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Neutron Physics
NUCLEARENGINEERING
Neutron Physics
Paul Reuss
Institutnationaldessciencesettechniquesnucléaires
17,avenueduHoggar
Parcd’activitésdeCourtabœuf,BP112
91944LesUlisCedexA,France
The author would like to thank Nova Traduction (K. Foster) and Chris Latham for the
translationofhisbook.
Cover illustrations: Jules Horowitz (1921-1995), a highly talented physicist, founded the French
schoolofneutronphysics.In2014,theJulesHorowitzreactorbeingbuiltatCadarachewillbecome
themainirradiationreactorintheworld(100MWth)forresearchonmaterialsandnuclearfuels.
In the background, the meshing for a neutron physics core calculation and in the foreground the
powerdistribution,resultofthiscalculation. (DocumentscourtesyofCEA.)
Coverconception:ThierryGourdin
PrintedinFrance
ISBN:978-2-7598-0041-4
Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis
concerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broad-
casting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of
thispublicationor parts thereof is onlypermitted under the provisionsof the French and German
Copyrightlaws of March 11, 1957and September 9, 1965, respectively. Violationsfall under the
prosecutionactoftheFrenchandGermanCopyrightLaws.
(cid:2)c EDPSciences2008
Introduction to the Nuclear
Engineering Collection
Within the French Atomic Energy Commission (CEA), the National Institute of Nuclear
ScienceandTechnology(INSTN)isahighereducationinstitutionoperatingunderthejoint
supervision of the Ministries of Education and Industry. The purpose of the INSTN is to
contributetodisseminatingtheCEA’sexpertisethroughspecialisedcoursesandcontinuing
education,notonlyonanationalscale,butacrossEuropeandworldwide.
Thismissionisfocusedonnuclearscienceandtechnology,andoneofitsmainfeatures
isaNuclearEngineeringdiploma. BolsteredbytheCEA’seffortstobuildpartnershipswith
universitiesandengineeringschools,theINSTNhasdevelopedlinkswithotherhighered-
ucationinstitutions,leadingtotheorganisationofmorethantwentyfivejointly-sponsored
Mastersgraduatediplomas. Therearealsocoursescoveringdisciplinesinthe healthsec-
tor: nuclearmedicine,radiopharmacy,andtrainingforhospitalphysicists.
Continuous educationisanotherimportantpartoftheINSTN’sactivitiesthatrelieson
theexpertisedevelopedwithintheCEAandbyitspartnersinindustry.
The Nuclear Engineering course (known as ’GA’, an abbreviation of its Frenchname)
was first taught in 1954 at the CEA Saclay site, where the first experimental piles were
built. It has also been taught since 1976 at Cadarache,wherefast neutron reactorswere
developed. GA has been taught since 1958 at the School for the Military Applications
of Atomic Energy (EAMEA), under the responsibility of the INSTN. Since its creation, the
INSTNhasawardeddiplomastoover4400engineerswhonowworkinmajorcompanies
or public-sector bodies in the French nuclear industry: CEA, EDF (the French electricity
board),AREVA,Cogema,MarineNationale(theFrenchnavy),IRSN(FrenchTSO)... Many
foreignstudentsfromavarietyofcountrieshavealsostudiedforthisdiploma.
Therearetwocategoriesofstudent: civilianandmilitary. Civilianstudentswillobtain
jobs in the design or operation of nuclear reactors for power plants or research estab-
lishments, or in fuel processing facilities. They can aim to become expert consultants,
analysing nuclear risks or assessing environmental impact. The EAMEA provides educa-
tionforcertainofficersassignedtoFrenchnuclearsubmarinesortheaircraftcarrier.
TheteachingfacultycomprisesCEAresearchscientists,expertsfromtheNuclearSafety
andRadiationProtectionInstitute(IRSN),andengineersworkinginindustry(EDF,AREVA,
etc.). The main subjects are: nuclear physics and neutron physics, thermal hydraulics,
nuclearmaterials,mechanics,radiologicalprotection,nuclearinstrumentation,operation
and safety of Pressurised Water Reactors (PWR), nuclear reactor systems, and the nu-
clear fuel cycle. These courses are taught over a six-month period, followed by a final
projectthatroundsoutthestudent’strainingbyapplyingittoanactualindustrialsituation.
vi NeutronPhysics
TheseprojectstakeplaceintheCEA’sresearchcentres,companiesinthenuclearindustry
(EDF,AREVA,etc.),andevenabroad(USA,Canada,UnitedKingdom,etc.). Akeyfeature
ofthisprogrammeistheemphasisonpracticalworkcarriedoutusingtheINSTNfacilities
(ISIStrainingreactor,PWRsimulators,radiochemistrylaboratories,etc.).
Evennow thatthenuclearindustry hasreachedfullmaturity,theNuclearEngineering
diploma is still unique in the Frencheducational system, and affirms its mission: to train
engineers who will have an in-depth, global vision of the science and the techniques
appliedineachphaseofthelifeofnuclearinstallationsfromtheirdesignandconstruction
totheiroperationand,finally,theirdismantling.
The INSTN has committed itself to publishing all the course materials in a collection
of books thatwillbecome valuabletools for students, and to publicise the contentsof its
coursesinFrenchandotherEuropeanhighereducationinstitutions. Thesebooksarepub-
lishedby EDPSciences,anexpertin the promotion ofscientific knowledge,andarealso
intended to be useful beyond the academic context as essential referencesfor engineers
andtechniciansintheindustrialsector.
The European Nuclear Education Network (ENEN) fully supported INSTN, one of it
foundermembers,inpublishingthisbook. ForENENthisbookconstitutesthefirstofase-
riesoftextbooksintendedforstudentsandyoungprofessionalsinEuropeandworldwide,
contributingtothecreationoftheEuropeanEducationalArea.
JosephSafieh
NuclearEngineeringCourseDirector
ENENPresident
Contents
Foreword ...................................................................... xxi
About the Author.............................................................xxiii
Part I Fundamentals of neutron physics
Chapter 1: Introduction: general facts about nuclear energy
1.1. Abriefhistory .......................................................... 3
1.1.1. Fermi’spile.................................................... 3
1.1.2. Theendofalongsearch... ..................................... 4
1.1.3. ... andthebeginningofagreatadventure ...................... 6
1.2. Principleofanuclearpowerplant....................................... 8
1.3. Fission ................................................................. 9
1.4. Principleofchainreactions.............................................. 10
1.5. Mainmoderatorsandcoolants;typesofreactor .......................... 11
1.6. Monitoringandcontrolofreactors....................................... 13
1.7. Nuclearfuelcycle ...................................................... 14
1.8. Nuclearsafetyandradiationprotection .................................. 16
1.9. Nuclearprogrammes: prospects ......................................... 17
Exercises
Chapter 2: Nuclear physics for neutron physicists
A.Structureofmatterandnuclearbindingenergy ............................... 26
2.1. Structureofmatter ...................................................... 26
2.1.1. Theclassicalatomicmodel..................................... 26
2.1.2. Elementsandisotopes ......................................... 26
2.1.3. Nuclidenotation .............................................. 27
2.1.4. Stableandunstablenuclei ..................................... 27
2.1.5. Patternofstablenuclei......................................... 28
viii NeutronPhysics
2.2. Nuclearbindingenergy ................................................. 29
2.2.1. Massdefectandnuclearbindingenergy ........................ 29
2.2.2. Nuclearunits.................................................. 30
2.2.3. Nuclearforces................................................. 30
2.2.4. Liquiddropmodel............................................. 31
2.2.5. Magicnumbersandthelayermodel............................ 32
2.2.6. Spinandparity ................................................ 32
2.2.7. Excitedlevelsofnuclei(isomericstates)......................... 33
2.2.8. Othernuclearmodels.......................................... 34
2.3. Principleofreleaseofnuclearenergy.................................... 34
2.3.1. Nuclearrecombination ........................................ 34
2.3.2. Reactionenergy ............................................... 35
2.3.3. Principleoffusionandfission .................................. 35
2.4.1. Regionsofinstability........................................... 38
2.4.2. Maintypesofradioactivity ..................................... 39
2.4.3. Lawofradioactivedecay....................................... 40
2.4.4. Examplesofradioactivedecay.................................. 42
2.4.5. Alphainstability ............................................... 43
2.4.6. Betainstability................................................. 44
2.4.7. Gammainstability ............................................. 45
2.4.8. Radioactiveseries.............................................. 45
2.4.9. Radioactiveseriesequations.................................... 45
2.5. Generalinformationaboutnuclearreactions............................. 47
2.5.1. Spontaneousreactionsandinducedreactions................... 47
2.5.2. Nuclearreactionexamples..................................... 47
2.5.3. Lawsofconservation........................................... 48
2.5.4. Cross-section .................................................. 48
2.5.5. Macroscopiccross-section ..................................... 50
2.6. Neutronreactions....................................................... 51
2.6.1. Generalremarks............................................... 51
2.6.2. Scatteringand“real”reactions ................................. 52
2.6.3. Mainreactionsinducedbyneutronsinreactors ................. 52
2.6.4. Partialcross-sectionsandadditivityofcross-sections............. 53
2.6.5. Neutroncross-sectioncurves................................... 54
2.7. Whyresonances? ....................................................... 57
2.7.1. Resonantcross-sections: Breit–Wignerlaw...................... 60
2.7.2. Resonantcross-sections: statisticalaspects ...................... 64
2.7.3. Cross-sectionsinthethermaldomain ........................... 65
2.8. Neutronsources ........................................................ 66
2.8.1. Spontaneoussources........................................... 66
2.8.2. Reactionsinducedbyradioactivity ............................. 67
2.8.3. Fusionreactions ............................................... 67
2.8.4. Spallationreactions............................................ 67
2.9. Spontaneousfissionandinducedfission ................................. 69
2.9.1. Thefissionbarrier.............................................. 69
2.9.2. Fission-relatedthresholds ...................................... 70
2.9.3. Parityeffect.................................................... 71
Contents ix
2.9.4. Quantumeffects: tunneleffectandanti-tunneleffect ............ 72
2.10. Fissionproducts ........................................................ 73
2.10.1. Neutrons...................................................... 73
2.10.2. Fissionfragments .............................................. 75
2.10.3. Energy ........................................................ 77
2.11. Measuringbasicneutronphysicsdata.................................... 78
2.11.1. Neutronsources............................................... 78
2.11.2. Detectionofneutrons.......................................... 79
2.11.3. Measurementoftotalcross-section ............................. 79
2.11.4. Measurement of partial cross-sections and number of neutrons
emittedperfission ............................................. 79
2.11.5. Integralmeasurements ......................................... 80
2.12. Evaluationandlibrariesofnucleardata .................................. 80
2.13. Processingofnucleardataforneutronphysicscodes ..................... 81
Exercises
Chapter 3: Introduction to neutron physics
3.1. Neutron–matterinteractions............................................. 97
3.1.1. Cross-sections(review)......................................... 97
3.1.2. Neutrondensity,neutronflux,reactionrate ..................... 98
3.1.3. Conceptofphaseflux.......................................... 99
3.1.4. Conceptofcurrent............................................. 100
3.1.5. Conceptofopacity ............................................ 101
3.1.6. TheBoltzmannequation: afirstapproximation.................. 102
3.2. Generalrepresentationofaneutronpopulation .......................... 104
3.2.1. Variablestointroduce.......................................... 104
3.2.2. Generalconceptofneutronflux................................ 104
3.2.3. Boltzmannequation ........................................... 104
3.2.4. ProbabilisticanddeterministicsolutionsoftheBoltzmann
equation ...................................................... 106
3.3. Neutronspectraandenergybalances.................................... 107
3.3.1. Fastneutronreactorsandthermalneutronreactors .............. 107
3.3.2. Neutronbalances: thefour-factorformulaandvariants .......... 108
Exercises
Chapter 4: Point kinetics
4.1. Kineticswithoutdelayedneutrons ....................................... 119
4.1.1. Firstapproach ................................................. 119
4.1.2. Chainreactionequations....................................... 120
4.1.3. Reactivity ..................................................... 121
4.2. Kineticswithdelayedneutrons .......................................... 121
4.2.1. Parametersofdelayedneutrons................................. 121
4.2.2. Qualitativeaspects............................................. 122
4.2.3. Chainreactionequations....................................... 123
