of flight (channels)
Figure 5.8: Two dimensional histogram of zero-cross time vs. time-of-flight.
The neutron yield obtained from ToF measurement was corrected for neu-
tron detection efficiency factor for each energy bin. The efficiency corrected
neutron yield distribution from Am-Be source is displayed in Fig. 5.10. For
comparison, the standard ISO 8529-2 (ISO 8529-2, 2000) is shown recom-
mended neutron energy distribution along with earlier measured data reported
in[65]. The data shown here are normalized with respect to the maximum yield
at ∼3 MeV. The data shows the neutron yield distribution from ∼0.3 MeV
to ∼6.5 MeV. The lowest energy corresponds to the hardware threshold set at
∼0.3 MeV neutron. As evidenced by the trigger condition set by detection of
γ-rays from 4.44 MeV de-excitation, data shows no yield beyond ∼7 MeV.
As per the kinetics of the reaction, with 4.44 MeV spent for de-excitation of
γ-rays, the available energies for time-correlated neutron is restricted to a max-
imum value ∼7 MeV. The results for Am-Be spectrum shown good agreement
Z/C time (channels)
Chapter 5. Measurement of neutron energy from Am-Be 80
0.8
0.6
0.4
0.2
0 2 4 6 8 10
Neutron energy (MeV)
Figure 5.9: Simulated intrinsic efficiency of 5 in. x 5 in. single cell BC501A
detector as a function of neutron energy.
with the reference spectrum for energy range from 0.3 MeV to 6.5 MeV. In the
measurement reported in[65], similar tagged ToF method was employed with
a 18.5GBq Am-Be source and NE-213 neutron detector. Though in general
there is good agreement between two data in overlapping energy range, signifi-
cant discrepancies were observed within the energy interval from 0.3 to 3 MeV.
However, the neutron yield distribution below 3 MeV from present measure-
ment is in excellent agreement with the ISO reference data Ref (ISO-8529-2,
2000). As the measurement had a lower hardware threshold, the neutron yield
is measured down to lowest energy 0.3 MeV. The contribution of any neutron
Intrinsic efficiency
Chapter 5. Measurement of neutron energy from Am-Be 81
scattering in the low energy part of the spectrum can be neglected in the earlier
study it is found that neutrons scattered from 4 mm thick scattering chamber
wall contributes only small fraction of the total events (0.04)[61]. As neu-
tron detection efficiency vary significantly in the measured low energy range
(0.3to 2 MeV), the good agreement of the measured data with ISO reference
data suggest the importance of detector efficiency correction in determining
the yield distribution.
Present data
ISO 8529-2
1200
Scherzinger et al. (2015)
800
400
2 4 6 8 10
Neutron energy (MeV)
Figure 5.10: The Am-Be neutron energy spectrum from present measurement
(solid line), compared with ISO 8529-2 reference spectrum[66] (red dashed line)
and spectrum obtained by Scherzinger (2015) (blue dash-dotted line).
Yield (arb. units)
Chapter 5. Measurement of neutron energy from Am-Be 82
5.6 Comparison of experimental results with
theoretical predictions
The neutron energy spectra measured vs EMPIRE-3.2 calculated are shown in
Fig. 5.11. The 4.4 MeV tagged neutron spectra are visible in the energy range
of 0.3 to ∼ 6.5 MeV beyond which there is no strength. Agreement between
measured data and simulated data is good between 2.5MeV to 6MeV. It is to
be considered that in simulation, the energy loss of alpha particle is also taken
into account.
 1400
TOF spectrum
EMPIRE-3.2
 1200
 1000
 800
 600
 400
 200
 0
 0  2  4  6  8  10
En(MeV)
Figure 5.11: The neutron energy spectrum of Am-Be source measured compared
with EMPIRE-3.2 calculated
Yield
Chapter 5. Measurement of neutron energy from Am-Be 83
Two prominent peaks energies corresponding to 2.8 MeV and 4.6 MeV
are identified. The neutron colony for energy around 9 MeV corresponding to
ground state of 12C could not be measured as there is no gamma produced for
tagging. Some of the weak lower energy colonies also could not be identified
due to limited neutron flux available for the experiment. The gamma gated
measurement made the present result more precise.
 1400
TOF spectrum
NeuCBOT
 1200
 1000
 800
 600
 400
 200
 0
 0  2  4  6  8  10
En(MeV)
Figure 5.12: The neutron energy spectrum of Am-Be source compared with
measured TOF and calculated NeuCBOT
The comparison of spectra of TOF and NeuCBOT is also shown in Fig. 5.12.
The measured spectrum with NeuCBOT would certainly be of interest.There
is a discrepancy observed for both specrta. The differences are largest in the
Yield
Chapter 5. Measurement of neutron energy from Am-Be 84
energy ranges, around 2 and 5 MeV. The way in which 241 Am–Be sources are
made (mixture, cavity size) seems to have an influence on the neutron emission
rate in these energy ranges.
5.7 Conclusion
In this chapter an experimental validation of model code was performed us-
ing Am-Be source, inorder to validate the predictions and ensure accuracy of
theoretical codes. The experimental data have been compared with the stan-
dard neutron reference spectrum(ISO 8529-2) as well as earlier measured data,
EMPIRE-3.2 and NeuCBOT code.The measured and calculated energy distri-
butions of neutrons produced in (α,n) reactions are represented in Fig. 5.11
and 5.12 using codes EMPIRE and NeuCBOT, agreement between measured
data and EMPIRE-3.2 evaluated spectrum is found to be good with 2.5MeV
to 6MeV, the two prominent peaks at 2.8MeV and 4.6MeV are estimated. The
comparison with NeuCBOT with measured spectra is also made, It is found a
discrepancy around 2MeV to 5MeV, this is due to the method in which Am-Be
source are made, as the NeuCBOT code works with material composition.
Chapter 6
Thick target neutron
yield-Intermediate energy
6.1 Introduction
So far this point, our focus has primarily been on compound reactions within
the area of low-energy scenarios. However, as we move into higher energy
regimes, we encounter a different phase of nuclear reactions, where mech-
anisms like pre-equilibrium emissions dominates. In this circumstance the
EMPIRE-3.2 code assumes significance. Notably, EMPIRE-3.2 not only in-
volves pre-equilibrium emission but also uses heavy ions as projectiles. As a
result, we have chosen EMPIRE-3.2 as our preferred tool to investigate and
understand the dynamics of pre-equilibrium neutron emissions in this context.
Few measurements of thick target neutron yield using heavy ion reaction have
been performed at 10 MeV/A or lower energies to get insights into the reac-
tion mechanisms. Inorder to calculate the neutron yield data from ion induced
reactions we use the code EMPIRE-3.2. EMPIRE-3.2 is the preferred choice
85
Chapter 6. Thick target neutron yield-Intermediate energy 86
as it involves a broader range of nuclear reactions beyond alpha-induced reac-
tions. It is found from the previous studies that at intermediate energy, the
pre-equilibrium neutron emission is preferred [22].
In the present study, the emission of neutron yield has been estimated for
systems: 12C on 56Fe,27Al, natTi. The corresponding pre-equilibrium (PEQ)
neutron contributions has been estimated using the code EMPIRE-3.2. Here
we have used the code PACE 4 for estimating the evaporation neutron yields
from heavy ion reaction. We investigated the effect of pre-equilibrium, vari-
ous level densities and optical potentials in this study. The calculations done
with PCROSS-1.5 and PCROSS-0 input parameters to understand the effect
of pre-equilibrium contribution in the yield. PCROSS is the input param-
eter which describes mean free path multiplier value in the Exciton model
formalism. The calculations of the level densities was performed on the base
of LEVDEN-0 option which is a default case for the level densities which is
used for Enhanced Generalized Superfluid Model (EGSM),LEVDEN-1, 2, and
3 are used for Generalized Superfluid model (GSM), Gilbert-Cameron level
densities and RIPL-3 microscopic HFB level densities. The following optical
potentials proposed by Koning et al and Morillon et al[10] were considered.
we are seeking for EMPIRE-3.2’s pre-equilibrium contribution and whichever
level density model and optical potential of EMPIRE-3.2 will produce the best
theoretical result. The comparison of the estimated neutron yields from both
the reaction model codes with the available experimental data is shown in the
next subsections.
Chapter 6. Thick target neutron yield-Intermediate energy 87
6.2 Study of intermediate energy neutron yield
6.2.1 12C on 27Al
The neutron energy data of 12C on 27Al at different angles are reported by V.
Suman[67], the available experimental datas are compared with EMPIRE-3.2
and PACE 4 at different available level density model is shown below.
 0.35
Experimental
ld0
ld1
ld2
 0.3
ld 3
Pace4
 0.25
 0.2
 0.15
 0.1
 0.05
 0
 0  20  40  60  80  100
En(MeV)
Figure 6.1: Comparison of Neutron yield data of 12C on 27Al at 00 reported by
V. Suman et al[67],with theoretical data from EMPIRE-3.2 and PACE 4.
Fig. 6.1 shows the neutron energy spectrum of 12C on 27Al at 00. The
experimental data is found to be in good agreement with the theoretical result
Yield
Chapter 6. Thick target neutron yield-Intermediate energy 88
made using ld model-3. Also the pre-equilibrium emission, is taken into ac-
count in theoretical calculations. It has been observed that the pre-equilibrium
parameters of the code EMPIRE-3.2 satisfactorily reproduces the calculated
data result, whereas PACE 4 predicts lower amount of high energy neutrons
this is because PACE do not account pre-equilibrium emission. PACE 4 pre-
dictions are underestimated when compared to experimental data at the most
forward angles and highest neutron energies.
 0.025
Experimental
ld0
ld1
ld2
ld 3
 0.02 Pace4
 0.015
 0.01
 0.005
 0
 0  20  40  60  80  100
En(MeV)
Figure 6.2: Comparison of Neutron yield data of 12C on 27Al at 300 reported
by V. Suman et al[67],with theoretical data from EMPIRE-3.2 and PACE 4.
The neutron energy data of 12C on 27Al at 300 reported by V. Suman[67],
is compared with EMPIRE-3.2 and PACE 4 at different available level density
Yield
Chapter 6. Thick target neutron yield-Intermediate energy 89
model is shown in Fig. 6.2. The reported experimental data is found to be
in good agreement with the theoretical result(shown in the yellow colour by
dotted line) made using ld model-3. At this angle the PACE 4 calculation falls
off faster than the EMPIRE-3.2 calculation, This is because the possibility of
pre-equilibrium effects causing more neutron emission at higher energy.
 0.0012
Experimental
ld0
ld1
ld2
 0.001 ld 3
Pace4
 0.0008
 0.0006
 0.0004
 0.0002
 0
 0  20  40  60  80  100
En(MeV)
Figure 6.3: Comparison of Neutron yield data of 12C on 27Al at 600 reported
by V. Suman et al[67] with theoretical data from EMPIRE-3.2 and PACE 4.
The experimental data of 12C on 27Al at 600 reported by V. Suman[67] is
compared with EMPIRE-3.2 and PACE 4 at different available level density
model is shown in Fig. 6.3. The reported experimental data is found to be in
good agreement with the theoretical result made using ld model-3, theoretical
Yield
Chapter 6. Thick target neutron yield-Intermediate energy 90
data follows the trend with experimental data, but slightly higher than the
experimental data in the energy range of about 0-15MeV. At this intermediate
angles EMPIRE-3.2 and PACE 4 calculations are fairly close with each other
but over predicted experimental data.
The experimental data of 12C on 27Al at 900 reported by V. Suman[67], is
compared with EMPIRE-3.2 and PACE 4 at different available level density
model is shown in Fig. 6.4. The theoretical results obtained using ldmodel-3
are in good agreement with the present experimental data and which follows
the trend of experimental results of this reaction, experimental data and PACE
4 estimates are quite similar for backward angle 90°.
 0.00014
Experimental
ld0
ld1
ld2
 0.00012
ld 3
Pace4
 0.0001
-5
 8x10
-5
 6x10
-5
 4x10
-5
 2x10
 0
 0  20  40  60  80  100
En(MeV)
Figure 6.4: Comparison of Neutron yield data of 12C on 27Al at 900 reported
by V. Suman et al[67],with theoretical data from EMPIRE-3.2 and PACE 4.
Yield
Chapter 6. Thick target neutron yield-Intermediate energy 91
Similarly, we test the validation of code EMPIRE-3.2 with and without
pre-equilibrium parameter(shown in Fig. 6.5). For that we done the calcula-
tion with PCROSS-1.5 and PCROSS-0 input parameter. The trend of result
obtained from calculation with pre-equilibrium shows consistent with experi-
mental data and without preeequillibrium results good agreement with PACE
4 data. This shows PACE 4 didnt account pre-equilibrium contribution while
EMPIRE gives an overall well fitted prediction.
-1
10
Experimental
EMPIRE-(wop)
EMPIRE-(wp)
Pace4
-2
10
-3
10
-4
10
-5
10
-6
10
 0  10  20  30  40  50
En(MeV)
Figure 6.5: Comparison of Neutron yield data of 12C on 27Al reported by V.
Suman et al[67],with theoretical data from EMPIRE-3.2 with pre-equilibrium(wp)
and without pre-equilibrium(wop) and PACE 4.
Yield
Chapter 6. Thick target neutron yield-Intermediate energy 92
From Figure 1-4 the neutron yield measured data reported by V.Suman et
al[67] for the system 12C on 27Al is compared with EMPIRE-3.2 and PACE 4,
here we found whichever parameters of EMPIRE-3.2 matches the experimental
data well and summerises the contribution of pre-equilibrium.
0.01000000 Experimental
Empire(wp)
Pace4
Empire(wop)
0.00100000
0.00010000
0.00001000
0.00000100
0.00000010
0.00000001
 0  10  20  30  40  50  60  70  80
En(MeV)
Figure 6.6: Comparison of neutron yield data reported by[24] with EMPIRE-3.2
and PACE 4 for 12C on Ti at 144 MeV
Yield
Chapter 6. Thick target neutron yield-Intermediate energy 93
Using the same set of input parameters for level density, PCROSS and op-
tical model potential of EMPIRE-3.2,in the following sections we are producing
the results for 12C on natTi, 56Fe systems along with the available experimental
data, calculated HIC-1 code data and PACE 4 data for validation purpose.
6.2.2 12C on natTi
It is clear from the Fig. 6.6 that the trend of neutron yield made from the theo-
retical calculation EMPIRE-3.2 well matches with the experimental data given
by Nandy et.al[24]. Here also we compared EMPIRE’s with pre-equilibrium
and without pre-equilibrium parameter.
6.2.3 12C on 56Fe
Based on the above two studies with the systems 12C on 27Al and 12C on
natTi, a comparison of neutron yield from the system 12C on 56Fe with nuclear
reaction model codes EMPIRE-3.2 and PACE 4 is considered, as for this study
we use the same parameters to optmize the result for the system 12C on 56Fe,
which is shown in Fig. 6.7 and Fig. 6.8 respectively. Since there is no available
experimental data for 12C on 56Fe in the incident energy of 12MeV/nucleon we
consider the available calcuated data of 12C on 56Fe reported by H.W.Bertini
[68].
Chapter 6. Thick target neutron yield-Intermediate energy 94
 100000
HIC-1 code
Empire
Pace4
 10000
 1000
 100
 10
 1
 0  10  20  30  40  50  60  70  80
En(MeV)
 100000
HIC-1 code
Empire
pace4
 10000
 1000
 100
 10
 1
 0  10  20  30  40  50  60  70  80
En(MeV)
Figure 6.7: Comparison of Calculated neutron yield data from HIC-1 code
data reported by H.W.Bertini[68] with those obtained from model calculations
EMPIRE-3.2 and PACE 4 for 12C on 56Fe reaction at 00 and 300
Yield Yield
Chapter 6. Thick target neutron yield-Intermediate energy 95
 100000
HIC-1 code.
Empire
Pace4
 10000
 1000
 100
 10
 1
 0  10  20  30  40  50  60  70  80
En(MeV)
 10000
HIC-1 code
Empire
Pace4
 1000
 100
 10
 1
 0.1
 0.01
 0  10  20  30  40  50  60  70  80
En(MeV)
Figure 6.8: Comparison of Calculated neutron yield data from HIC-1 code
data reported by H.W.Bertini[68] with those obtained from model calculations
EMPIRE-3.2 and PACE 4 for 12C on 56Fe reaction at 600 and 900.
Yield Yield
Chapter 6. Thick target neutron yield-Intermediate energy 96
6.3 Conclusion
It is interesting to examine that in all the three cases, it is observed that
there is a fall in the PACE 4 calculations at high energies (above 5 MeV).
At forward angles less than 500 there is a significant discrepancy between
PACE 4 and EMPIRE-3.2. In this region, the PACE 4 calculation drastically
underestimates the experimental result. This is to be expected because of pre-
equilibrium emission. At backward angles higher than 50 degrees, PACE 4 cal-
culation falls off faster than the EMPIRE-3.2 calculation, but the experimental
and calculated data are in good agreement with EMPIRE-3.2 prediction. It is
also observed that pre-equilibrium contributions increase with increase in in-
cident energy of the neutron. Thus it is concluded that at intermediate beam
energies significant amount of high energy neutrons are produced this neutrons
in turn induces secondary reactions with core and structural materials. This
will affect the criticality of the reactor. Such neutrons may be produced other
structural materials like Nb,Ni,Cr etc.
Chapter 7
Summary and Conclusion
In summary, this extensive research work has been focused to the compre-
hensive evaluation of neutron yield from thick target materials, that spans
a broad spectrum of nuclear reactions and scenarios. One of the central as-
pects of this study involved the detailed evaluation of neutron yield. This
was achieved through the utilization of two prominent nuclear reaction model
codes, EMPIRE and NeuCBOT. These codes served as powerful tools for pre-
dicting neutron production across a range of scenarios. Notably, several alpha
bombardment experiments involving light target materials were also conducted
and their neutron yields were calculated using the NeuCBOT code. A signifi-
cant part of this research was the in-depth examination of model codes. The
neutron spectra generated by EMPIRE and NeuCBOT were subject to de-
tailed investigation. This analysis was conducted with a special emphasis on
the Am-Be (Americium-Beryllium) system, which was selected as a relevant
case study. The Am-Be system provided unique insights into the neutron spec-
tra generation under specific conditions, offering a valuable benchmark for the
performance of the model codes.
97
Chapter 7. Summary and Conclusion 98
Furthermore, our investigations extended into the field of the intermediate
energy range, a domain where EMPIRE-3.2 can be used . This comprehensive
code not only calculated ion-induced reactions but also shed light on the con-
tribution of pre-equilibrium emission. The study of neutron yield in this energy
range expanded our understanding of nuclear reactions and their associated
emissions.
7.1 Conclusion
The current work meets a demand for nuclear reaction model codes that can
estimate neutron yields at low and intermediate projectile energies. In the
present work a theoretical estimate of neutron yield from thick targets for
low and intermediate energy projectile system for different energies has been
carried out. The nuclear model codes were used as a tool to study the results.
These nuclear models were used to predict the neutron emission results at
various selected incident energies. The models are in accordance with the
nuclear data available in experimental data library EXFOR. The theoretical
code EMPIRE-3.2, NeuCBOT(TALYS+SRIM) and PACE 4 is used in the
present work for the code validation.
The present work focuses on two distinct case studies, both involving neu-
tron emission in thick targets and the validation of nuclear reaction model
codes. In the first case study, the focus is on low-energy neutron emission
from thick targets. This involves a comprehensive comparison of neutron
yield predictions obtained from two nuclear reaction model codes,EMPIRE-
3.2 and NeuCBOT, with experimental results. The experimental data is de-
rived from α bombardment of several light elements, including Boron, Car-
bon, Oxygen, Fluorine, Magnesium, Aluminium and Silicon at four distinct
Chapter 7. Summary and Conclusion 99
monoenergetic α-particle energies (4.0, 4.5, 5.0 and 5.5MeV). Furthermore, to
generate neutron energy spectra theoretically, a special case of Am-Be source
is explored, The neutron yield from Am-Be is evaluated as it is a case of
(α,n) reaction. The spectra generated by NeuCBOT, calculates the neutron
yield using TALYS, The mass stopping power are read from a library gener-
ated by SRIM. In EMPIRE-3.2 total neutron yield was achieved by integrat-
ing the neutron spectra over the range 0-9.37MeV. We computed the strag-
gling and energy loss for alpha particle in Am-Be using SRIM code. It shows
the peak corresponding to ground(0MeV), first(4.4MeV) and second-excited
states(7.65MeV)respectively. To test the code validation the resultant spec-
trum from EMPIRE-3.2 code is compared with spectrum generated by Geiger.
The code predicted a good spectrum with peaks of n0 colony around 8MeV
and 9MeV. Prominent peaks around 1.9MeV, 2.2MeV and 4.8MeV contribute
n1 colony and the spikes formed from thermal to 1.5MeV results the n2 colony
respectively. This work will be helpful in calibration facilities, in laboratories,
shielding and the radiation protection protocols etc.
Furthermore, Inorder to validate these predictions and ensure their ac-
curacy, an experimental validation of model code was also performed using
Am-Be source. α-particles from 241Am fuses with 9Be at an incident α energy
of 5.48MeV is measured using TOF method. experiment was performed using
one of the BC501A neutron detector from NAND facility, IUAC, New Delhi.
The neutron yield obtained from present TOF measurement shows the neu-
tron yield distribution from 0.3 to ∼ 6.5MeV. The experimental data have been
compared with the standard neutron reference spectrum as well as earlier mea-
sured data. In the overlapping energy region of 0.3 - 6.5MeV, our data agrees
well with the ISO 8529-2 reference neutron radiation spectrum. As compared
to earlier measurements, we have extended the neutron yield measurements
Chapter 7. Summary and Conclusion 100
down to 0.3MeV and applied neutron detection efficiency correction to the
data. With respect to earlier measured data, we observed significant improve-
ment within the energy interval from 0.3 to 3MeV. The technique provides a
simple means for characterization of the neutron sources used in calibrating
and optimizing the performance of BC501A based neutron ToF facility. The
measured data is also compared with EMPIRE-3.2 and NeuCBOT code, agree-
ment between measured data and EMPIRE-3.2 evaluated spectrum is found to
be good between 2.5MeV to 6MeV, the two prominent peaks at 2.8MeV and
4.6MeV are estimated. The comparison with NeuCBOT with TOF spectra is
also made. It is found a discrepancy around 2MeV to 5MeV, this is due to
the method in which Am-Be source are made, this seems to have an influence
on the neutron emission rate in these energy ranges, as the NeuCBOT code
works with material composition.
So far we studied on compound reactions within the area of low-energy
scenarios. However, as we move into higher energy regimes, we observed a
different phase of nuclear reactions, where mechanisms like pre-equilibrium
emissions dominates. Here we use the nuclear reaction model code EMPIRE-
3.2 as it can account pre-equilibrium contribution. Inorder to study the pre-
equilibrium emission, the neutron emission in intermediate energy range has
been estimated for different target-projectile systems 12C on 56Fe, 27Al,natTi.
The chosen targets are important because these are prominent accelerator
structural materials. This study results to understand the effect of PEQ con-
tribution in intermediate energy range. Here we have used the code EMPIRE-
3.2 and PACE 4 for estimating neutron yields. We investigated the effect of
pre-equilibrium, various level densities and optical potentials in this study.
The comparison of the estimated neutron yield from both the reaction model
codes EMPIRE-3.2 and PACE 4 with available experimental data has been
Chapter 7. Summary and Conclusion 101
made. In 12C on 27Al and 12C on natTi, available experimental data were
compared with EMPIRE-3.2 and PACE 4 code, the data is found to be in
good agreement with theoretical results made using level density model-3 of
code EMPIRE-3.2. It has been also observed that the PEQ parameters of
the code EMPIRE-3.2 satisfactorily reproduces the result, whereas, the code
PACE 4 calculations falls of faster than the EMPIRE-3.2 code because PACE
4 do not have the PEQ model included. For the system 12C on 56Fe available
calculated data is compared with the codes with same optimized parameters
of above systems. This comparison allows us to evaluate the reliability of our
calculations by expecting experimental data to fall within the same region as
our computational results.
Above findings concluded that in low energy neutron emission studies
NeuCBOT code gives a better results as it can calculate energy loss in case of
thick targets, while in intermediate data neutron emission EMPIRE-3.2 code
gives better prediction and simulation as it can calculate for high energy ion
projectiles. Also it is understood that at intermediate energy range approx 7 A
MeV, the PEQ neutron emission is prefered and PEQ emission increases with
increase in energy range. Theoretical codes based on various models, poten-
tials, and phenomenological parameters made use of this model calculations
to improve its working. These model calculation of neutron emission studies
for different structural materials are important for evaluation of nuclear data
which are having application in accelerator environment and nuclear energy
programs.
Chapter 8
Recommendation
In the present work the nuclear reaction tool NeuCBOT and code EMPIRE-
3.2 has reproduced different experimental systems. While there are scope for
other reaction model codes like ALICE or HION by incorporating various for-
malisms. Alpha-neutron yield for compounds may not be readily available or
well-documented in NeuCBOT hence a concerted effort is required to collect
data on alpha neutron yields of compounds as well as developing theoretical
models to predict these yields accurately. Also the future scope of alpha bom-
barded on heavy ions holds promising applications in advanced nuclear reactor
designs, such as thorium based reactors or accelerator-driven systems, to im-
prove efficiency, safety and waste management. Further the code EMPIRE-3.2
requires a modification for accurate calculations at high energies, the code is
not optimized or designed to handle the computational demands associated
with reactions above 500MeV. The model parameters and and assumptions
are often tuned and validated for specific energy regimes and extrapolating
beyond these limits could lead to unreliable results, resolving the problem will
make the code better suitable for the energy range above 500 MeV.
103
Chapter 8. Recommendation 104
In the pre-equilibrium regime the investigation of neutron yields at higher
energies above 10 A MeV is also a demanding area for future research. The
studies on measurement of neutron yield from thick targets of various metals
which are widely used in building accelerators and cavities when bombarded
by 12C will improve our understanding on Pre-equilibrium neutron emission,
the new data are useful to the application of accelerator shielding design. Also
there are finite probability of producing carbon in ternary fission of 235U in
reactors that promotes the study of secondary neutron generation. There are
very few works reported in literature on neutron energy distribution from heavy
ion reaction on thick target above 10MeV/amu energies. Thus new data on
equilibrium and pre-equilibrium neutron emissions are very important for a
better understanding of the nuclear reaction mechanism. Furthermore, there
is an exciting opportunity for experimental work at institutions such as IUAC
(Inter-University Accelerator Centre) to expand the scope of our research. By
obtaining data in higher energy ranges, one can contribute valuable informa-
tion to the NNDC (National Nuclear Data Center) nuclear reaction database,
enriching this resource for public use and benefiting the broader scientific com-
munity.
Bibliography
[1] H. Becquerel, “compt.rend.,” vol. 122, p. 450, 1896.
[2] N. Bohr, “Neutron capture and nuclear constitution,,” Nature, vol. 137,
pp. 344–348, 1936.
[3] A. Lane and J. Lynn, “Analysis of experimental data on nucleon capture
reactions,” Nuclear Physics, vol. 11, pp. 646–669, 1959.
[4] P. Hodgson, “Heavy ion collision,” proceedings of International Summer
School, La Rabia, p. 220, 1992.
[5] M. Blann, “Precompound decay calculations for reactions induced by 10–
100 mev/nucleon heavy ions,” Phys. Rev. C, vol. 31, pp. 1245–1254, Apr
1985.
[6] H. Machner, “Pre-equilibrium emission in heavy ion reactions,” Phys.
Rev. C, vol. 28, pp. 2173–2175, Nov 1983.
[7] J. Pal, S. Saha, C. C. Dey, P. Banerjee, S. Bose, B. K. Sinha, M. B.
Chatterjee, and S. K. Basu, “Pre-equilibrium and equilibrium emission of
neutrons in 114Cd(α, xn) reactions,” Phys. Rev. C, vol. 71, p. 034605, Mar
2005.
[8] A. Iwamoto, “Exciton-model approach to fast-particle emission in heavy-
ion collisions,” Phys. Rev. C, vol. 35, pp. 984–993, Mar 1987.
105
Bibliography 106
[9] G. Friedlander, J. W. Kennedy, E. S. Macias, and J. M. Miller, “Nuclear
and radiochemistry, 3rd edition,” John Wiley and Sons, 1 1981.
[10] B. V. Raju and S. Jnanananda, “Fast neutron spectrum of Ra-Be source,”
Nuclear Instruments and Methods, vol. 31, no. 1, pp. 87–89, 1964.
[11] J. Pal, S. Saha, C. Dey, B. Sinha, and M. Chatterjee, “Neutron energy
spectrum of an Am–Be source by gamma gated ntof technique,” Radiation
Physics and Chemistry, vol. 51, no. 4, pp. 475–477, 1998.
[12] K.W.Geiger and L.Vanderzwan, “The neutron spectrum of a Am-Be (α,
n) source as simulated by accelerator produced -particles,” International
Journal of Applied Radiation and Imtopcs, vol. 21, pp. 193–198, 1969.
[13] H. Liskien and A. Paulsen, “Neutron yields of light elements under α-
bombardment,” Atomkernenergie (ATKE), pp. 59–61, 1977.
[14] H. Liskien and A. Paulsen, “Neutron production cross sections and en-
ergies for the reactions T(p,n)3He, D(d,n)3He, and T(d,n)4He,” Report
CBNM/VG/21/78, Geel, Belgium, pp. 1–2, 1978.
[15] J. K. Bair and J. G. del Campo, “Neutron yields from alpha-particle
bombardment,” J., Nucl. Sci. Eng.,, pp. 18–28, 7 1979.
[16] R. Macklin Nucl. Instr. Meth., pp. 335–339, 1957.
[17] R. Macklin and J. Gibbons, “Absolute neutron yield from thick target
NATC(α,n),” J., Nucl. Sci. Eng.,, vol. 31, p. 343, 1968.
[18] J. Bair, “Absolute neutron yields from alpha-particle interaction with tick
targets of natural carbon,” J., Nucl. Sci. Eng.,, vol. 51, pp. 83–84, 1973.
Bibliography 107
[19] D. West and A. Sherwood Report Atomic Energy Research Establish-
ment(AERE) Harwell, pp. 1–5, 1978.
[20] D. West and A. Sherwood, “Measurements of thick-target (α,n) yields
from light elements,” Ann. Nucl. Ener., vol. 9, pp. 551–577, 1982.
[21] G. Jacobs, Neutron energy spectra produced by alpha-bombardment of light
elements in thick targets. Phd thesis 1 (research TU/e / graduation TU/e),
Applied Physics and Science Education, 1982. Proefschrift.
[22] M. Nandy, T. Bandyopadhyay, and P. K. Sarkar, “Measurement and anal-
ysis of neutron spectra from a thick Ta target bombarded by 7.2AMeV
16O ions,” Phys. Rev. C, vol. 63, p. 034610, Feb 2001.
[23] C. Sunil, M. Nandy, and P. K. Sarkar, “Measurement and analysis of en-
ergy and angular distributions of thick target neutron yields from 110MeV
19F on 27Al,” Phys. Rev. C, vol. 78, p. 064607, Dec 2008.
[24] M. Nandy, P. Sarkar, T. Sanami, T. Shibata, and M. Takada, “Neutron
dose distribution from 12C induced reactions on Ti and Ag using proton
recoil scintillator,” Radiation Measurements, vol. 45, no. 10, pp. 1276–
1280, 2010.
[25] J. Acharya, S. Mukherjee, A. Chatterjee, N. L. Singh, K. Ramachandran,
P. C. Rout, K. Mahata, V. Desai, E. T. Mirgule, S. V. Suryanarayana,
B. K. Nayak, A. Saxena, and G. F. Steyn, “Neutron emission in 19F-
induced reactions,” Phys. Rev. C, vol. 97, p. 034607, Mar 2018.
[26] E. Holub, D. Hilscher, G. Ingold, U. Jahnke, H. Orf, and H. Rossner,
“Neutron emission in central heavy-ion collisions of 165Ho + 20Ne at 11,
Bibliography 108
14.6, and 20.1 MeV/nucleon,” Phys. Rev. C, vol. 28, pp. 252–270, Jul
1983.
[27] D. Hilscher, H. Rossner, A. Gamp, U. Jahnke, B. Cheynis, B. Chambon,
D. Drain, C. Pastor, A. Giorni, C. Morand, A. Dauchy, P. Stassi, and
G. Petitt, “Energy and linear-momentum dissipation in the fusion reaction
of 165Ho + 20Ne at 30 MeV/nucleon,” Phys. Rev. C, vol. 36, pp. 208–219,
Jul 1987.
[28] H. Singh, K. S. Golda, S. Pal, Ranjeet, R. Sandal, B. R. Behera, G. Singh,
A. Jhingan, R. P. Singh, P. Sugathan, M. B. Chatterjee, S. K. Datta,
A. Kumar, G. Viesti, and I. M. Govil, “Role of nuclear dissipation and
entrance channel mass asymmetry in pre-scission neutron multiplicity en-
hancement in fusion-fission reactions,” Phys. Rev. C, vol. 78, p. 024609,
Aug 2008.
[29] V. Singh, B. R. Behera, M. Kaur, P. Sugathan, K. S. Golda, A. Jhingan,
J. Sadhukhan, D. Siwal, S. Goyal, S. Santra, A. Kumar, R. K. Bhowmik,
M. B. Chatterjee, A. Saxena, S. Pal, and S. Kailas, “Search for an effect
of shell closure on nuclear dissipation via a neutron-multiplicity measure-
ment,” Phys. Rev. C, vol. 86, p. 014609, Jul 2012.
[30] N. K. Rai, A. Gandhi, A. Kumar, N. Saneesh, M. Kumar, G. Kaur,
A. Parihari, D. Arora, K. S. Golda, A. Jhingan, P. Sugathan, T. K. Ghosh,
J. Sadhukhan, B. K. Nayak, N. K. Deb, S. Biswas, and A. Chakraborty,
“Measurement of neutron multiplicity to investigate the role of entrance
channel parameters on the nuclear dissipation,” Phys. Rev. C, vol. 100,
p. 014614, Jul 2019.
Bibliography 109
[31] S. Westerdale and P. D. Meyers, “Radiogenic neutron yield calcula-
tions for low-background experiments,” Nucl. Instrum. Meth. in Phys.,
vol. 875, p. 57–64, 04 2017.
[32] E. Mendoza, D. Cano-Ott, P. Romojaro, V. Alcayne, P. G. Abia, V. Pe-
sudo, L. Romero, and R. Santorelli, “Neutron production induced by α-
decay with geant4,” Nuclear Instruments and Methods in Physics Re-
search Section A: Accelerators, Spectrometers, Detectors and Associated
Equipment, vol. 960, p. 163659, 2020.
[33] W. B. Wilson, R. T. Perry, W. S. Charlton, T. A. Parish, and E. F. Shores,
“SOURCES: a code for calculating (α,n), spontaneous fission, and delayed
neutron sources and spectra,” Radiation Protection Dosimetry, vol. 115,
pp. 117–121, 12 2005.
[34] A. C. Fernandes, A. Kling, and G. N. Vlaskin, “Comparison of thick-
target (alpha, n) yield calculation codes,” vol. 153, p. 07021, 2017.
[35] V. F. Weisskopf and D. H. Ewing, “On the yield of nuclear reactions with
heavy elements,” Phys. Rev., vol. 57, pp. 472–485, Mar 1940.
[36] W. Hauser and H. Feshbach, “The inelastic scattering of neutrons,” Phys.
Rev., vol. 87, pp. 366–373, Jul 1952.
[37] G. Breit and E. Wigner, “Capture of slow neutrons,” Phys. Rev., vol. 49,
pp. 519–531, Apr 1936.
[38] J. J. Griffin, “Statistical model of intermediate structure,” Phys. Rev.
Lett., vol. 17, pp. 478–481, Aug 1966.
Bibliography 110
[39] C. Kalbach-Cline, “Residual two-body matrix elements for pre-
equilibrium calculations,” Nuclear Physics A, vol. 210, no. 3, pp. 590–604,
1973.
[40] C. Kalbach and F. M. Mann, “Phenomenology of continuum angular dis-
tributions. i. systematics and parametrization,” Phys. Rev. C, vol. 23,
pp. 112–123, Jan 1981.
[41] H. A. Bethe, “Nuclear physics b. nuclear dynamics, theoretical,” Rev.
Mod. Phys., vol. 9, pp. 69–244, Apr 1937.
[42] M. Herman, “Empire-3.2 malta modular system for nuclear reaction cal-
culations and nuclear data evaluation,” Nucl. Phys, 2013.
[43] A. Gilbert and A. G. W. Cameron, “A composite nuclear-level density
formula with shell corrections,” Canadian Journal of Physics, vol. 43,
pp. 1446–1496, 1965.
[44] W. Dilg, W. Schantl, H. Vonach, and M. Uhl, “Level density parameters
for the back-shifted fermi gas model in the mass range 40 < A < 250,”
Nuclear Physics A, vol. 217, no. 2, pp. 269–298, 1973.
[45] A. V. Ignatyuk, K. Istekov, and G. N. Smirenkin Sov. J. Nucl. Phys,
vol. 4, p. 450, 1979.
[46] A. V. Ignatyuk, J. L. Weil, S. Raman, and S. Kahane, “Density of discrete
levels in 116Sn,” Phys. Rev. C, vol. 47, pp. 1504–1513, Apr 1993.
[47] A. D’Arrigo, G. Giardina, M. Herman, A. Ignatyuk, and A. Taccone,
“Semi-empirical determination of the shell correction temperature and
spin dependence by means of nuclear fission,” Journal of Physics G: Nu-
clear and Particle Physics, vol. 20, no. 2, p. 365, 1994.
Bibliography 111
[48] S. Goriely, F. Tondeur, and J. Pearson, “A Hartree–Fock nuclear mass
table,” Atomic Data and Nuclear Data Tables, vol. 77, no. 2, pp. 311–381,
2001.
[49] S. Goriely, S. Hilaire, and A. J. Koning, “Improved microscopic nuclear
level densities within the Hartree-Fock-Bogoliubov plus combinatorial
method,” Phys. Rev. C, vol. 78, p. 064307, Dec 2008.
[50] S. Goriely, M. Samyn, and J. M. Pearson, “Further explorations of
Skyrme-Hartree-Fock-Bogoliubov mass formulas. VII. Simultaneous fits
to masses and fission barriers,” Phys. Rev. C, vol. 75, p. 064312, Jun
2007.
[51] A. Koning, S. Hilaire, and S. Goriely, “Talys-1.6 a nuclear reaction pro-
gram,” User Manual, NRG, The Netherlands, 2013.
[52] S. Westerdale, Meyers, and P. Daniel, “Radiogenic neutron yield calcula-
tions for low-background experiments,” Nuclear Instruments and Methods
in Physics Research Section A: Accelerators, Spectrometers, Detectors and
Associated Equipment, vol. 875, pp. 57–64, 2017.
[53] M. Herman, R. Capote, and B. V. Carlson, “Empire: Nuclear reaction
model code system for data evaluation,” Nuclear Data Sheets, vol. 108,
pp. 2655–2715, 2007.
[54] J. Tuli, “Evaluated nuclear structure data file,” Nuclear Instruments and
Methods in Physics Research Section A: Accelerators, Spectrometers, De-
tectors and Associated Equipment, vol. 369, no. 2, pp. 506–510, 1996.
[55] J. F. Ziegler and J. P. Biersack, The Stopping and Range of Ions in Matter,
pp. 93–129. Boston, MA: Springer US, 1985.
Bibliography 112
[56] P. De Biévre and P. Taylor, “Table of the isotopic compositions of the
elements,” International Journal of Mass Spectrometry and Ion Processes,
vol. 123, no. 2, pp. 149–166, 1993.
[57] D. Kumar, M. Maiti, and S. Lahiri, “Experimental probe for the pro-
duction of 97Ru from the 7Li +93 Nb reaction: A study of precompound
emissions,” Phys. Rev. C, vol. 94, p. 044603, Oct 2016.
[58] R. Bass, “Nucleus-nucleus potential deduced from experimental fusion
cross sections,” Phys. Rev. Lett., vol. 39, pp. 265–268, Aug 1977.
[59] P. Sugathan, A. Jhingan, K. S. Golda, T. Varughese, S. Venkataramanan,
N. Saneesh, V. V. Satyanarayana, S. K. Suman, J. Antony, R. Shanti,
K. Singh, S. K. Saini, A. Gupta, A. Kothari, P. Barua, R. Kumar,
J. Zacharias, R. P. Singh, B. R. Behera, S. K. Mandal, I. M. Govil, and
R. K. Bhowmik, “Neutron detector array at iuac: Design featuresand in-
strumentation developments,” PRAMANA- Journal of Physics, vol. 83,
pp. 807–815, 2014.
[60] M. Moszynski, G. Bizard, G. Costa, D. Durand, Y. E. Masri, G. Guil-
laume, F. Hanappe, B. Heusch, A. Huck, J. Peter, C. . Ring, and
B. Tamain, “Study of n-γ discrimination by digital charge comparison
method for a large volume liquid scintillator,” Nucl. Instr. and Meth. in
Physics Research A, vol. 317, pp. 262–272, 1992.
[61] N. Saneesh, K. Golda, A. Jhingan, S. Venkataramanan, T. Varughese,
M. Kumar, M. Thakur, R. Mahajan, B. Behera, P. Sugathan, A. Chatter-
jee, and M. Chatterjee, “Performance results of national array of neutron
detectors (nand) facility at iuac,” Nuclear Instruments and Methods in
Bibliography 113
Physics Research Section A: Accelerators, Spectrometers, Detectors and
Associated Equipment, vol. 986, p. 164754, 2021.
[62] M. Roush, M. Wilson, and W. Hornyak, “Pulse shape discrimination,”
Nuclear Instruments and Methods, vol. 31, no. 1, pp. 112–124, 1964.
[63] S. Venkataramanan, A. Gupta, K. S. Golda, H. Singh, R. Kumar, R. P.
Singh, and R. K. Bhowmik, “A compact pulse shape discriminator module
for large neutron detector arrays,” Nuclear Instruments and Methods in
Physics Research Section A: Accelerators, Spectrometers, Detectors and
Associated Equipment, vol. 596, no. 2, pp. 248 – 252, 2008.
[64] R. Brun and F. Rademakers, “Root — an object oriented data analysis
framework,” Nuclear Instruments and Methods in Physics Research Sec-
tion A: Accelerators, Spectrometers, Detectors and Associated Equipment,
vol. 389, no. 1, pp. 81–86, 1997.
[65] J. Scherzinger, R. Al Jebali, J. Annand, K. Fissum, R. Hall-Wilton,
S. Koufigar, N. Mauritzson, F. Messi, H. Perrey, and E. Rofors, “A com-
parison of untagged gamma-ray and tagged-neutron yields from 241Am-
Be and 238Pu-Be sources,” Nuclear Instruments and Methods in Physics
Research Section A: Accelerators, Spectrometers, Detectors and Associ-
ated Equipment, vol. 127, pp. 98–102, 2017.
[66] “Reference neutron radiations. characteristics and methods of produc-
tion,” International Organization for Standardization.ISO-Standard 8529,
2001.
[67] V. Suman, C. Sunil, S. Nair, S. Paul, K. Biju, G. Sahoo, and P. Sarkar,
“Thick target double differential neutron energy distribution from 12C+
27Al at 115MeV,” Nuclear Instruments and Methods in Physics Research
Bibliography 114
Section A: Accelerators, Spectrometers, Detectors and Associated Equip-
ment, vol. 800, pp. 29–33, 2015.
[68] H. W. Bertini, R. T. Santoro, and O. W. Hermann, “Calculated nucleon
spectra at several angles from 192-, 500-, 700-, and 900-MeV 12C on 56Fe,”
Phys. Rev. C, vol. 14, pp. 590–595, Aug 1976.