NAT'L INST. OF STAND & TECH III III III Hill HI AlllOb 243004 NIST RESEARCH INFORMATION NISTIR 5632 NIST MAY 1 6 1995 PUBLICATIONS 1 CENTER Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients 1 keV to 20 MeV for Elements Z = 1 to 92 and 48 Additional Substances of Dosimetric Interest J. H. Hubbell S. M. Seltzer U.S. DEPARTMENT OF COMMERCE Technology Administration National Institute of Standards and Technology Physics Laboratory Ionizing Radiation Division Gaithersburg, MD 20899 qo. \n> • fUlO NIST NISTIR 5632 Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients 1 keV to 20 MeV for Elements Z = 1 to 92 and 48 Additional Substances of Dosimetric Interest J. H. Hubbell S. M. Seltzer U.S. DEPARTMENT OF COMMERCE Technology Administration National Institute of Standards and Technology Physics Laboratory Ionizing Radiation Division Gaithersburg, MD 20899 May 1995 U.S. DEPARTMENT OF COMMERCE Ronald H. Brown, Secretary TECHNOLOGY ADMINISTRATION Mary L. Good, Under Secretary for Technology NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY Arati Prabhakar, Director TABLES OF X-RAY MASS ATTENUATION COEFFICIENTS AND MASS ENERGY- ABSORPTION COEFFICIENTS 1 keV TO 20 MeV FOR ELEMENTS Z = 1 TO 92 AND 48 ADDITIONAL SUBSTANCES OF DOSIMETRIC INTEREST* + J. H. Hubbell 11830 Rocking Horse Road, Rockville, MD 20852 and S. M. Seltzer Ionizing Radiation Division, Physics Laboratory National Institute of Standards and Technology Technology Administration, U.S. Department of Commerce Gaithersburg, MD 20899 U.S. A. Abstract Tables and graphs of the photon mass attenuation coefficient p/p and the mass = 1 energy-absorption coefficient pen/p are presented for all of the elements Z to 92, and for 48 compounds and mixtures of radiological interest. The tables cover energies of the photon (x ray, gamma ray, bremsstrahlung) from 1 keV to 20 MeV. The p/p values are taken from the current photon interaction database at values the National Institute of Standards and Technology, and the pen/p are based on the new calculations by Seltzer described in Radiation Research 136, 147 the tables given (1993). These tables of p/p and pen/p replace and extend by Hubbell in the International Journal of Applied Radiation and Isotopes 33, 1269 (1982). KEYWORDS cross section, gamma-ray, mass attenuation coefficient, mass energy-absorption coefficient, photon, x-ray *Work supported by the Office of Standard Reference Data of the National Institute of Standards and Technology. 'Work carried out for the National Institute of Standards and Technology under contract 43NANB412756. 1. Introduction The mass attenuation coefficient, /i/p, and the mass energy-absorption coefficient, pen/p, are basic quantities used in calculations of the penetration and the energy deposition by photons (x-ray, 7 -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 been treated in some detail elsewhere, for example by Berger (1961), Allison (1961), Evans (1968), Hubbell and Berger (1968), Hubbell (1969, 1977, 1982), Storm and Israel (1970), Carlsson (1971), Ribberfors and Carlsson (1985), Cunningham and Johns (1980), Johns and Higgins et al. and by Seltzer Cunningham (1983), (1992) (1993). Compilations of both pen/p and p/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 of p/p and pen/p given in Hubbell (1982) which have been widely used as reference data in radiation shielding and dosimetry computations. The present tables differ from those in Hubbell (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 included. 2) Instead of using a common energy grid from 1 keV to 20 MeV, without photoelectric absorption edges (K, L 1? etc.), now all edge energies are included and identified, and values are given just above to facilitate accurate of p/p and pen/p and below each edge interpolation. 3) Somewhat different 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 1 factors given by Scofield (1973) to his calculated values of the cross section . An evaluation by Saloman et al. (1988) compared the Scofield theoretical values with the measured-value database, and concluded that overall agreement was better without this renormalization. The present work therefore uses the "un-renormalized" Scofield (1973) theoretical values of the photoeffect cross section for all elements 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 p/p can be obtained by simple additivity, i.e., combining values for the elements according to their proportions by weight. To the losses (bremsstrahlung extent that values for pen/p are affected by the radiative 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 compilation 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. Although Scofield (1973) calculated the cross sections for all Z > 2, he gave renormalization factors only for 2 < Z < 54. 1 These and other refinements, such as a more complete treatment of the atomic shell vacancy and fluorescence cascades, are discussed briefly in the sections 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). 2. The Mass Attenuation Coefficient, p/p incident intensity 7 penetrating a A narrow beam of monoenergetic photons with an 0 , 2 layer of material with mass thickness x and density p, emerges with intensity 7 given by the exponential attenuation law . W l/l0 = exp[- (n/p)x\ Equation (1) can be rewritten as 2 fx/p = In (/„//) < > from which can be obtained from measured values of 7 7 and x. The various experimental p/p 0 , arrangements and techniques from which p/p can be obtained, particularly in the crystallographic 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 p/p in the 1992 International Tables for Crystallography (Creagh and Hubbell, 1992). The current status of p/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 p/p rely heavily on theoretical values for the total cross section per atom, a which is related to according to tot , p/p = a /(uA) . (3) p/p tot Na 23 -1 In is Eq. (3), NA Avogadro’s number (6.022045 x 10 mol ), u is the atomic mass unit (1/12 12 of the mass of an atom of nuclide C), A is the relative atomic mass of the target element, and 3 <r is the total cross section for interaction tot an by the photon. The total cross section can be written as the sum over contributions from the principal photon interactions, a “ + a + a + + + tot °pe coh incoh °pair °trip °ph.n. ^ where cr is the atomic photoeffect cross section, and pe acoh and ajncoh are the coherent (Rayleigh) the inconerent (Compton) scattering cross sections, respectively, a and a are the cross pair trip 2 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. 3 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. 2 sections for electron-positron production in the fields of the nucleus and of the atomic electrons, respectively, and is photonuclear aph n the cross section. Photonuclear absorption of the photon by the atomic nucleus results most usually in the ejection of one or more neutrons and/or protons. This interaction can contribute as much as 5 — 10% to the total photon interaction cross section in a fairly narrow energy region usually occurring somewhere between 5 and 40 MeV, depending on where the giant resonance of the target nuclide falls (see, e.g., Hayward, 1970; Fuller and 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 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 isotopic mixtures; (c) the lack of theoretical models to available and for aph n comparable those for calculations of the other cross sections 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, along with the neglect of other less-probable photon-atom interactions, such as nuclear-resonance scattering and Delbriick scattering.