Mass attenuation coefficient质量衰减系数.docx
- 文档编号:9013505
- 上传时间:2023-05-16
- 格式:DOCX
- 页数:19
- 大小:58.65KB
Mass attenuation coefficient质量衰减系数.docx
《Mass attenuation coefficient质量衰减系数.docx》由会员分享,可在线阅读,更多相关《Mass attenuation coefficient质量衰减系数.docx(19页珍藏版)》请在冰点文库上搜索。
Massattenuationcoefficient质量衰减系数
TablesofX-RayMassAttenuationCoefficients
andMassEnergy-AbsorptionCoefficients
from1keVto20MeVforElements Z = 1 to 92
and48AdditionalSubstancesofDosimetricInterest*
J.H.Hubbell+ and S.M.Seltzer
RadiationandBiomolecularPhysicsDivision, PML, NIST
©1989,1990,1996copyrightbytheU.S.SecretaryofCommerceonbehalfoftheUnitedStatesofAmerica.Allrightsreserved.NISTreservestherighttochargeforthesedatainthefuture.
Abstract
Tablesandgraphsofthephotonmassattenuationcoefficient μ/ρ andthemassenergy-absorptioncoefficient μen/ρ arepresentedforalloftheelements Z = 1to92,andfor48 compoundsandmixturesofradiologicalinterest.Thetablescoverenergiesofthephoton(x-ray,gammaray,bremsstrahlung)from1 keVto20 MeV.The μ/ρ valuesaretakenfromthecurrentphotoninteractiondatabaseattheNationalInstituteofStandardsandTechnology,andthe μen/ρ valuesarebasedonthenewcalculationsbySeltzerdescribedinRadiationResearch 136, 147(1993).Thesetablesof μ/ρ and μen/ρreplaceandextendthetablesgivenbyHubbellintheInternationalJournalofAppliedRadiationandIsotopes 33, 1269(1982).
NoteonNISTX-rayAttenuationDatabases
TableofContents
1.Introduction
2.X-RayMassAttenuationCoefficients
Table1. Materialconstantsfor elementalmedia.
Table2. Materialconstantsandcompositionfor compoundsandmixtures.
Valuesofthemassattenuationcoefficientandthemassenergy-absorptioncoefficientasafunctionofphotonenergy,for:
Table3. [Data] elementalmedia.
Table4. [Data] compoundsandmixtures.
3.TheMassEnergy-AbsorptionCoefficient
4.Summary
5.References
X-RayMassAttenuationCoefficients
1.Introduction
Themassattenuationcoefficient, μ/ρ,andthemassenergy-absorptioncoefficient, μen/ρ,arebasicquantitiesusedincalculationsofthepenetrationandtheenergydepositionbyphotons(x-ray, γ-ray,bremsstrahlung)inbiological,shieldingandothermaterials.Thesecoefficientsaredefinedin ICRUReport 33 (1980)andarediscussedinSections 2and3ofthiswork.Theyhavebeentreatedinsomedetailelsewhere,forexamplebyBerger (1961), Allison (1961), Evans (1968), HubbellandBerger (1968), Hubbell (1969,1977,1982), StormandIsrael (1970), Carlsson (1971), RibberforsandCarlsson (1985), CunninghamandJohns (1980), JohnsandCunningham (1983), Higgins etal. (1992)andby Seltzer (1993).Compilationsofboth μen/ρand μ/ρ includethoseby Plechaty etal. (1978)andby Cullen etal. (1989).
Thepresentcompilationisanextensionoftherecentcalculationsof Seltzer (1993),andisintendedtoreplacethevaluesof μ/ρ and μen/ρ giveninHubbell (1982)whichhavebeenwidelyusedasreferencedatainradiationshieldinganddosimetrycomputations.ThepresenttablesdifferfromthoseinHubbell (1982)inthefollowingrespects:
1.Insteadofprovidingresultsforonly40selectedelementswithatomicnumbersspanning Z = 1to92,nowall92 elementsareincluded.
2.Insteadofusingacommonenergygridfrom1 keVto20 MeV,withoutphotoelectricabsorptionedges(K,L1,etc.),nowalledgeenergiesareincludedandidentified,andvaluesof μ/ρ and μen/ρ aregivenjustaboveandbeloweachedgetofacilitateaccurateinterpolation.
3.Somewhatdifferentvaluesfortheatomicphotoeffectcrosssectionhavebeenusedfor Z = 2to54.The1982compilationwasbasedontheapplicationofrenormalizationfactorsgivenby Scofield (1973)tohiscalculatedvaluesofthecrosssection.AlthoughScofield(1973)calculatedthecrosssectionsforall Z ≥ 2,hegaverenormalizationfactorsonlyfor2 ≤ Z ≤ 54.Anevaluationby Saloman etal. (1988)comparedtheScofieldtheoreticalvalueswiththemeasured-valuedatabase,andconcludedthatoverallagreementwasbetterwithoutthisrenormalization.Thepresentworkthereforeusesthe"un-renormalized" Scofield (1973)theoreticalvaluesofthephotoeffectcrosssectionforallelements Z ≥ 2.Theanalyticalresultsusedfor Z = 1arethesameasthoseusedinthe1982compilation.
4.Forcompoundsandmixtures,valuesfor μ/ρ canbeobtainedbysimpleadditivity,i.e.,combiningvaluesfortheelementsaccordingtotheirproportionsbyweight.Totheextentthatvaluesfor μen/ρ areaffectedbytheradiativelosses(bremsstrahlungproduction,annihilationinflight,etc.)sufferedduringthecourseofslowingdowninthemediumbytheelectronsandpositronsthathavebeensetinmotion,simpleadditivityisnolongeradequate.The1982compilationignoredsuchmatrixeffects(theytendtobesmallatphotonenergiesbelow20 MeV);inthepresenttablestheyhavebeentakenintoaccount.
Theseandotherrefinements,suchasamorecompletetreatmentoftheatomicshellvacancyandfluorescencecascades,arediscussedbrieflyinthesectionsthatfollow.Moredetailscanbefoundin Seltzer (1993).Asimilarversionofthesetables,withtextinJapanese,isgivenin SeltzerandHubbell (1995).
Abstract | Introduction | MassAtten.Coef. | MassEnergy-Absorp.Coef. | Summary | References
X-RayMassAttenuationCoefficients
2.TheMassAttenuationCoefficient, μ/ρ
Anarrowbeamofmonoenergeticphotonswithanincidentintensity Io,penetratingalayerofmaterialwithmassthickness x anddensity ρ,emergeswithintensity I givenbytheexponentialattenuationlaw
(eq1)
Equation
(1)canberewrittenas
(eq2)
fromwhich μ/ρ canbeobtainedfrommeasuredvaluesof Io, I and x.
Notethatthemassthicknessisdefinedasthemassperunitarea,andisobtainedbymultiplyingthethickness t bythedensity ρ,i.e., x = ρt.
Thevariousexperimentalarrangementsandtechniquesfromwhich μ/ρ canbeobtained,particularlyinthecrystallographicphotonenergy/wavelengthregime,haverecentlybeenexaminedandassessedby CreaghandHubbell (1987,1990)aspartoftheInternationalUnionofCrystallography(IUCr)X-RayAttenuationProject.Thishasledtonewtablesof μ/ρ inthe1992 InternationalTablesforCrystallography (CreaghandHubbell, 1992).Thecurrentstatusof μ/ρ measurementshasalsobeenreviewedrecentlyby Gerward (1993),andanupdatedbibliographyofmeasureddataisavailablein Hubbell(1994).
Presenttabulationsof μ/ρ relyheavilyontheoreticalvaluesforthetotalcrosssectionperatom, σtot,whichisrelatedto μ/ρ accordingto
(eq3)
In(eq 3), u (= 1.660 540 2 × 10-24 g CohenandTaylor1986)istheatomicmassunit(1/12ofthemassofanatomofthenuclide 12C), A istherelativeatomicmassofthetargetelement,and σtot isthetotalcrosssectionforaninteractionbythephoton,frequentlygiveninunitsofb/atom(barns/atom),whereb = 10-24 cm2.
Theattenuationcoefficient,photoninteractioncrosssectionsandrelatedquantitiesarefunctionsofthephotonenergy.Explicitindicationofthisfunctionaldependencehasbeenomittedtoimprovereadability.
Thetotalcrosssectioncanbewrittenasthesumovercontributionsfromtheprincipalphotoninteractions,
(eq4)
where σpe istheatomicphotoeffectcrosssection, σcoh and σincoh arethecoherent(Rayleigh)andtheincoherent(Compton)scatteringcrosssections,respectively, σpair and σtrip arethecrosssectionsforelectron-positronproductioninthefieldsofthenucleusandoftheatomicelectrons,respectively,and σph.n. isthephotonuclearcrosssection.
Photonuclearabsorptionofthephotonbytheatomicnucleusresultsmostusuallyintheejectionofoneormoreneutronsand/orprotons.Thisinteractioncancontributeasmuchas5 %to10 %tothetotalphotoninteractioncrosssectioninafairlynarrowenergyregionusuallyoccurringsomewherebetween5 MeVand40 MeV,dependingonwherethegiantresonanceofthetargetnuclidefalls(see,e.g., Hayward, 1970; FullerandHayward,1976;and DietrichandBerman, 1988;alsotheillustrativetablesin Hubbell, 1969,1982).Theeffectsofthisinteractioncanbeobservedinmeasurementsofthetotalattenuationcoefficient(see,e.g., GimmandHubbell, 1978).However,thiscrosssectionhasnotbeenincludedinprevioustabulationsbecauseofthedifficultiesdueto(a) theirregulardependenceofboththemagnitudeandresonance-shapeofthecrosssectionasafunctionofboth Z and A;(b) thegapsintheavailableinformation,muchofwhichisforseparatedisotopesortargetsotherwisedifferingfromnaturalisotopicmixtures;and(c) thelackoftheoreticalmodelsfor σph.n. comparabletothoseavailableforcalculationsoftheothercrosssectionsofinterest.Thepracticeofomittingthecontributionofthephotonuclearcrosssectionintablesofthemassattenuationcoefficienthasbeencontinuedinthiswork,alongwiththeneglectofotherless-probablephoton-atominteractions,suchasnuclear-resonancescatteringandDelbrückscattering.
Ourresultsfortheelementsaregivenin Table 3 forelements Z = 1to92andphotonenergies1 keVto20 MeV,andhavebeencalculatedaccordingto
(eq 5)
Valuesfortherelativeatomicmass A ofthetargetelementsweretakenfrom Martin (1988)andcanbeextractedfromthevaluesof Z/A givenin Table 1;valuesfortheindividualcontributingcrosssectionsarethosefoundinthecurrentNISTdatabase(see BergerandHubbell, 1987),asoutlinedbelow.
Atomicphotoeffect.Forphotonenergiesfrom1 keVto1.5 MeV,valuesofthephotoelectriccrosssection, σpe,arethosecalculatedby Scofield (1973),basedonhissolutionoftheDiracequationfortheorbitalelectronsmovinginastaticHartree-Slatercentralpotential.NorenormalizationwasperformedusingthosefactorsgivenbyScofieldfortheelementswith Z = 2to54toconverttovaluesexpectedfromarelativisticHartree-Fockmodel.Thisrepresentsabreakwiththepracti
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- Mass attenuation coefficient质量衰减系数 coefficient 质量 衰减系数