Mass attenuation coefficient(质量衰减系数)

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1、Tables of X-Ray Mass Attenuation Coefficientsand Mass Energy-Absorption Coefficientsfrom 1 keV to 20 MeV forElements Z = 1 to 92and 48 Additional Substances of Do si metricInterest*J. H. Hubbell+ and S. M. SeltzerRadiati on and Biomolecular Physics Divisio n, PML, NIST 1989, 1990, 1996 copyright by

2、the U.S. Secretary of Commerce on behalf of the United States of America. All rights reserved. NIST reserves the right to charge for these data in the future.Abst ractu/pTables and gr aphs of the photon mass attenuation coefficient and the massu /pene rgy-abs or ption coefficient enare pr esented fo

3、r all of the elements Z = 1 to 92, andfor 48 compounds and mixt ures of r adiological inte rest. The tables cove r ene rgies of theu/pphoton (x-r ay, gamma r ay, br emsst rahlung) from 1 keV to 20 MeV. The values aretaken from the cur rent photon inte raction database at the National Institute of St

4、anda rds and the tables given by Hubbell in the Intenational Jour nal of Applied Radiation and Isotopes 33, 1269 (1982).Technology, and theu /penvalues are based on the new calculations by Seltzer described inRadiation Resea rch 136, 147 (1993). These tables ofandu /penr eplace and extendNote on NIS

5、T X-ray Attenuation DatabasesTable of Contents2. X-Ray Mass Attenuation CoefficientsTable 1. Mate rial constants for elemental media Table 2. Mate rial constants and composition for compounds and mixtures.Values of the mass attenuation coefficient and the mass ene rgy-abs or ption coefficient as a f

6、unction of photon ene rgy, for:Table 3. Data elemental mediaTable 4. Data compounds and mixtures3. The Mass Ene rgy-Abs or ption Coefficient4. Summa ry5. Refe rencesX-Ray Mass Attenuation Coefficients1. IntroductionThe mass attenuation coefficient, y/p, and the mass energy-absorption coefficient, “

7、Ip, are basic quantities used in calculations of the penetration and the energy deposition by photons (x-ray, y-ray, bremsstrahlung) in biological, shielding and other materials. These coefficients are defined in ICRU Report 33 (1980) and are discussed in Sections 2 and 3 of this work. They have bee

8、n treated in some detail elsewhere, for example byBerger (1961), Allison (1961), Evans (1968), Hubbell andBerger (1968), Hubbell (1969, 1977, 1982), Storm andIsrael (1970), Carlsson (1971), Ribberfors and Carlsson (1985), Cunningham and Johns (1980), Johns and Cunningham (1983), Higgins et al. (1992

9、) and by Seltzer (1993). Compilations of both“ /pand y/p include those by Plechaty et al. (1978) and by Cullen et al. (1989).The present compilation is an extension of the recent calculations of Seltzer (1993), and is intended to replace the values ofy/p and y /p givenen inHubbell (1982) which have

10、been widely used as reference data in radiation shielding and dosimetry computations. The present tables differ from those inHubbell (1982) in the following respects:1. Instead of providing results for only 40 selected elements with atomic numbers spanning Z = 1 to 92, now all 92 elements are includ

11、ed.2. Instead of using a common energy grid from 1 keV to 20 MeV, without photoelectric absorption edges (K, L1, etc.), now all edge energies are included and identified, and values of y/p and y /p areen given just above and below each edge to facilitate accurate interpolation.3. Somewhat different

12、values for the atomic photoeffect cross section have been used for Z = 2 to 54. The 1982 compilation was based on the application of renormalization factors given by Scofield (1973) to his calculated values of the cross section. Although Scofield (1973) calculated the cross sections for all Z 2, he

13、gave renormalization factors only for 2 Z 2. The analytical results used for Z = 1 are the same as those used in the 1982 compilation.4. For compounds and mixtures, values for卩/p can be obtained by simple additivity, i.e., combining values for the elements according to their proportions by weight. T

14、o the extent that values for “ /p are affected by the radiative losses (bremsstrahlung production, annihilation in flight, etc.) suffered during the course of slowing down in the medium by the electrons and positrons that have been set in motion, simple additivity is no longer adequate. The 1982 com

15、pilation ignored such matrix effects (they tend to be small at photon energies below 20 MeV); in the present tables they have been taken into account.These and other refinements, such as a more complete treatment of the atomic shell vacancy and fluorescence cascades, are discussed briefly in the sec

16、tions that follow. More details can be found in Seltzer (1993). A similar version of these tables, with text in Japanese, is given in Seltzer and Hubbell (1995).Abstract I Introduction I Mass Atten. Coef. I Mass Energy-Absorp.Coef. I Summary I ReferencesX-Ray Mass Attenuation Coefficients2. The Mass

17、 Attenuation Coefficient,A narrow beam of monoenergetic photons with an incident intensity I, penetrating a layer of material with mass thickness x and density p, emerges with intensity I given by the exponential attenuation law(eq 1)(eq 2)Equation (1) can be rewritten as/Vp = 山仏“)from which 卩/p can

18、 be obtained from measured values of I。, I and x.Note that the mass thickness is defined as the mass per unit area, and is obtained by multiplying the thickness t by the density p, i.e., x = pt.The various experimental arrangements and techniques from which卩/p can be obtained, particularly in the cr

19、ystallographic photon energy/wavelength regime, have recently been examined and assessed by Creagh and Hubbell (1987, 1990) as part of the International Union of Crystallography (IUCr) X-Ray Attenuation Project. This has led to new tables of卩/p in the 1992 International Tables for Crystallography (C

20、reagh and Hubbell, 1992). The current status of 卩/p measurements has also been reviewed recently by Gerward (1993), and an updated bibliography of measured data is available in Hubbell(1994).Present tabulations of 卩/p rely heavily on theoretical values for the total cross section per atom,which is r

21、elated to 卩/p according to门打-=-r . i (eq 3)In (eq 3), u (= 1.660 540 2 x 10-24 g Cohen and Taylor 1986) is the atomic mass unit (1/12 of the mass of an atom of the nuclide 12C), A is the relative atomic mass of the target element, and is the total cross section for an interaction by the photon, freq

22、uently given in units of b/atom (barns/atom), where b = 10-24 cm2.The attenuation coefficient, photon interaction cross sections and related quantities are functions of the photon energy. Explicit indication of this functional dependence has been omitted to improve readability.The total cross sectio

23、n can be written as the sum over contributions from the principal photon interactions,小弋八 i： _i. _ 八 i： _ 八- _ 2 i. .(eq 4)where o is the atomic photoeffect cross section, o , and a . are the coherent (Rayleigh) and the incoherent (Compton) scattering cross sections, respectively, o . and o . are th

24、e cross sections for electron-positronpairtripproduction in the fields of the nucleus and of the atomic electrons, respectively, and oph n is the photonuclear cross section.Photonuclear absorption of the photon by the atomic nucleus results most usually in the ejection of one or more neutrons and/or

25、 protons. This interaction can contribute as much as 5 % to 10 % to the total photon interaction cross section in a fairly narrow energy region usually occurring somewhere between 5 MeV and 40 MeV, depending on where the giant resonance of the target nuclide falls (see, e.g., Hayward, 1970; Fuller a

26、nd Hayward,1976; and Dietrich and Berman, 1988; also the illustrative tables in Hubbell, 1969, 1982). The effects of this interaction can be observed in measurements of the total attenuation coefficient (see, e.g.,Gimm and Hubbell, 1978). However, this cross section has not been included in previous

27、 tabulations because of the difficulties due to (a) the irregular dependence of both the magnitude and resonance-shape of the cross section as a function of both Z and A; (b) the gaps in the available information, much of which is for separated isotopes or targets otherwise differing from natural is

28、otopic mixtures; and (c) the lack of theoretical modelscomparable to those available for calculations of the other crosssections of interest. The practice of omitting the contribution of the photonuclear cross section in tables of the mass attenuation coefficient has been continued in this work, alo

29、ng with the neglect of other less-probable photon-atom interactions, such as nuclear-resonance scattering and Delbruck scattering.Our results for the elements are given in Table 3 for elements Z = 1 to 92 and photon energies 1 keV to 20 MeV, and have been calculated according to:= 1 _ i _ 1 . -(eq 5

30、)Values for the relative atomic mass A of the target elements were taken from Martin (1988) and can be extracted from the values of Z/A given in Table 1;values for the individual contributing cross sections are those found in the current NIST database (see Berger and Hubbell, 1987), as outlined belo

31、w.Atomic photoeffect. For photon energies from 1 keV to 1.5 MeV, values of the photoelectric cross section, o , are those calculated by Scofield (1973), pebased on his solution of the Dirac equation for the orbital electrons moving in a static Hartree-Slater central potential. No renormalization was

32、 performed using those factors given by Scofield for the elements with Z = 2 to 54 to convert to values expected from a relativistic Hartree-Fock model. This represents a break with the practice by Hubbell (1977, 1982) and Hubbell et al. (1980) in which this renormalization had been done.Absorption-

33、edge fine structure can be experimentally observed using continuum-energy photon sources and high-resolution detectors (see, e.g., Faessler,1955; Deslattes, 1969; Hubbell et al., 1974; Lytle et al., 1984; and Del Grande, 1986, 1990), and the observed variations are subject to chemical, phase and oth

34、er environmental effects, such as temperature (Lytle, 1963). As has been done in the past, this fine structure is ignored in the present compilation. The cross sections in the vicinity of absorption edges are instead assumed to have simple sawtooth shapes. Values at the edge have been obtained by ex

35、trapolation of the near-edge subshell cross sections of Scofield (1973) to the threshold edge energies given by Bearden and Burr (1967), according to the same procedure used by Berger and Hubbell (1987) to prepare the NIST database. The interpolation procedures used for the present tables are slight

36、ly different from those used by Berger and Hubbell; here we use a cubic Hermite interpolant for the individual subshell cross sections rather than a cubic spline for the total photoeffect cross section, which results in occasional small differences in the vicinity of M- and N-shell edges of high-Z e

37、lements.Scofields (1973) photoeffect calculations were limited to photon energies of 1.5 MeV and below. His data were extended to higher energies (where the photoelectric cross section is quite small) by connecting them to the high-energy asymptotic values of Pratt (1960) through use of a semi-empir

38、ical formula (Hubbell, 1969).Coherent and incoherent scattering. Values for the coherent (Rayleigh) scattering cross section,零。彳 are taken from Hubbell and 0verb0 (1979). These were calculated by numerical integration of the Thomson (1906) formula weighted by F2(q,Z), where F(q,Z) is the relativisti

39、c Hartree-Fock atomic form factor and q is the momentum transfer. The compilation of F(q,Z) by Hubbell and 0verb0 was based on piecing together, over the different ranges of q andZ, values given by Pirenne (1946) for Z = 1, and those of Doyle and Turner (1968), Cromer and Waber (1974) and 0verb0 (19

40、77, 1978) for the other elements.Values for the incoherent (Compton) scattering cross section, qncoh，are from Hubbell et al. (1975), obtained from numerical integration of the Klein-Nishina (1929) differential formula weighted by the incoherent scattering function S(q,Z). For their compilation of S(

41、q,Z), Hubbell et al. (1975) pieced together results given by Pirenne (1946) (Z = 1), Brown (1970a, 1970b, 1971, 1972, 1974) (Z = 2 to 6, with configuration interaction) and by Cromer and Mann (1967) and Cromer (1969) (Z = 7 to 100, from a non-relativistic Hartree-Fock model). Radiative and double-Co

42、mpton corrections from Mork (1971) were applied to the integrated values forElectron-positron pair and triplet production cross sections. Cross sections for the production of electron-positron pairs (e-, e+) in the field of the atomic nucleus, o ., and for the production of triplets (2e-, e+) in the

43、 field of the atomic electrons, o . , are taken from the compilation ofHubbell et al. (1980). Their synthesis combined the use of formulas from Bethe-Heitler theory with various other theoretical models to take into account screening, Coulomb, and radiative corrections. Different combinations were u

44、sed in the near-threshold, intermediate and high-energy regions to obtain the best possible agreement with experimental cross sections (Gimm and Hubbell, 1978).Mixtures and compounds. Values of the mass attenuation coefficient, yip, for the 48 mixtures and compounds (assumed homogeneous) are given i

45、n Table 4,and were obtained according to simple additivity:(eq 6)where w. is the fraction by weight of the ith atomic constituent, and the (y/p). values are from Table 3. The assumed fractions by weight are given inTable 2. To obtain (yip), values at all the absorption edges of all constituent eleme

46、nts, interpolation has been performed separately for the cross sections indicated in (eq 5), including the photoeffect cross sections for the individual atomic subshells.Abstract I Introduction I Mass Atten. Coef. I Mass Energy-Absorp.Coef. I Summary I References3. The Mass EnerX-Ray Mass Attenuatio

47、n Coefficients-Absorption Coefficient, ppThe methods used to calculate the mass energy-absorption coefficient,y Ip, are described perhaps more clearly through the use of an intermediate quantity, the mass energy-transfer coefficient, yjp.The mass energy-transfer coefficient, yjp, when multiplied by

48、the photon energy fluence 屮(肖=E, where is the photon fluence and E the photon energy), gives the dosimetric quantity kerma. As discussed in depth by Carlsson (1985), kerma has been defined (ICRU Report 33, 1980) as (and is an acronym for) the sum of the kinetic energies of all those primary charged

49、particles released by uncharged particles (here photons) per unit mass. Thustr/p takes into account the escape only of secondary photon radiations produced at the initial photon-atom interaction site, plus, by convention, the quanta of radiation from the annihilation of positrons (assumed to have co

50、me to rest) originating in the initial pair- and triplet-production interactions.Hence yjp is defined as他r/卩=(+ /incdh-inccih +pair + 仇山卩丹川“/且且- (eq 7)In (eq 7), coherent scattering has been omitted because of the negligible energy transfer associated with it, and the factors f represent the average

51、 fractions of the photon energy E that is transferred to kinetic energy of charged particles in the remaining types of interactions. These energy-transfer fractions are given by(eq 8)where X is the average energy of fluorescence radiation (characteristic x rays) emitted per absorbed photon;上二 l - I

52、： 一 丿一.(eq 9)where 人- is the average energy of the Compton-scattered photon;(eq 10)where me2 is the rest energy of the electron; and(eq 11)The fluorescence energy X in (eq 8), (eq 9), and ( 11) depends on the distribution of atomic-electron vacancies produced in the process under consideration and i

53、s in general evaluated differently for photoelectric absorption, incoherent scattering, and triplet production. Moreover, X isassumed to include the emission of cascade fluorescence x rays associated with the complete atomic relaxation process initiated by the primary vacancy, the significance of wh

54、ich has been pointed out by Carlsson (1971).(eq 12)As only the characteristics of the target atom are involved in calculating yjp, the mass energy-transfer coefficient for homogeneous mixtures and compounds can be obtained in a manner analogous to that for Mp:The mass energy-absorption coefficient i

55、nvolves the further emission of radiation produced by the charged particles in traveling through the medium, and is defined as:- 二 | I 1(eq 13)The factor g in (eq. 13) represents the average fraction of the kinetic energy of secondary charged particles (produced in all the types of interactions) tha

56、t is subsequently lost in radiative (photon-emitting) energy-loss processes as the particles slow to rest in the medium. The evaluation of g is accomplished by integrating the cross section for the radiative process of interest over the differential tracklength distribution established by the partic

57、les in the course of slowing down. In the continuous-slowing-down approximation, the tracklength distribution is replaced by the reciprocal of the electron or positron total stopping power of the medium. Even assuming Bragg additivity for the stopping power (that now appears in the denominator of th

58、e integral), simple additivity form /p or - as suggested by Attix (1984)- for g is formally incorrect. When the numerical values ofg are relatively small, the errors in m /p incurred by using simple additivity schemes are usually small, a consequence partially mitigating the use additivity, particul

59、arly for photon energies below 20 MeV. However, additivity has not been used in the present work.For the values of m /p given in Table 3 and Table 4, the evaluation of g takes into explicit account (a) the emission of bremsstrahlung, (b) positron annihilation in flight, (c) fluorescence emission as

60、a result of electron- and positron-impact ionization, and (d) the effects on these processes of energy-loss straggling and knock-on electron production as the secondary particles slow down (i.e., of going beyond the continuous-slowing-down approximation). This scheme thus goes beyond that of ICRU Re

61、port 33 (1980) which, perhaps by oversight, formally includes only (a) above, and of previous work, which usually includes (a) and (b).For the calculation of g, the radiative (bremsstrahlung) stopping powers used are based on the results by Seltzer and Berger (1985, 1986) and Kim et al. (1986), and

62、are very slightly different from the values used in ICRU Report 37 (1984). The collision stopping powers, evaluated according to the prescriptions in ICRU Report 37 (1984), include departures from simple Bragg additivity due to chemical-binding, phase, and density effects, as reflected in the choice

63、 of the mean excitation energy I and density p for the medium. These departures from Bragg additivity for the stopping power of the matrix can result in discernable differences in the mass energy-absorption coefficient, such as between those for water vapor and liquid.Further details of the calculat

64、ions are given in Seltzer (1993) and will not be repeated here. Instead, a summary of expressions used for the calculation of g is given below. The formulas include the integration over the initial particle spectra, and have been generalized to include mixtures and compounds.Photoelectric Absorption. The radiative losses for the photoelectrons have been evaluated according to(eq 14)where “ /p is the total photoef