An Introduction to Nuclear Fission

198 Pages·2021·3.998 MB·English

by  Walid Younes, Walter D. Loveland

Graduate Texts in Physics
Walid Younes
Walter D. Loveland
An Introduction
to Nuclear Fission
Graduate Texts in Physics
SeriesEditors
KurtH.Becker,NYUPolytechnicSchoolofEngineering,Brooklyn,NY,USA
Jean-Marc Di Meglio, Matière et Systèmes Complexes, Bâtiment Condorcet,
UniversitéParisDiderot,Paris,France
SadriHassani,DepartmentofPhysics,IllinoisStateUniversity,Normal,IL,USA
MortenHjorth-Jensen,DepartmentofPhysics,Blindern,UniversityofOslo,Oslo,
Norway
BillMunro,NTTBasicResearchLaboratories,Atsugi,Japan
RichardNeeds,CavendishLaboratory,UniversityofCambridge,Cambridge,UK
William T. Rhodes, Department of Computer and Electrical Engineering and
ComputerScience,FloridaAtlanticUniversity,BocaRaton,FL,USA
SusanScott,AustralianNationalUniversity,Acton,Australia
H. Eugene Stanley, Center for Polymer Studies, Physics Department, Boston
University,Boston,MA,USA
Martin Stutzmann, Walter Schottky Institute, Technical University of Munich,
Garching,Germany
Andreas Wipf,InstituteofTheoreticalPhysics,Friedrich-Schiller-University Jena,
Jena,Germany
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Walid Younes (cid:129) Walter D. Loveland
An Introduction to Nuclear
Fission
WalidYounes WalterD.Loveland
Livermore,CA,USA DepartmentofChemistry
OregonStateUniversity
Corvallis,OR,USA
ISSN1868-4513 ISSN1868-4521 (electronic)
GraduateTextsinPhysics
ISBN978-3-030-84591-9 ISBN978-3-030-84592-6 (eBook)
https://doi.org/10.1007/978-3-030-84592-6
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Preface
It has been over 80 years since the discovery of fission by Hahn and Strassman.
During the intervening years, there have been virtually countless studies of the
fissionprocessandrelatedphenomena.Thecomplexityofthefissionprocessandits
practical importance have attracted some of our best minds. The field has enjoyed
the guidance offered by numerous review articles and monographs, especially the
iconicbooksbyVandenboschandHuizenga,Wagemans,andKrappeandPomorski.
Thatposesthequestionofwhyanotherbookonfissionisneeded.Thefirstanswer
to that question is to point out that Vandenbosch and Huizenga was published in
1973andtheWagemansbookwaspublishedin1991,whilethemorerecentbook
byKrappeandPomorskiin2012presentsamoreadvancedtreatmentofthetheory
of fission. There has been significant progress in our understanding of fission in
recent years, leading to a renaissance in the field. Presentation and discussion of
this recent research seems important. We have written this book in a manner that
we hope will be attractive to students. The first chapter contains a discussion of
fissionandtheworkofsomeearlypioneersinthefieldandsomeelementarymodels
of fission. The second chapter gives an overview of the general characteristics of
fission and the important quantities involved. The third chapter reviews various
modelsoffissionandillustratestheirapplication.Chapter4containsadiscussionof
theproductsoffission.Chapter5containsadiscussionoftheneutronandgamma
rays emitted in fission. Chapters 6 and 7 contain a more sophisticated treatment
of the structure and dynamics of fission. It is our hope that beginning students
and advanced professionals will find something of interest in this book. The book
contains a number of solved problems that illustrate important points and lead the
reader to investigate fission in the time-tested manner of solving real problems.
Someoftheseproblemsaredifficultbutallpromiseasuitablepedagogicreward.
Livermore,CA,USA WalidYounes
Corvallis,OR,USA WalterD.Loveland
v
Acknowledgments
The authors gratefully acknowledge the support of their fission research programs
by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics,
the National Science Foundation, the National Nuclear Security Agency, and our
home institutions, the Lawrence Livermore National Laboratory (WY, prior to his
retirement)andOregonStateUniversity(WL).Thecontributionstothismanuscript
by WY were written by the author acting on his own independent capacity, and
notonbehalfoftheLawrenceLivermoreNationalLaboratory.WethankDr.Mark
Stoyerforhiscarefulreviewofthemanuscriptandformanyusefulsuggestions.We
thankournumerouscolleaguesfortheircommentsandpatienttutoring.
vii
Contents
1 History ........................................................................ 1
1.1 FissionasBasicScience............................................... 1
1.2 TheDiscoveryofFission.............................................. 2
1.3 Focus:ThreeImportantScientists .................................... 3
1.3.1 IdaTackeNoddack(1896–1978)............................. 3
1.3.2 IrèneJoliot-Curie(1897–1956)............................... 4
1.3.3 LiseMeitner(1878–1968) .................................... 4
1.3.4 ClosingRemarks .............................................. 5
1.4 AFirstModelofFission .............................................. 6
1.4.1 TheViewoftheNucleusBefore1932 ....................... 6
1.4.2 TheLiquid-DropModel....................................... 6
1.4.3 TheBohr-WheelerFissionModel............................ 9
1.5 FissionintheCosmos ................................................. 14
1.6 StructureoftheBook.................................................. 14
1.7 AdditionalResources.................................................. 15
1.8 Questions............................................................... 16
1.9 Exercises............................................................... 16
References..................................................................... 18
2 GeneralCharacteristics..................................................... 21
2.1 SpontaneousandInducedFission..................................... 21
2.2 ChronologyoftheFissionProcess.................................... 23
2.3 FissionCrossSections................................................. 25
2.4 FragmentMassandChargeDistributions............................ 25
2.5 FissionEnergetics ..................................................... 28
2.6 FissionBarriers........................................................ 31
2.7 FissionIsomers ........................................................ 31
2.8 NeutronandGamma-RayDistributions.............................. 33
2.9 SpallationVersusFission.............................................. 37
2.10 OnlineResourcesforFissionData.................................... 37
2.11 Questions............................................................... 38
ix
x Contents
2.12 Exercises............................................................... 39
References..................................................................... 42
3 Models......................................................................... 45
3.1 TheLiquid-DropModel............................................... 45
3.1.1 TheNuclearShape ............................................ 46
3.1.2 FromShapetoEnergy ........................................ 47
3.2 IntroductiontotheStrutinskyShellCorrectionMethod............. 51
3.3 PotentialEnergySurfaces............................................. 51
3.4 ScissionPointModels................................................. 52
3.5 KinematicsofFissionReactions...................................... 53
3.6 FissionCross-SectionModels ........................................ 56
3.7 Questions............................................................... 58
3.8 Exercises............................................................... 59
References..................................................................... 64
4 FissionFragmentsandProducts........................................... 67
4.1 Fission-FragmentDetectors........................................... 67
4.2 FragmentMass,Charge,andKineticEnergy ........................ 68
4.2.1 Double-EnergyMeasurements................................ 68
4.2.2 ModelingFragmentsMassandChargeDistributions ....... 72
4.3 ExcitationEnergyoftheFragments .................................. 74
4.4 AngularMomentumandAngularDistributionofFragments ....... 75
4.5 DecayofFragments ................................................... 78
4.6 ComputerModelsofFission-FragmentProperties................... 82
4.7 Questions............................................................... 82
4.8 Exercises............................................................... 82
References..................................................................... 86
5 FissionNeutronsandGammaRays........................................ 89
5.1 NeutronBeams ........................................................ 90
5.2 NeutronDetection ..................................................... 91
5.3 NeutronsEmittedBeforeandatScission............................. 92
5.4 PromptNeutrons....................................................... 94
5.4.1 NeutronSpectrum............................................. 94
5.4.2 NeutronMultiplicity .......................................... 96
5.5 DelayedNeutrons...................................................... 98
5.6 Photon-InducedFission ............................................... 99
5.7 Gamma-RayDetection................................................ 99
5.8 TheUseofLargeArraysofGamma-RayDetectorsinFission ..... 101
5.9 GeneralPropertiesofFissionGammaRays.......................... 101
5.10 FromDetectorCountstoFragmentYield............................ 102
5.11 FragmentAngularMomentumDeducedfromMeasured
GammaRays........................................................... 105
5.12 Questions............................................................... 106
Contents xi
5.13 Exercises............................................................... 106
References..................................................................... 111
6 FissionModelsRevisited:Structure ....................................... 115
6.1 Single-ParticleModels ................................................ 115
6.2 TheStrutinskyShellCorrectionMethodRevisited.................. 118
6.3 Pairing.................................................................. 124
6.4 LevelDensities......................................................... 128
6.4.1 TheMany-BodyStateDensity:EnergyDependence........ 128
6.4.2 The Many-Body State Density: Angular
MomentumandParityDependence.......................... 131
6.4.3 TheMany-BodyStateDensity:Collective
Enhancements ................................................. 132
6.4.4 AdditionalImprovements..................................... 132
6.5 AdvancedTopics....................................................... 133
6.5.1 MoreRealisticSingle-ParticleModels....................... 133
6.5.2 MatrixFormulationoftheSchrödingerEquation............ 135
6.5.3 TheHartree-FockApproximation............................ 138
6.6 Questions............................................................... 143
6.7 Exercises............................................................... 144
References..................................................................... 148
7 FissionModelsRevisited:ReactionsandDynamics ..................... 151
7.1 ScatteringTheory...................................................... 151
7.1.1 Introduction.................................................... 151
7.1.2 ResonancesandWidths....................................... 154
7.2 Hauser-FeshbachTheory.............................................. 156
7.2.1 GeneralFormalism............................................ 156
7.2.2 TransitionStateTheory ....................................... 157
7.3 OtherTypesofReactionsLeadingtoFission ........................ 161
7.3.1 QuasifissionReactions........................................ 161
7.3.2 Direct-Reaction-InducedFission ............................. 162
7.4 BriefSurveyofAdvancedTopics..................................... 164
7.4.1 Semi-classicalMethods....................................... 164
7.4.2 Quantum-MechanicalMethods............................... 165
7.5 Questions............................................................... 166
7.6 Exercises............................................................... 167
References..................................................................... 171
8 SolutionstoSelectedProblems............................................. 173
8.1 SolutionsforChap.1 .................................................. 173
8.2 SolutionsforChap.2 .................................................. 174
8.3 SolutionsforChap.3 .................................................. 175
8.4 SolutionsforChap.4 .................................................. 177
8.5 SolutionsforChap.5 .................................................. 179