Nuclear Fission: Theories, Experiments and Applications

486 Pages·2023·17.679 MB·English

by  Patrick Talou, Ramona Vogt

Patrick Talou
Ramona Vogt   Editors
Nuclear
Fission
Theories, Experiments and Applications
Nuclear Fission
Patrick Talou • Ramona Vogt
Editors
Nuclear Fission
Theories, Experiments and Applications
Editors
PatrickTalou RamonaVogt
XComputationalPhysicsDivision NuclearandChemicalSciencesDiv.,L-59
LosAlamosNationalLaboratory LawrenceLivermoreNatlLab
LosAlamos,NM,USA Livermore,CA,USA
ISBN978-3-031-14544-5 ISBN978-3-031-14545-2 (eBook)
https://doi.org/10.1007/978-3-031-14545-2
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Preface
ThedawnoftheAtomicAgecameaboutwithtwobreakthroughsthatwouldreshape
mankind forever. The first event came on December 2, 1942, at the University of
Chicago, USA. An experimental team led by the already famous Enrico Fermi
producedthefirstsustainablefissionchainreactionwithabigpileofgraphiteand
alittlebitofuranium.Thefirst-evermanmadenuclearreactorwasborn,andhopes
for an infinite supply of cheap energy that would lift up humanity were high. The
second dramatic event happened on July 16, 1945, in Alamogordo, New Mexico,
USA, where the “Trinity” test became the first successful test of an atomic bomb.
Onlyafewweekslater,atomicexplosionsinHiroshimaandNagasaki,Japan,would
shocktheworldandputanendtoWorldWarII.Itishardtobelievethatthenuclear
fission process at the source of this amazing yet potentially devastating source of
energywasdiscoveredonlyafewyearsearlier,in1938.
Eighty-plus years later, nuclear energy produces about 10% of the electricity
consumed worldwide and is thought once again to be a game changer to combat
thedirepredictedconsequencesofclimatechange.Significantstockpilesofnuclear
weapons exist today in the hands of a few “nuclear powers,” while international
nuclear global security and nonproliferation efforts are continuously being devel-
oped to keep those powerful weapons from getting out of control. Aside from
thesedramaticdevelopments,thenuclearfissionprocessremainsafascinatingand
daunting challenge to study for physicists and chemists alike. Often viewed as a
drastic collective rearrangement of nuclear matter, classical approximations have
gonealongwayinprovidingasimpleyetsurprisinglyaccuratepictureofthefission
process.Modeledinitiallyasthesplittingofachargedliquiddropintotwosmaller
oneswhilereleasingamassiveamountofenergy,thisearlyandsomewhatsimplistic
picture remains useful to this day. In contrast, microscopic theories attempt to
describenuclearfissionfromthemorefundamentalinteractingneutronsandprotons
(morethan200ofthem!)thatmakeuptheatomicnucleus.Meanwhile,experimental
setups, methods, and facilities have progressed immensely since those early days.
Neutrons, photons, protons, and electrons have all been used to induce fission
andunravelitssecrets.Inversekinematicsapproaches,multi-nucleontransfers,and
surrogatereactionshaveopenednewpathwaysforexploringsomeoftheremaining
mysteries of this process. The massive increase in calculational power offered by
modernhigh-performancecomputersallowsustoaddresssomeofthecomplexities
v
vi Preface
of the nucleon-nucleon interactions at the quantum level. Finally, scientists and
engineersaredevisingincreasinglycomplexexperimentalandtechnologicalsetups
to capture the intrinsic correlations among all emitted particles accompanying the
fissionprocess,potentiallymakinguseoftheminmodernnucleartechnologies.
The last comprehensive review book on nuclear fission, The Nuclear Fission
Process, Ed. C. Wagemans [1], was published more than 30 years ago. Since
then,majorbreakthroughshavebeenmadeonallfronts:experimental,theoretical,
computational, and technological. The time is ripe for a new review that would
attempttoaddressmanyofthoseadvancesandcomplementthistimelessreference.
The idea for this book emerged from the organization of the first two editions
of the FIESTA school and workshop on fission, held in Santa Fe, New Mexico,
USA, in 2014 and 20171. Some of the detailed lecture notes were transformed
into sections of this book, while completely new material was written to address
topics not covered in the school. That being said, many fission-related subjects
are intentionally ignored in this book, if only to keep it to a manageable size and
endeavor. However, it is our intention to create a reference book that physicists as
wellasengineersinterestedinthetopiccanextractvaluableinformationfrom.
In addition to the FIESTA lectures, we have been fortunate to write the book
at this particular point in time, following the recent publications of three review
articles on the topic: first, an excellent review article by Andreyev et al. [2] on
experimentaladvancesinthefield;second,acollectivework[3]onnuclearfission
theorythatstemmedfromaworkshoporganizedattheUniversityofYorkin2019,
whichprovidesareviewoftheoreticaldevelopmentsinfission;andfinally,areview
articlethatweco-wroteonthedevelopmentoftheories,models,experiments,and
technologiesonthetopicofcorrelationsamongfissionobservables[4].
Eachchaptercoversaparticulartopicfromthepointofviewofwhatweknow
from observation, which instruments, facilities, and experimental techniques have
beendevisedtoexplorethistopic,whichtheoriesandmodelsarebeingdeveloped
tobetterinformourfundamentalunderstandingoftheprocess,aswellastoolsand
methodsusedtoproduceevaluatedfissiondatathatthenucleardatacommunityat
largecanusewithconfidence.Tyingacademicresearchtoengineeringapplications
was an important goal in writing this book. We certainly do not expect anyone to
read it from cover to cover. However, it is our sincere hope that theorists will be
attracted to experimental sections, that experimentalists will want to understand
how their data are being interpreted or compared to theoretical models, and that
physicistswilltakeakeeninterestinhowfundamentaldataareusedtoimpactthe
worldthroughtechnologies.
Chapter1treatsthevastandwidelystudiedtopicoffissioncrosssections.The
mostimportant,fortheirtechnologicalimpact,aretheneutron-inducedfissioncross
sections from thermal up to 20 MeV incident neutron energies. Higher incident
neutron energy reactions are only briefly mentioned and could be the topic of
1TheFIESTAschoollecturesandworkshopcontributionscanstillbefoundonlineathttps://t2.
lanl.gov/fiesta2014andhttps://t2.lanl.gov/fiesta2017.
Preface vii
an entire separate volume. Photo-induced fission reactions as well as charged-
particle transfer-induced-reactions provide a complementary tool to study cross
sections and constrain fission models that aim at a more comprehensive view of
theprocess.Insomecases,theycanalsoprobefissioningnucleibelowtheirfission
barrier,unreachablethroughthemorecommonneutron-inducedreactions.Atheory
based on the R-matrix formalism for fission is presented in detail. Simplifications
and approximations used in the data evaluation community are also discussed.
Recentdevelopmentsinfissioncrosssectionmeasurementssuchasthefissiontime
projectionchamberarereviewed.
Chapter 2 discusses fission fragments and fission products, their distributions
in mass and charge, and their characteristics in kinetic and excitation energies,
which in large part are responsible for many characteristics of the neutrons and
photonstheyemitatalaterstage.Manyfascinatingrecentexperimental,theoretical,
andcomputationaldevelopmentsarepresented.Thepresentstatusofsemiclassical
macroscopic-microscopic and purely microscopic theories is reviewed. Important
developments in the measurements of fission fragments have also taken place
recently and are presented in this chapter. Finally, a renewed interest in the
evaluation of fission product yields and their uncertainties has recently spun from
thedevelopmentofmodernphysicsmodelsandcodesthatcanonlynowattemptto
capturetheintricatecorrelationsamongpost-scissiondata.
Chapter 3 addresses the prompt and delayed emissions of neutron and γ rays
infission.Thelasttwodecadeshaveseenimportantdevelopmentsinthemodeling
andmeasurementofthoseparticlesandtheircorrelations,providinganincreasingly
consistent picture of all post-scission data. Important questions that challenge our
fundamentalunderstandingofthefissionprocessnearthescissionpointarerevealed
and informed through probing those complex correlations. They also offer the
prospecttohelpnewtechnologiesandsupportexistingones.
Chapter4concludesthebookbyprovidingexamplesofwherethefissionprocess
plays a particularly important role, namely nuclear reactors, nuclear security, and
astrophysics.Withtheannouncedrenaissanceofnuclearenergyandthedeployment
ofavarietyofinnovativenuclearreactors,ourcurrentknowledgeofnuclearfission
is being challenged to provide adequate evaluated data to support new safety
and efficiency features. Nuclear security and nonproliferation concerns have been
central to any discussion related to nuclear technologies since their inception.
Nuclearfissionisattheheartofthoseconcernsandafewexamplesareprovidedto
illustratethediversityofquestionsbeingaskedbythecommunityatlarge.Finally,
the fission process is being studied for its significant role in the formation of the
heaviest elements in the universe, possibly in the most cataclysmic astrophysical
eventsthatweknowof.
Throughoutthosechapters,thecrucialroleplayedbytheestimationofrealistic
uncertaintiesassociatedwithfissiondataisarecurringtheme.Beyondmeanvalues,
uncertaintiesneedtobeknownaccuratelyenoughtosimulatereactorsafetymargins
to licensing target accuracies, to distinguish between the existence of a sterile
neutrino and an unreasonably incorrect fission product yield, and to identify the
existence of a third well in the potential energy surface that describes the shapes
viii Preface
of a nucleus on its way to fission. While uncertainties have always played a role
in science, the more recent and ubiquitous growth of computer simulations in our
interpretationofphysicalphenomenamakesitevenmoreurgenttounderstandand
quantify sources of uncertainties, biases, and correlations that can often lead us
astrayonourpathtodiscovery.
We are not claiming to be exhaustive with this book. We do not think that
any book on fission could reasonably claim to be. This is a vast and expanding
field that remains extremely difficult to delineate fully. We hope however that we
will have covered enough material, provided a robust enough bibliography, and
instilledahumblesenseofaweforthecuriousreaderstofurtherexploretheirown
interrogationsandfollowtheirthoughtprocesses,wherevertheymaylead.
LosAlamos,NM,USA PatrickTalou
Livermore,CA,USA RamonaVogt
July3,2022
References
1. C.Wagemans(Ed.),TheNuclearFissionProcess(CRCPress,BocaRaton,1991)
2. A.N. Andreyev, K. Nishio, K.-H. Schmidt, Nuclear fission: a review of experi-
mentaladvancesandphenomenology.Rep.Prog.Phys.81,016301(2018)
3. M. Bender et al., Future of nuclear fission theory. J. Phys. G Nucl. Phys. 47,
113002(2020)
4. P.Talouetal.,Correlatedpromptfissiondataintransportsimulations.Eur.Phys.
J.A54,9(2018)
Contents
1 FissionCrossSections ....................................................... 1
J.EricLynn,LucasSnyder,andPatrickTalou
1.1 GeneralObservations................................................... 2
1.1.1 HistoricalNotes................................................. 2
1.1.2 SomeTerminology:Fissile,Fissionable,andFertile.......... 2
1.1.3 Low-EnergyFissionCrossSections........................... 3
1.1.4 Multi-ChanceFissionatHigherExcitationEnergies ......... 8
1.1.5 OtherEntranceChannels....................................... 9
1.1.6 FissionProductAngularDistributions......................... 12
1.1.7 ShapeIsomers................................................... 13
1.2 ExperimentalSetupsandData.......................................... 14
1.2.1 HowtoMeasureFissionCrossSections....................... 14
1.2.2 DetectorsforCrossSectionMeasurements ................... 16
1.2.3 FissionCrossSectionData..................................... 26
1.2.4 FissionFragmentAngularDistributionData.................. 28
1.2.5 Directvs.Transfer(Surrogate)FissionReactions ............ 29
1.3 TheoreticalInterpretation............................................... 30
1.3.1 CompoundNucleusReactionCrossSectionTheory.......... 30
1.3.2 TheFissionDecayModeandTransmissionCoefficient...... 38
1.3.3 R-MatrixTheoryIncorporatingFission ....................... 47
1.3.4 ShellEffectsintheFissionProcess............................ 54
1.3.5 AngularDistributionsofFissionProducts..................... 96
1.3.6 MoreComplexFissionBarriers................................ 109
1.3.7 SummaryofBarrierProperties................................. 118
1.4 Evaluations.............................................................. 118
1.4.1 FissionPathsandFissionBarriers............................. 118
1.4.2 TransitionStates ................................................ 122
1.4.3 TransmissionCoefficients...................................... 123
1.4.4 Multi-ChanceFission........................................... 125
1.4.5 EvaluatedFissionCrossSections.............................. 127
References..................................................................... 128
ix
x Contents
2 FissionFragmentsandFissionProducts.................................. 141
ToshihikoKawano,JørgenRandrup,NicolasSchunck,PatrickTalou,
andFredrikTovesson
2.1 GeneralObservations................................................... 142
2.1.1 BasicDefinitions................................................ 142
2.1.2 ExperimentalData.............................................. 143
2.2 Experiments............................................................. 158
2.2.1 TheDoubleKineticEnergy(2E)Method..................... 159
2.2.2 MassIdentificationBasedonTime-of-Flight ................. 160
2.2.3 MassSeparators................................................. 165
2.2.4 GammaSpectroscopyTechniques ............................. 167
2.2.5 InverseKinematics.............................................. 168
2.2.6 Gamma-RaySpectroscopyofFissionFragments............. 173
2.3 FissionYieldTheories.................................................. 174
2.3.1 FissionShapeDynamics ....................................... 177
2.3.2 MicroscopicApproachestoFission............................ 204
2.3.3 Summary........................................................ 226
2.4 EvaluationofFissionProductYields .................................. 229
2.4.1 EvaluationMethod.............................................. 229
2.4.2 EvaluationofExperimentalData .............................. 230
2.4.3 β DecaysofFissionProducts.................................. 232
2.4.4 FPYModels..................................................... 234
2.4.5 IsomericRatios ................................................. 241
2.4.6 EnergyDependenceofFPYs................................... 243
2.4.7 EnergyDependenceoftheDelayedNeutronYield........... 249
References..................................................................... 250
3 PromptandDelayedEmission ............................................. 263
Matthew Devlin, Alf Göök, Olivier Serot, Patrick Talou,
andRamonaVogt
3.1 GeneralObservations................................................... 264
3.1.1 TimeScalesinFission.......................................... 264
3.1.2 NeutronEmission............................................... 268
3.1.3 GammaEmission............................................... 283
3.1.4 Correlations..................................................... 295
3.2 ExperimentalMeasurements ........................................... 307
3.2.1 PromptNeutronMeasurements................................ 308
3.2.2 Promptγ-RayMeasurements.................................. 319
3.2.3 CorrelatedNeutron-Neutron,Neutron-LightFragment
andNeutron-GammaMeasurements........................... 326
3.3 TheoryandModelingofPromptEmission............................ 327
3.3.1 MechanismsofPromptNeutronEmission .................... 328
3.3.2 MechanismsofPromptGammaEmission..................... 336