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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]. 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).

2 Itcanbethoughtofasvirtualpairproduc-tion inthe 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.[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].)}

3 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); uorescenceX-rayisemittedfromtheatom,with aphotonenergyequaltothedi erencebetweenthevacancy-siteinner-shelle nergylevelandenergyleveloftheparticularo utershellwhichhappenstosupplytheelectron to llthevacancy( uorescenceyield,!))

4 ,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:!+a+f=1(2)Experim entalandtheoretical 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].The eldpublishedKandL uorescenceX-rayintensitiescalculatedwith therelativisticHatree-Slatertheoryforele mentswithZ=5to104[14].

5 HisdataarecitedinaTableofIsotopesEighthE dition[13],butareslightlydi 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;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:Ratioofthebound-electronCompt onscatteringcrosssection, BDC[9],tothatforfreeelectrons, KNC, ,themotionoftheatomicelectronsaroundthea tomicnucleusgivesrisetoaDopplerbroadenin goftheapparentenergyoftheincidentphoton, resultinginacorrespondingbroadeningofthe Compton\modi edline"foragivende \Comptonpro le.

6 "AvailabledataonComptonpro leshavebeensurveyedbyHubbell,andareprese ntedinRef.[4].Ifoneisinterestedinthespec traldistributionofCompton-scatteredphoto ns,andnotjusttheintegratedcrosssection,N amitoetal.[19]havemadeitdramaticallyclea rbycomputingthescatteredspectrumwithandw ithoutincludingDopplerbroadeningintheEGS 4code[20], (KEK-PF)( ).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;Z)fromNelmsandOp penheim[21], ,Fe, (at1 MeVmorethanhalfthephotonsarescatteredbyl eethan5 ).

7 Atlowenergies,particularlyforhigh-Zmater ials, (degree)Photon Energy, MeV95%75%50%25% (degree)Photon Energy, MeV95%75%50%25% (degree)Photon Energy, MeV95%75%50%25%Figure8:Openinghalf-angle , ,ofconecontaining25%,50%,and95%,respecti vely,ofphotonsRayleighscatteredfromC,Fe, ectsLinearpolarizationisimportantinlow-e nergyphotontransport,becausephotonsareli nearlypolarizedinscattering;further, ,theKlein-Nishinaangulardistributionfunc tionpersteradianofsolidangle is[16]d KNCd =14r20 kk0 2 kk0+k0k 2+4cos2 :(12)Here, istheanglebetweentheincidentpolarization vector(~e0)andthescatteredpolarizationve ctor(~e).AccordingtoHeitler[22],twodirec tionsareconsideredfor~e, ~eeitherinthesameplaneas~e0(~ek)orperpen dicularto~e0(~e?). [23]d Td =r20cos2 :(13)Linearlypolarizedphotonscatteringfo rbothCompton-andRayleigh-scatteringhaveb eenimplementedtotheEGS4codebyNamitoetal[ 24].Thee [25], 40 keVExp HExp VEGS4 H DefaultEGS4 V DefaultCounts (/ )Energy Deposition (keV)ComtonRayleigh(a)10-610-510-410-310 -2323436384042Pb 40 keVExp HExp VEGS4 H LP+DBEGS4 V LP+DBCounts (/ )Energy Deposition (keV)(b)Figure9 ,respectively(k0=40keV, =90 ).

8 (a)isthecomparisonwiththeEGS4calculation withoutincludinglinearpolarizationandDop plerbroadeningand(b) ect,whichisthemostlikelyphotoninteractio nathighenergies,aphotondisappearsinthe eldofachargedparticle, +M2 !M3+M4+M5+Q,itcanbeshownfromtheconservat ionofenergyandmomentumthatthethresholden ergyforthereactioninlaboratorysystemisTl abth=Q2M2c2[Q 2(M1c2+M1c2)](14) ( +M !M+me+me+Q),M1=0;M2=M3=M;M4=M5=me;sothat Q= 2mec2( TCMth)(15)andTlabthh=2mec2(m2c2+Mc2)Mc2: (16)Thus; eldofanucleusofmassM(M me):Tlabth'2mec2Mc2(Mc2)=2mec2=1:022)MeV )(17) eldofanelectron(M=me):Tlabth=2mec2mec2(m ec2+mec2)=4mec2=2:044)MeV)(18)Thecrossse ction nforpairproductioninthe eldofanucleusvariesas n Z2:(19)Forlowphotonenergies, n(=NAuA n) ln(h ):(20)Forhighenergies[26], n 79X0;(21) ( nfor1000 MeV). eldofanucleus[27].MaterialX0(gcm 2)79X0(cm2g 1) n(cm2g 1)%Di , [22]. ( pair(E+)/ )(E++E-)E+/(E++E-)h =infinity 100050106 Figure10 +andE arethekineticenergyofapositronandanelect ron,respectively.

9 Pair(E+)dE+meansthedi erentialcrosssectionwhichproducesapositr onbetweenE+andE++dE+. =Z2r2e= , trip(triplet),inthe eldofoneoftheatomicelectronsvariesasZtim esthesquareoftheunitcharge,or trip Z;(22)andisofminorimportance, \triplet"crosssection,sincetheatomicelec troninvolvedinthisprocessisalsoejectedfr omtheatom,givingrisetotridentsignature,i ncludingthecreatedelectronandpositron, ,the\characteristic"anglebetweenthedirec tionofmotionofthephotonandone(ortheother )oftheelectrons( )isgivenby mec2h (inradian):(23)136 MassAttenuationCoe cientandEnergy-AbsorptionCoe cient, = Anarrowbeamofmonoenergeticphotonswithani ncidentintensityI0,penetratingalayerofma terialwithmassthicknessxanddensity ,emergeswithintensityI,givenbytheexponen tialattenuationlaw,I=I0=exp[ ( = )x]:(24)Thisequationcanberewrittenas = =x 1ln(I0=I);(25)fromwhich = canbeobtainedfrommeasuredvaluesofI0; = canbeobtained,particularlyinthecrystallo -graphicphotonenergy/wavelengthregime,ha vebeenexaminedandassessedbyCreaghandHubb ell[29,30]aspartoftheInternationalUniono fCrystallography(IUCr) = isde nedwiththetotalcrosssectionperatom, tot,whichisrelatedto = accordingto = = totNAuA:(26)Inthisequation,NAisAvogadro' snumber(6:022045 1023mol 1),uistheatomicmassunit(1/12ofthemassofa natomofnuclide12C), , tot= pe+ coh+ incoh+ pair+ trip+ ph:n:(27)Photonuclearabsorptioncancontri butedasmuchas5-10%tothetotalphotonintera ctioncrosssectioninafairlynarrowenergyre gion, cultiesdueto(a)theirregulardependenceofb oththemagnitudeandresonance-shapeofthecr osssectionasafunctionofbothZandA;(b)theg apsintheavailableinformation,muchofwhich isforseparatedisotopesortargetsotherwise di eringfromnaturalisotopemixtures;and(c)th elackoftheoreticalmodelsfor ph:n:comparabletothoseavailableforcalcul ationsoftheothercrosssectionsofinterest.

10 = withoutincludingphotonuclearabsorptionis calculatedaccordingto = =NAuA( pe+ coh+ incoh+ pair+ trip):(28) cient, en= Themassenergy-absorptioncoe cients, en= (cm2/gorm2=kg, isadensityofthemedium),isausefulparamete rincomputationsofenergydepositedinmedias ubjectedtophotonirradiation. en= canbedescribedmoreclearlythroughtheuseof anintermediatequantity,themassenergy-tra nsfercoe cient, tr= .Themassenergy-transfercoe cients, tr= ,whenmultipliedbythephotonenergy uence ( = h ,where isthephoton uenceandh isthephotonenergy), ned[28]asthesumofthekineticenergiesofall thoseprimarychargedparticlesreleasedbyun chargedparticles(herephotons) , tr= takesintoaccounttheescapeofsecondaryphot onradiationsproducedattheinitialphoton-a tominteractionsite,plus,byconvention,the quantaofradiationfromtheannihilationofpo sitrons(assumedtohavecometorest) , tr= isde nedas tr= =NAuA(fpe pe+finco incoh+fpair pair+ftrip trip):(29)Inthisexpression,coherentscatt eringhasbeenomittedbecauseofthenegligibl eenergytransferassociatedwithit,andthefa ctorfrepresentstheaveragefractionoftheph otonen-ergy,h 0, (X=h 0);(30)whereXistheaverageenergyof uorescenceradiationemittedperabsorbedpho ton,fincoh=1 (<h >+X)=h 0.