KEK

1 ,HighEnergyAcceleratorResearchOrganizati on,1-1,Oho,Tsukuba,Ibaraki,305-0801 JapanAbstractThisisthelecturenoteusedatt he\TutorialsforElectron/GammaMonteCarlo: buildingblocksandapplications"aspartofth eInternationalConferenceontheMonteCarlo2 000,AdvancedMonteCarloonRadiationPhysics ,ParticleTransportSimulationandApplicati ons(MonteCarlo2000)heldatLisbonPortugal, 23-26 October, ,absorption,andpairproductionthatarenece ssaryforphotontransportcalculations, [1,2,3,4,5,6]inthis cationofInteractionTheinteractionofphoto nswithmattermaybeclassi , ,electrons,atoms,ornuclei,withwhichtheph otonsinteract, , ,scattering,absorption,pairproduction,et c:, [7]Asanexample, [8].

2 Ect, pe, , C, ,( pair+ trip).Rayleighscattering, R,isusuallyofminorimportanceforthebroadb eamconditionstypi-callyfoundinshielding, butmustbeknownfortheinteractionofattenua tioncoe ect, ph:n,ismostlyrestrictedtotheregionoftheg iantresonancearound10to30 MeVwhere,attheresonancepeak,itmayamountt oasmuchas10percentofthetotal\electronic" ,inelasticnuclearscatteringandDelbr , , eldofanucleusiscalledDelbr uckscattering(alsocallednuclearpotential scattering).Itcanbethoughtofasvirtualpai rproduc-tioninthe eldofthenucleus{thatis, 1000 104105Cu (barn/atom) (10-24cm2)Photon Energy (MeV)TotalPhotoelectricEffectRayleighsca tteringPair production(nucleus)ComptonPair production(electron)( ,n)Quasi-deutrondisintegrationPionproduc tionFigure1:CrosssectionofCuforphotonsbe tween10keVand100 GeV.}

3 [8]. (Coherent)(Incoherent)with:AtomicPhotoel ectricRayleighComptonelectronse ectscatteringscattering pe( Z4(L:E:) Z5(H:E:) R Z2(L:E:) C ZNucleusPhotonuclearElasticInelasticreac tionsnuclearnuclear( ,n),( ,p),scatteringscatteringphoto ssion,etc.( ; ) Z2( ; 0) ph:n: Z(h 10 MeV)Electric eldElectron-positronDelbr ucksurroundingpairproductioninscattering charged eldofnucleus,particles pair Z2(h 1:02 MeV)Electron-positronpairproductioninele ctron eld, trip Z2(h 2:04 MeV)Nucleon-antinucleonpairproduction(h 3 GeV)MesonsPhotomesonModi edproduction,( ; )(h 150 MeV)3 PhotoelectricE ectStudiesrelatedtothephotoelectrice ectarereviewedhistoricallybyHubbellinNSR DS-NBS29[1].)

4 Intheatomicphotoe ect, , ,andarethemostimportantcontributionstoth eatomicphotoe ,ifthephotonenergydropsbelowthebindingen ergyofagivenshell, ,particularlyformedium-andhigh-Zelements ,aplotof peversusthephotonenergyexhibitsthecharac teristicsawtoothabsorptionedges, ,whichshowsthetotalphotoelectriccrosssec tion, pe,forAgtogetherwithsubshellones[9].3101 102103104105106110100 AgTotalKL1L2L3M Photoelectric cross section (barn/atom)Photon Energy (keV)K-edgeL1-edgeL2-edgeL3-edgeFigure2: Totalandpartialatomicphotoe ectofAg.[9].Theorderofmagnitudeofthephot oelectricatomic-absorptioncrosssectionis pe( Z4=(h )3lowenergy Z5=h highenergy:(1)Dramaticresonancestructure softheorderof10% ,chemicalbindingandothervariableatomicen vironments,thisextendedX-rayabsorption nestructure(EXAFS) ,EXAFS canbeamajoranalyticaltoolinX-raydi ectAvacancycreatedbytheejectionofanelect ronfromaninnershellsis lledbyanouterelectronfallingintoit(de-ex citation).)

5 UorescenceX-rayisemittedfromtheatom,with aphotonenergyequaltothedi erencebetweenthevacancy-siteinner-shelle nergylevelandenergyleveloftheparticularo utershellwhichhappenstosupplytheelectron to llthevacancy( uorescenceyield,!,isthefractionof uorescenceX-rayemission). (Augeryield,a,isthefractionofAugeremissi on). lledbyanelectroninahighersubshell, ,anewvacancyiscreated,inwhichis lledbyoneofthemodes(Coster-Kronigyield,f ,isthefractionofCoster-Kronig).4 Thesumof uorescenceyield,!,Augeryield,a,andCoster -Kronigyield,f,isunity:!

6 +a+f=1(2)Experimentalandtheoretical uorescence-yieldinformationhavebeenrevie wedbyFinketal.[10],Bambyneketal.[11],Kra use[12]andHubbell[2].Theyieldsof uorescence,AugerelectronsandCoster-Kroni gaftertheK-,L1-,L2-orL3-photoelectrice ect[13] 20406080100K-FluorescenceK-AugerYieldsAt omic Number, 20406080100L1-FluorescenceL2-L1 Coster-KronigL3-L1 Coster-KronigL1 AugerYieldsAtomic Number, 20406080100L2 FluorescenceL3-L2 Coster-KronigL2 AugerYieldsAtomic Number, 20406080100L3 FluorescenceL3 AugerYieldsAtomic Number, ZFigure3:Yieldsof uorescence,AugerelectronsandCoster-Kroni gaftertheK-,L1-,L2-orL3-photoelectrice ect[13].

7 The eldpublishedKandL uorescenceX-rayintensitiescalculatedwith therelativisticHatree-Slatertheoryforele mentswithZ=5to104[14].Hisdataarecitedina TableofIsotopesEighthEdition[13],butares lightlydi erentwiththeexperimentalresults,aspresen tedbySalemetal[15]. ,Klein-NishinaFormulaInComptonscattering ,aphotoncollideswithanelectron,losessome ofitsenergyandisde ectedfromitsoriginaldirectionoftravel( ).Thebasictheoryofthise ect,assumingtheelectrontobeinitiallyfree andatrest,isthatofKleinandNishina[16].h 0 YXOEh Figure4 :h =h 01+ h 0mec2 (1 cos );(3)E=h 0 h =mec22(h 0)2cos2 (h 0+mec2)2 (h 0)2cos2 ;(4)tan =11+ h 0mec2 cot 2;(5)whereh 0istheenergyofincidentphoton,h istheenergyofscatteredphoton,Eistheenerg yofrecoilelectron,meistherestmassofanele ctron, ,theKlein-Nishinaangulardistributionfunc tionpersteradianofsolidangle isd KNcd ( )=r201+cos2 21[1+h (1 cos )]2(1+h 2(1 cos )2(1+cos2 )[1+h (1 cos )])=12r20 kk0 2 kk0+k0k sin2 (cm2sr 1electron 1);(6)k0=h 0mec2.

8 K=h C/d , :Di erentialcrosssectionofComptonscattering( original gurefrom[17]). , KNC=2 r20 1+kk2 2(1+k)1+2k ln(1+2k)k +ln(1+2k)2k 1+3k(1+2k)2 (cm2electron 1):(7) ,whichisagoodapproximationforphotonsofth eorderof1 MeVorhigher, [18],takingaccountnotonlyoftheK-shell, ,theso-called\incoherentscatteringfuncti on",S(q;X),tothedi erentialKlein-Nishinaformula,d BDCd ( )=S(q;Z)d KNC( )d :(8)Themomentumtransfer,q,isrelatedtothe photonenergiesandde ectionangle, ,accordingtoq=qk20+k2 2k0kcos ;(9)whereqisinmec2unitsandk0andkaretheph otonenergies(inmec2units)beforeandafterd e [3,4]andarepresentedforallelementsZ=1to1 00, BDCto KNCforphotonenergiesof1,10, 20406080100 CBD/ CKNA tomic Number, Z100 keV10 keV1 keVFigure6.

9 Ratioofthebound-electronComptonscatterin gcrosssection, BDC[9],tothatforfreeelectrons, KNC, ,themotionoftheatomicelectronsaroundthea tomicnucleusgivesrisetoaDopplerbroadenin goftheapparentenergyoftheincidentphoton, resultinginacorrespondingbroadeningofthe Compton\modi edline"foragivende \Comptonpro le."AvailabledataonComptonpro leshavebeensurveyedbyHubbell,andareprese ntedinRef.[4].Ifoneisinterestedinthespec traldistributionofCompton-scatteredphoto ns,andnotjusttheintegratedcrosssection,N amitoetal.[19]havemadeitdramaticallyclea rbycomputingthescatteredspectrumwithandw ithoutincludingDopplerbroadeningintheEGS 4code[20], (KEK-PF)( ).

10 810-610-510-410-310-2303234363840 MeasurementEGS4(CP)EGS4(S)Photons keV-1 per sourcePhoton Energy, keVC(a)10-610-510-410-310-2303234363840 MeasurementEGS4(CP)EGS4(S)Photons keV-1 per sourcePhoton Energy, keVCu(b)Figure7 ,respectively(k0=40keV, =90 ).TheEGS4calculationincludingDopplerbroa deningisshownasEGS4(CP).TheEGS4calculati onwithoutDopplerbroadeningisshownasEGS4( S). erentpartsoftheatomicchargedistributioni sthus\coherent," ,thereareinterferencee ,inthesameregionwhereelectronbindinge ectsin , \atomicformfactor",F(q;Z),basedontheThom as-Fermi,Hartree, ,[F(q;Z)]2,istheprobabilitythattheZelect ronsofanatomtakeuptherecoilmomentum,q, ,sinceitisassumedthatk0 k=0:q=2ksin 2:(10)Thedi erentialRayleighscatteringcrosssectionfo runpolarizedphotonsis Rd ( )=r202(1+cos2 )[F(q;Z)]2(cm2sr 1atom 1):(11)Thecumulativeangulardistributions of R,basedonthevaluesofF(q.)