International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 4.2, pp. 220-229

Section 4.2.4. X-ray absorption (or attenuation) coefficients

D. C. Creaghb and J. H. Hubbelld

4.2.4. X-ray absorption (or attenuation) coefficients

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4.2.4.1. Introduction

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This data set is intended to supersede those data sets given in International Tables for X-ray Crystallography, Vols. III (Koch, MacGillavry & Milledge, 1962[link]) and IV (Hubbell, McMaster, Del Grande & Mallett, 1974[link]).

It is not intended here to give a detailed bibliography of experimental data that have been obtained in the past 90 years. This has been the subject of a number of publications, e.g. Saloman & Hubbell (1987[link]), Hubbell, Gerstenberg & Saloman (1986[link]), Saloman & Hubbell (1986[link]), and Saloman, Hubbell & Scofield (1988[link]). Further commentary on the validity and the quality of the experimental data in existing tabulations has been given by Creagh & Hubbell (1987[link]) and Creagh (1987a[link]).

Existing tabulations of X-ray attenuation (or absorption) cross sections fall into three distinct categories: purely theoretical, purely experimental, and an evaluated mixture of theoretical and experimental data.

Compilations of the purely theoretically derived data exist for:

  • photo-effect absorption cross sections (Storm & Israel, 1970[link]; Cromer & Liberman, 1970[link]; Scofield, 1973[link]; Hubbell, Veigele, Briggs, Brown, Cromer & Howerton, 1975[link]; Band, Kharitonov & Trzhaskovskaya, 1979[link]; Yeh & Lindau, 1985[link]);

  • Compton scattering cross sections (Hubbell et al., 1975[link]);

  • Rayleigh scattering cross sections (Hubbell et al., 1975[link]; Hubbell & Øverbø, 1979[link]; Schaupp, Schumacher, Smend, Rullhusen & Hubbell, 1983[link]).

Many purely experimental compilations exist, and the cross-section data given in computer programs used in the analysis of results in X-ray-fluorescence spectroscopy, electron-probe microanalysis, and X-ray diffraction are usually (evaluated) compilations of several of the following compilations: Allen (1935[link], 1969[link]), Victoreen (1949[link]), Liebhafsky, Pfeiffer, Winslow & Zemany (1960[link]), Koch et al. (1962[link]), Heinrich (1966[link]), Theisen & Vollath (1967[link]), Veigele (1973[link]), Leroux & Thinh (1977[link]), Montenegro, Baptista & Duarte (1978[link]), and Plechaty, Cullen & Howerton (1981[link]). If a comparison is made between these data sets, significant discrepancies are found, and questions must be asked concerning the reliability of the data sets that are compared. Jackson & Hawkes (1981[link]) and Gerward (1986[link]) have produced sets of parametric tables to simplify the application of X-ray attenuation data for the solution of problems in computer-aided tomography and X-ray-fluorescence analysis.

Compilations by Henke, Lee, Tanaka, Shimambukuro & Fujikawa (1982[link]) and the earlier tables of McMaster, Del Grande, Mallett & Hubbell (1969/1970[link]) are examples of the judicious application of both theoretical and experimental data to produce a comprehensive data set of X-ray interaction cross sections.

Because of the discrepancies that appear to exist between experimental data sets, the IUCr Commission on Crystallographic Apparatus set up a project to establish which, if any, of the existing methods for measuring X-ray interaction cross sections (X-ray attenuation coefficients) and which theoretical calculations could be considered to be the most reliable. A discussion of some of the major results of this project is given in Section 4.2.3[link]. A more detailed description of this project has been given by Creagh & Hubbell (1987[link], 1990[link]).

In this section, tabulations of the total X-ray interaction cross sections σ and the mass absorption coefficient [\mu_m] are given for a range of characteristic X-ray wavelengths [Ti Kα 2.7440 Å (or 4.509 keV) to Ag Kβ 0.4470 Å (or 24.942 keV)]. The interaction cross sections are expressed in units of barns/atom (1 barn = 10−28 m2) whilst the mass absorption coefficient is given in cm2 g−1. Table 4.2.4.1[link] sets out the wavelengths of the characteristic wavelengths used in Tables 4.2.4.2[link] and 4.2.4.3[link], which list values of σ and [\mu_m], respectively.

Table 4.2.4.1| top | pdf |
Table of wavelengths and energies for the characteristic radiations used in Tables 4.2.4.2[link] and 4.2.4.3[link]

Radiationλ (Å)E (keV)
Ag [K \bar \alpha] 0.5608 22.103
Ag [K \beta _1] 0.4970 24.942
Pd [K \bar \alpha] 0.5869 21.125
Pd [K \beta _1] 0.5205 23.819
Rh [K \bar \alpha] 0.6147 20.169
Rh [K \beta _1] 0.5456 22.724
Mo [K \bar \alpha] 0.7107 17.444
Mo [K \beta _1] 0.6323 19.608
Zn [K \bar \alpha] 1.4364 8.631
Zn [K \beta _1] 1.2952 9.572
Cu [K \bar \alpha] 1.5418 8.041
Cu [K \beta _1] 1.3922 8.905
Ni [K \bar \alpha] 1.6591 7.472
Ni [K \beta _1] 1.5001 8.265
Co [K \bar \alpha] 1.7905 6.925
Co [K \beta _1] 1.6208 7.629
Fe [K \bar \alpha] 1.9373 6.400
Fe [K \beta _1] 1.7565 7.038
Mn [K \bar \alpha] 2.1031 5.895
Mn [K \beta _1] 1.9102 6.490
Cr [K \bar \alpha] 2.2909 5.412
Cr [K \beta _1] 2.0848 5.947
Ti [K \bar \alpha] 2.7496 4.509
Ti [K \beta _1] 2.5138 4.932

Table 4.2.4.2| top | pdf |
Total phonon interaction cross section (barns/atom)

RadiationEnergy (MeV)12345678
HydrogenHeliumLithiumBerylliumBoronCarbonNitrogenOxygen
Ag K[\beta _1] 2.494E−02 6.10E−01 1.26E+00 2.01E+00 2.97E+00 4.40E+00 6.59E+00 1.00E+01 1.52E+01
Pd K[\beta _1] 2.382E−02 6.10E−01 1.26E+00 2.01E+00 2.99E+00 4.44E+00 6.68E+00 1.02E+01 1.55E+01
Rh K[\beta _1] 2.272E−02 6.12E−01 1.27E+00 2.04E+00 3.06E+00 4.47E+00 6.78E+00 1.05E+01 1.62E+01
Ag K[\bar {\alpha }] 2.210E−02 6.14E−01 1.28E+00 2.06E+00 3.13E+00 4.79E+00 7.45E+00 1.17E+01 1.82E+01
Pd K[\bar {\alpha }] 2.112E−02 6.16E−01 1.29E+00 2.09E+00 3.23E+00 5.05E+00 8.02E+00 1.28E+01 2.02E+01
Rh K[\bar {\alpha }] 2.017E−02 6.18E−01 1.30E+00 2.13E+00 3.35E+00 5.35E+00 8.68E+00 1.41E+01 2.25E+01
Mo K[\beta _1] 1.961E−02 6.19E−01 1.31E+00 2.16E+00 3.42E+00 5.56E+00 9.14E+00 1.50E+01 2.41E+01
Mo K[\bar {\alpha }] 1.744E−02 6.24E−01 1.34E+00 2.28E+00 3.83E+00 6.61E+00 1.15E+01 1.96E+01 3.25E+01
Zn K[\beta _1] 9.572E−03 6.47E−01 1.69E+00 4.19E+00 1.07E+01 2.54E+01 5.37E+01 1.03E+02 1.80E+02
Cu K[\beta _1] 8.905E−03 6.50E−01 1.78E+00 4.74E+00 1.28E+01 3.10E+01 6.64E+01 1.27E+02 2.24E+02
Zn K[\bar {\alpha }] 8.631E−03 6.51E−01 1.82E+00 5.02E+00 1.38E+01 3.39E+01 7.28E+01 1.40E+02 2.46E+02
Ni K[\beta _1] 8.265E−03 6.53E−01 1.89E+00 5.46E+00 1.54E+01 3.83E+01 8.28E+01 1.59E+02 2.80E+02
Cu K[\bar {\alpha}] 8.041E−03 6.55E−01 1.94E+00 5.76E+00 1.66E+01 4.15E+01 8.99E+01 1.73E+02 3.04E+02
Co K[\beta _1] 7.649E−03 6.58E−01 2.04E+00 6.40E+00 1.90E+01 4.80E+01 1.04E+02 2.01E+02 3.54E+02
Ni K[\bar {\alpha}] 7.472E−03 6.59E−01 2.09E+00 6.73E+00 2.02E+01 5.14E+01 1.12E+02 2.16E+02 3.80E+02
Fe K[\beta _1] 7.058E−03 6.63E−01 2.23E+00 7.65E+00 2.37E+01 6.09E+01 1.33E+02 2.57E+02 4.51E+02
Co K[\bar {\alpha}] 6.925E−03 6.64E−01 2.28E+00 7.99E+00 2.50E+01 6.45E+01 1.41E+02 2.72E+02 4.78E+02
Mn K[\beta _1] 6.490E−03 6.69E−01 2.48E+00 9.34E+00 3.01E+01 7.84E+01 1.72E+02 3.31E+02 5.81E+02
Fe K[\bar {\alpha}] 6.400E−03 6.70E−01 2.53E+00 9.67E+00 3.13E+01 8.18E+01 1.79E+02 3.46E+02 6.06E+02
Cr K[\beta _1] 5.947E−03 6.77E−01 2.83E+00 1.16E+01 3.88E+01 1.02E+02 2.24E+02 4.32E+02 7.56E+02
Mn K[\bar {\alpha}] 5.895E−03 6.78E−01 2.87E+00 1.19E+01 3.99E+01 1.05E+02 2.30E+02 4.44E+02 7.76E+02
Cr K[\bar {\alpha}] 5.412E−03 6.89E−01 3.31E+00 1.50E+01 5.14E+01 1.36E+02 2.99E+02 5.75E+02 1.00E+03
Ti K[\beta _1] 4.932E−03 7.04E−01 3.94E+00 1.94E+01 6.82E+01 1.81E+02 3.98E+02 7.62E+02 1.33E+03
Ti K[\bar {\alpha}] 4.509E−03 7.24E−01 4.73E+00 2.51E+01 8.97E+01 2.39E+02 5.23E+02 1.00E+03 1.73E+03

RadiationEnergy (MeV)910111213141516
FluorineNeonSodiumMagnesiumAluminiumSiliconPhosphorusSulfur
Ag K[\beta _1] 2.494E−02 2.27E+01 3.33E+01 4.77E+01 6.68E+01 9.16E+01 1.23E+02 1.62E+02 2.10E+02
Pd K[\beta _1] 2.382E−02 2.32E+01 3.40E+01 4.88E+01 6.85E+01 9.40E+01 1.26E+02 1.67E+02 2.16E+02
Rh K[\beta _1] 2.272E−02 2.50E+01 3.62E+01 5.07E+01 8.26E+01 1.05E+02 1.40E+02 1.85E+02 2.02E+02
Ag K[\bar {\alpha }] 2.210E−02 2.77E+01 4.12E+01 5.96E+01 8.42E+01 1.16E+02 1.56E+02 2.06E+02 2.67E+02
Pd K[\bar {\alpha }] 2.112E−02 3.11E+01 4.65E+01 6.75E+01 9.55E+01 1.32E+02 1.78E+02 2.35E+02 3.05E+02
Rh K[\bar {\alpha }] 2.017E−02 3.50E+01 5.26E+01 7.67E+01 1.09E+02 1.51E+02 2.03E+02 2.69E+02 3.49E+02
Mo K[\beta _1] 1.961E−02 3.76E+01 5.68E+01 5.30E+01 1.18E+02 1.63E+02 2.20E+02 2.92E+02 3.78E+02
Mo K[\bar {\alpha }] 1.744E−02 5.15E+01 7.86E+01 1.16E+02 1.65E+02 2.29E+02 3.10E+02 4.10E+02 5.32E+02
Zn K[\beta _1] 9.572E−03 2.95E+02 4.57E+02 6.77E+02 9.67E+02 1.34E+03 1.79E+03 2.36E+03 3.03E+03
Cu K[\beta _1] 8.905E−03 3.66E+02 5.67E+02 8.39E+02 1.20E+03 1.65E+03 2.21E+03 2.90E+03 3.72E+03
Zn K[\bar {\alpha }] 8.631E−03 4.02E+02 6.22E+02 9.20E+02 1.31E+03 1.81E+03 2.42E+03 3.17E+03 4.06E+03
Ni K[\beta _1] 8.265E−03 4.58E+02 7.08E+02 1.05E+03 1.49E+03 2.05E+03 2.75E+03 3.59E+03 4.60E+03
Cu K[\bar {\alpha }] 8.041E−03 4.98E+02 7.68E+02 1.14E+03 1.61E+03 2.22E+03 2.97E+03 3.88E+03 4.97E+03
Co K[\beta _1] 7.649E−03 5.78E+02 8.92E+02 1.32E+03 1.87E+03 2.57E+03 3.43E+03 4.48E+03 5.72E+03
Ni K[\bar {\alpha }] 7.472E−03 6.20E+02 9.56E+02 1.41E+03 2.00E+03 2.75E+03 3.67E+03 4.78E+03 6.11E+03
Fe K[\beta _1] 7.058E−03 7.36E+02 1.13E+03 1.67E+03 2.36E+03 3.24E+03 4.32E+03 5.62E+03 7.17E+03
Co K[\bar {\alpha }] 6.925E−03 7.79E+02 1.20E+03 1.76E+03 2.50E+03 3.42E+03 4.56E+03 5.93E+03 7.56E+03
Mn K[\beta _1] 6.490E−03 9.46E+02 1.45E+03 2.13E+03 3.02E+03 4.13E+03 5.49E+03 7.12E+03 9.06E+03
Fe K[\bar {\alpha }] 6.400E−03 9.86E+02 1.51E+03 2.22E+03 3.14E+03 4.29E+03 5.71E+03 7.41E+03 9.42E+03
Cr K[\beta _1] 5.947E−03 1.23E+03 1.88E+03 2.75E+03 3.88E+03 5.30E+03 7.03E+03 9.10E+03 1.15E+04
Mn K[\bar {\alpha }] 5.895E−03 1.26E+03 1.93E+03 2.83E+03 3.98E+03 5.43E+03 7.20E+03 9.33E+03 1.18E+04
Cr K[\bar {\alpha }] 5.412E−03 1.62E+03 2.48E+03 3.62E+03 5.09E+03 6.93E+03 9.16E+03 1.18E+04 1.50E+04
Ti K[\beta _1] 4.932E−03 2.14E+03 3.26E+03 4.74E+03 6.64E+03 9.01E+03 1.19E+04 1.53E+04 1.93E+04
Ti K[\bar{\alpha}] 4.509E−03 2.79E+03 4.23E+03 6.13E+03 8.57E+03 1.16E+04 1.52E+04 1.95E+04 2.45E+04

RadiationEnergy (MeV)1718192021222324
ChlorineArgonPotassiumCalciumScandiumTitaniumVanadiumChromium
Ag K[\beta _1] 2.494E−02 2.68E+02 3.36E+02 4.17E+02 5.12E+02 6.20E+02 7.44E+02 8.85E+02 1.04E+03
Pd K[\beta _1] 2.382E−02 2.75E+02 3.45E+02 4.29E+02 5.26E+02 6.37E+02 7.64E+02 9.09E+02 1.07E+03
Rh K[\beta _1] 2.272E−02 3.15E+02 3.84E+02 4.84E+02 6.30E+02 7.25E+02 8.63E+02 9.98E+02 1.19E+03
Ag K[\bar {\alpha }] 2.210E−02 3.41E+02 4.29E+02 5.32E+02 6.52E+02 7.89E+02 9.47E+02 1.12E+03 1.33E+03
Pd K[\bar {\alpha }] 2.112E−02 3.89E+02 4.89E+02 6.06E+02 7.42E+02 8.99E+02 1.08E+03 1.28E+03 1.51E+03
Rh K[\bar {\alpha }] 2.017E−02 4.45E+02 5.59E+02 6.93E+02 8.48E+02 1.03E+03 1.23E+03 1.46E+03 1.72E+03
Mo K[\beta _1] 1.961E−02 4.83E+02 6.06E+02 7.52E+02 9.20E+02 1.11E+03 1.33E+03 1.58E+03 1.86E+03
Mo K[\bar {\alpha }] 1.744E−02 6.78E+02 8.51E+02 1.05E+03 1.29E+03 1.56E+03 1.86E+03 2.20E+03 2.58E+03
Zn K[\beta _1] 9.572E−03 3.82E+03 4.74E+03 5.80E+03 7.02E+03 8.38E+03 9.93E+03 1.16E+04 1.33E+04
Cu K[\beta _1] 8.905E−03 4.68E+03 5.80E+03 7.09E+03 8.57E+03 1.02E+04 1.21E+04 1.41E+04 1.60E+04
Zn K[\bar {\alpha }] 8.631E−03 5.11E+03 6.34E+03 7.73E+03 9.34E+03 1.11E+04 1.32E+04 1.53E+04 1.73E+04
Ni K[\beta _1] 8.265E−03 5.78E+03 7.15E+03 8.72E+03 1.05E+04 1.25E+04 1.48E+04 1.72E+04 1.96E+04
Cu K[\bar {\alpha }] 8.041E−03 6.24E+03 7.72E+03 9.40E+03 1.13E+04 1.35E+04 1.39E+04 1.85E+04 2.13E+04
Co K[\beta _1] 7.649E−03 7.17E+03 8.86E+03 1.08E+04 1.30E+04 1.54E+04 1.80E+04 2.11E+04 2.53E+04
Ni K[\bar {\alpha }] 7.472E−03 7.66E+03 9.46E+03 1.15E+04 1.38E+04 1.64E+04 1.91E+04 2.25E+04 2.74E+04
Fe K[\beta _1] 7.058E−03 8.97E+03 1.11E+04 1.34E+04 1.61E+04 1.91E+04 2.20E+04 2.62E+04 3.32E+04
Co K[\bar {\alpha }] 6.925E−03 9.46E+03 1.17E+04 1.41E+04 1.69E+04 2.01E+04 2.31E+04 2.75E+04 3.53E+04
Mn K[\beta _1] 6.490E−03 1.13E+04 1.39E+04 1.69E+04 2.01E+04 2.39E+04 2.74E+04 3.26E+04 4.15E+04
Fe K[\bar {\alpha }] 6.400E−03 1.18E+04 1.44E+04 1.75E+04 2.09E+04 2.47E+04 2.85E+04 3.37E+04 4.25E+04
Cr K[\beta _1] 5.947E−03 1.44E+04 1.76E+04 2.13E+04 2.54E+04 3.01E+04 3.53E+04 4.05E+04 5.79E+03
Mn K[\bar {\alpha }] 5.895E−03 1.47E+04 1.80E+04 2.18E+04 2.60E+04 3.08E+04 3.63E+04 4.14E+04 5.93E+03
Cr K[\bar {\alpha }] 5.412E−03 1.86E+04 2.27E+04 2.74E+04 3.26E+04 3.85E+04 4.69E+04 6.32E+03 7.50E+03
Ti K[\beta _1] 4.932E−03 2.38E+04 2.91E+04 3.49E+04 4.15E+04 4.87E+04 6.79E+03 8.16E+03 9.68E+03
Ti K[\bar {\alpha }] 4.509E−03 3.01E+04 3.69E+04 4.41E+04 5.20E+04 6.03E+04 8.68E+03 1.04E+04 1.24E+04

RadiationEnergy (MeV)2526272829303132
ManganeseIronCobaltNickelCopperZincGalliumGermanium
Ag K[\beta _1] 2.494E−02 1.22E+03 1.42E+03 1.64E+03 1.88E+03 2.14E+03 2.43E+03 2.74E+03 3.08E+03
Pd K[\beta _1] 2.382E−02 1.25E+03 1.46E+03 1.68E+03 1.93E+03 2.20E+03 2.49E+03 2.81E+03 3.16E+03
Rh K[\beta _1] 2.272E−02 1.37E+03 1.65E+03 1.89E+03 2.19E+03 2.49E+03 2.88E+03 3.21E+03 3.55E+03
Ag K[\bar {\alpha }] 2.210E−02 1.55E+03 1.80E+03 2.07E+03 2.38E+03 2.71E+03 3.07E+03 3.46E+03 3.87E+03
Pd K[\bar {\alpha }] 2.112E−02 1.76E+03 2.04E+03 2.35E+03 2.70E+03 3.07E+03 3.47E+03 3.91E+03 4.38E+03
Rh K[\bar {\alpha }] 2.017E−02 2.01E+03 2.33E+03 2.68E+03 3.07E+03 3.49E+03 3.95E+03 4.44E+03 4.97E+03
Mo K[\beta _1] 1.961E−02 2.17E+03 2.52E+03 2.90E+03 3.31E+03 3.77E+03 4.26E+03 4.80E+03 5.37E+03
Mo K[\bar {\alpha }] 1.744E−02 3.02E+03 3.49E+03 4.01E+03 4.57E+03 5.18E+03 5.86E+03 6.60E+03 7.38E+03
Zn K[\beta _1] 9.572E−03 1.55E+04 1.78E+04 2.02E+04 2.27E+04 2.53E+04 3.90E+03 4.46E+03 5.08E+03
Cu K[\beta _1] 8.905E−03 1.88E+04 2.15E+04 2.43E+04 2.72E+04 4.13E+03 4.75E+03 5.44E+03 6.19E+03
Zn K[\bar {\alpha }] 8.631E−03 2.05E+04 2.34E+04 2.63E+04 2.94E+04 4.50E+03 5.18E+03 5.92E+03 6.75E+03
Ni K[\beta _1] 8.265E−03 2.29E+04 2.61E+04 2.93E+04 4.41E+03 5.07E+03 5.83E+03 6.67E+03 7.60E+03
Cu K[\bar {\alpha }] 8.041E−03 2.46E+04 2.80E+04 3.14E+04 4.76E+03 5.47E+03 6.29E+03 7.19E+03 8.19E+03
Co K[\beta _1] 7.649E−03 2.80E+04 3.17E+04 4.71E+03 5.46E+03 6.27E+03 7.21E+03 8.24E+03 9.38E+03
Ni K[\bar {\alpha }] 7.472E−03 2.97E+04 3.35E+04 5.02E+03 5.82E+03 6.68E+03 7.68E+03 8.79E+03 1.00E+04
Fe K[\beta _1] 7.058E−03 3.42E+04 5.04E+03 5.87E+03 6.80E+03 7.81E+03 8.98E+03 1.03E+04 1.17E+04
Co K[\bar {\alpha }] 6.925E−03 3.58E+04 5.31E+03 6.18E+03 7.16E+03 8.23E+03 9.46E+03 1.08E+04 1.23E+04
Mn K[\beta _1] 6.490E−03 5.40E+03 6.34E+03 7.39E+03 8.56E+03 9.83E+03 1.13E+04 1.29E+04 1.47E+04
Fe K[\bar {\alpha }] 6.400E−03 5.62E+03 6.59E+03 7.68E+03 8.89E+03 1.02E+04 1.17E+04 1.34E+04 1.53E+04
Cr K[\beta _1] 5.947E−03 6.87E+03 8.06E+03 9.40E+03 1.09E+04 1.25E+04 1.43E+04 1.64E+04 1.86E+04
Mn K[\bar {\alpha }] 5.895E−03 7.04E+03 8.26E+03 9.62E+03 1.11E+04 1.28E+04 1.47E+04 1.68E+04 1,91E+04
Cr K[\bar {\alpha }] 5.412E−03 8.90E+03 1.04E+04 1.22E+04 1.41E+04 1.61E+04 1.85E+04 2.12E+04 2.41E+04
Ti K[\beta _1] 4.932E−03 1.15E+04 1.35E+04 1.57E+04 1.81E+04 2.08E+04 2.39E+04 2.72E+04 3.09E+04
Ti K[\bar {\alpha }] 4.509E−03 1.47E+04 1.72E+04 2.00E+04 2.31E+04 2.65E+04 3.04E+04 3.46E+04 3.93E+04

RadiationEnergy (MeV)3334353637383940
ArsenicSeleniumBromineKryptonRubidiumStrontiumYttriumZirconium
Ag K[\beta _1] 2.494E−02 3.44E+03 3.84E+03 4.26E+03 4.72E+03 5.21E+03 5.72E+03 6.25E+03 6.79E+03
Pd K[\beta _1] 2.382E−02 3.53E+03 3.94E+03 4.37E+03 4.84E+03 5.34E+03 5.86E+03 6.41E+03 6.96E+03
Rh K[\beta _1] 2.272E−02 4.04E+03 4.53E+03 5.00E+03 5.50E+03 5.98E+03 6.48E+03 7.27E+03 7.80E+03
Ag K[\bar {\alpha }] 2.210E−02 4.33E+03 4.82E+03 5.35E+03 5.92E+03 6.52E+03 7.15E+03 7.80E+03 8.47E+03
Pd K[\bar {\alpha }] 2.112E−02 4.89E+03 5.45E+03 6.04E+03 6.68E+03 7.35E+03 8.06E+03 8.79E+03 9.52E+03
Rh K[\bar {\alpha }] 2.017E−02 5.55E+03 6.18E+03 6.83E+03 7.55E+03 8.30E+03 9.09E+03 9.90E+03 1.07E+04
Mo K[\beta _1] 1.961E−02 5.99E+03 6.66E+03 7.36E+03 8.13E+03 8.94E+03 9.78E+03 1.06E+04 1.15E+04
Mo K[\bar {\alpha }] 1.744E−02 8.22E+03 9.11E+03 1.00E+04 1.10E+04 1.21E+04 1.32E+04 1.43E+04 2.47E+03
Zn K[\beta _1] 9.572E−03 5.77E+03 6.52E+03 7.34E+03 8.24E+03 9.21E+03 1.03E+04 1.14E+04 1.26E+04
Cu K[\beta _1] 8.905E−03 7.03E+03 7.94E+03 8.94E+03 1.00E+04 1.12E+04 1.25E+04 1.39E+04 1.54E+04
Zn K[\bar {\alpha }] 8.631E−03 7.65E+03 8.64E+03 9.73E+03 1.09E+04 1.22E+04 1.36E+04 1.51E+04 1.67E+04
Ni K[\beta _1] 8.265E−03 8.62E+03 9.73E+03 1.10E+04 1.23E+04 1.37E+04 1.53E+04 1.70E+04 1.88E+04
Cu K[\bar {\alpha }] 8.041E−03 9.29E+03 1.05E+04 1.18E+04 1.32E+04 1.48E+04 1.65E+04 1.83E+04 2.03E+04
Co K[\beta _1] 7.649E−03 1.06E+04 1.20E+04 1.35E+04 1.52E+04 1.69E+04 1.89E+04 2.09E+04 2.32E+04
Ni K[\bar {\alpha }] 7.472E−03 1.13E+04 1.28E+04 1.44E+04 1.61E+04 1.80E+04 2.01E+04 2.23E+04 2.47E+04
Fe K[\beta _1] 7.058E−03 1.32E+04 1.49E+04 1.68E+04 1.88E+04 2.10E+04 2.34E+04 2.60E+04 2.87E+04
Co K[\bar {\alpha }] 6.925E−03 1.39E+04 1.57E+04 1.77E+04 1.98E+04 2.22E+04 2.47E+04 2.73E+04 3.02E+04
Mn K[\beta _1] 6.490E−03 1.66E+04 1.88E+04 2.11E+04 2.36E+04 2.64E+04 2.94E+04 3.26E+04 3.60E+04
Fe K[\bar {\alpha }] 6.400E−03 1.73E+04 1.95E+04 2.19E+04 2.45E+04 2.74E+04 3.05E+04 3.38E+04 3.74E+04
Cr K[\beta _1] 5.947E−03 2.11E+04 2.38E+04 2.67E+04 2.99E+04 3.34E+04 3.72E+04 4.12E+04 4.55E+04
Mn K[\bar {\alpha }] 5.895E−03 2.16E+04 2.44E+04 2.74E+04 3.07E+04 3.42E+04 3.81E+04 4.22E+04 4.66E+04
Cr K[\bar {\alpha }] 5.412E−03 2.72E+04 3.07E+04 3.45E+04 3.85E+04 4.30E+04 4.78E+04 5.29E+04 5.84E+04
Ti K[\beta _1] 4.932E−03 3.50E+04 3.94E+04 4.42E+04 4.94E+04 5.51E+04 6.12E+04 6.77E+04 7.47E+04
Ti K[\bar {\alpha }] 4.509E−03 4.44E+04 5.00E+04 5.61E+04 6.27E+04 6.98E+04 7.75E+04 8.56E+04 9.43E+04

RadiationEnergy (MeV)4142434445464748
NiobiumMolybdenumTechnetiumRutheniumRhodiumPalladiumSilverCadmium
Ag K[\beta _1] 2.494E−02 7.41E+03 9.36E+03 8.65E+03 9.33E+03 1.00E+04 1.00E+04 2.00E+03 2.18E+03
Pd K[\beta _1] 2.382E−02 7.59E+03 9.61E+03 8.86E+03 9.56E+03 1.03E+04 1.88E+03 2.05E+03 2.23E+03
Rh K[\beta _1] 2.272E−02 8.57E+03 9.30E+03 9.95E+03 1.07E+04 1.18E+03 2.10E+03 2.29E+03 2.49E+03
Ag K[\bar {\alpha }] 2.210E−02 9.22E+03 1.15E+04 1.07E+04 1.92E+03 2.10E+03 2.30E+03 2.51E+03 2.73E+03
Pd K[\bar {\alpha }] 2.112E−02 1.04E+04 1.23E+04 1.20E+04 2.17E+03 2.38E+03 2.60E+03 2.84E+03 3.09E+03
Rh K[\bar {\alpha }] 2.017E−02 1.16E+04 1.27E+04 2.24E+03 2.46E+03 2.70E+03 2.94E+03 3.21E+03 3.50E+03
Mo K[\beta _1] 1.961E−02 1.25E+04 2.19E+03 2.42E+03 2.65E+03 2.91E+03 3.18E+03 3.47E+03 3.78E+03
Mo K[\bar {\alpha }] 1.744E−02 2.73E+03 3.00E+03 3.32E+03 3.64E+03 3.99E+03 4.36E+03 4.76E+03 5.18E+03
Zn K[\beta _1] 9.572E−03 1.40E+04 1.54E+04 1.69E+04 1.85E+04 2.02E+04 2.21E+04 2.40E+04 2.61E+04
Cu K[\beta _1] 8.905E−03 1.70E+04 1.87E+04 2.05E+04 2.25E+04 2.45E+04 2.67E+04 2.91E+04 3.16E+04
Zn K[\bar {\alpha }] 8.631E−03 1.85E+04 2.03E+04 2.23E+04 2.44E+04 2.67E+04 2.91E+04 3.16E+04 3.44E+04
Ni K[\beta _1] 8.265E−03 2.07E+04 2.28E+04 2.51E+04 2.74E+04 3.00E+04 3.27E+04 3.55E+04 3.86E+04
Cu K[\bar {\alpha }] 8.041E−03 2.23E+04 2.46E+04 2.70E+04 2.95E+04 3.23E+04 3.52E+04 3.82E+04 4.15E+04
Co K[\beta _1] 7.649E−03 2.55E+04 2.81E+04 3.08E+04 3.37E+04 3.68E+04 4.01E+04 4.36E+04 4.73E+04
Ni K[\bar {\alpha }] 7.472E−03 2.72E+04 2.99E+04 3.28E+04 3.59E+04 3.92E+04 4.27E+04 4.64E+04 5.03E+04
Fe K[\beta _1] 7.058E−03 3.17E+04 3.48E+04 3.82E+04 4.18E+04 4.56E+04 4.96E+04 5.39E+04 5.84E+04
Co K[\bar {\alpha }] 6.925E−03 3.33E+04 3.66E+04 4.02E+04 4.39E+04 4.79E+04 5.21E+04 5.66E+04 6.14E+04
Mn K[\beta _1] 6.490E−03 3.96E+04 4.36E+04 4.77E+04 5.22E+04 5.69E+04 6.19E+04 6.72E+04 7.28E+04
Fe K[\bar {\alpha }] 6.400E−03 4.12E+04 4.52E+04 4.95E+04 5.42E+04 5.91E+04 6.42E+04 6.97E+04 7.55E+04
Cr K[\beta _1] 5.947E−03 5.01E+04 5.50E+04 6.02E+04 6.58E+04 7.17E+04 7.79E+04 8.45E+04 9.15E+04
Mn K[\bar {\alpha }] 5.895E−03 5.13E+04 5.63E+04 6.16E+04 6.73E+04 7.34E+04 7.97E+04 8.64E+04 9.36E+04
Cr K[\bar {\alpha }] 5.412E−03 6.42E+04 7.05E+04 7.71E+04 8.41E+04 9.16E+04 9.94E+04 1.08E+05 1.17E+05
Ti K[\beta _1] 4.932E−03 8.21E+04 8.99E+04 9.83E+04 1.07E+05 1.17E+05 1.27E+05 1.37E+05 1.48E+05
Ti K[\bar {\alpha }] 4.509E−03 1.04E+05 1.13E+05 1.24E+05 1.35E+05 1.47E+05 1.59E+05 1.72E+05 1.86E+05

RadiationEnergy (MeV)4950515253545556
IndiumTinAntimonyTelluriumIodineXenonCaesiumBarium
Ag K[\beta _1] 2.494E−02 2.37E+03 2.57E+03 2.79E+03 3.02E+03 3.26E+03 3.52E+03 3.79E+03 4.08E+03
Pd K[\beta _1] 2.382E−02 2.43E+03 2.64E+03 2.86E+03 3.09E+03 3.34E+03 3.61E+03 3.89E+03 4.18E+03
Rh K[\beta _1] 2.272E−02 2.64E+03 3.00E+03 3.20E+03 3.50E+03 3.71E+03 4.04E+03 4.04E+03 4.76E+03
Ag K[\bar {\alpha }] 2.210E−02 2.97E+03 3.23E+03 3.50E+03 3.78E+03 4.09E+03 4.41E+03 4.75E+03 5.11E+03
Pd K[\bar {\alpha }] 2.112E−02 3.36E+03 3.65E+03 3.95E+03 4.28E+03 4.62E+03 4.98E+03 5.37E+03 5.78E+03
Rh K[\bar {\alpha }] 2.017E−02 3.81E+03 4.13E+03 4.48E+03 4.85E+03 5.24E+03 5.65E+03 6.09E+03 6.55E+03
Mo K[\beta _1] 1.961E−02 4.11E+03 4.46E+03 4.84E+03 5.23E+03 5.65E+03 6.09E+03 6.57E+03 7.06E+03
Mo K[\bar {\alpha }] 1.744E−02 5.63E+03 6.11E+03 6.62E+03 7.16E+03 7.73E+03 8.34E+03 8.98E+03 9.65E+03
Zn K[\beta _1] 9.572E−03 2.83E+04 3.06E+04 3.31E+04 3.57E+04 3.84E+04 4.13E+04 4.44E+04 4.76E+04
Cu K[\beta _1] 8.905E−03 3.43E+04 3.71E+04 4.00E+04 4.32E+04 4.64E+04 4.99E+04 5.36E+04 5.74E+04
Zn K[\bar {\alpha }] 8.631E−03 3.72E+04 4.03E+04 4.35E+04 4.69E+04 5.04E+04 5.42E+04 5.81E+04 6.23E+04
Ni K[\beta _1] 8.265E−03 4.18E+04 4.52E+04 4.88E+04 5.25E+04 5.65E+04 6.07E+04 6.51E+04 6.98E+04
Cu K[\bar {\alpha }] 8.041E−03 4.50E+04 4.86E+04 5.25E+04 5.65E+04 6.07E+04 6.52E+04 7.00E+04 7.50E+04
Co K[\beta _1] 7.649E−03 5.12E+04 5.54E+04 5.98E+04 6.43E+04 6.92E+04 7.42E+04 7.96E+04 8.52E+04
Ni K[\bar {\alpha }] 7.472E−03 5.45E+04 5.89E+04 6.35E+04 6.84E+04 7.35E+04 7.88E+04 8.45E+04 9.04E+04
Fe K[\beta _1] 7.058E−03 6.32E+04 6.83E+04 7.37E+04 7.94E+04 8.52E+04 9.14E+04 9.77E+04 1.04E+05
Co K[\bar {\alpha }] 6.925E−03 6.64E+04 7.18E+04 7.74E+04 8.34E+04 8.96E+04 9.60E+04 1.03E+05 1.09E+05
Mn K[\beta _1] 6.490E−03 7.87E+04 8.50E+04 9.17E+04 9.88E+04 1.06E+05 1.13E+05 1.21E+05 1.29E+05
Fe K[\bar {\alpha }] 6.400E−03 8.17E+04 8.82E+04 9.51E+04 1.02E+05 1.10E+05 1.18E+05 1.26E+05 1.34E+05
Cr K[\beta _1] 5.947E−03 9.90E+04 1.07E+05 1.15E+05 1.24E+05 1.33E+05 1.42E+05 1.60E+05 1.47E+05
Mn K[\bar {\alpha }] 5.895E−03 1.01E+05 1.09E+05 1.18E+05 1.27E+05 1.36E+05 1.45E+05 1.63E+05 1.50E+05
Cr K[\bar {\alpha }] 5.412E−03 1.26E+05 1.36E+05 1.46E+05 1.57E+05 1.68E+05 1.57E+05 1.77E+05 1.34E+05
Ti K[\beta _1] 4.932E−03 1.60E+05 1.73E+05 1.85E+05 1.98E+05 2.11E+05 2.48E+05 5.70E+04 7.16E+04
Ti K[\bar {\alpha }] 4.509E−03 2.00E+05 2.15E+05 2.00E+05 1.60E+05 6.17E+04 5.78E+04 7.28E+04 7.62E+04

RadiationEnergy (MeV)5758596061626364
LanthanumCeriumPraseodymiumNeodymiumPromethiumSamariumEuropiumGadolinium
Ag K[\beta _1] 2.494E−02 3.97E+03 4.26E+03 4.56E+03 4.89E+03 5.22E+03 5.57E+03 5.93E+03 6.32E+03
Pd K[\beta _1] 2.382E−02 4.05E+03 4.82E+03 5.15E+03 5.51E+03 5.90E+03 6.29E+03 6.71E+03 7.15E+03
Rh K[\beta _1] 2.272E−02 5.10E+03 5.47E+03 5.85E+03 6.25E+03 6.69E+03 7.14E+03 7.59E+03 8.09E+03
Ag K[\bar {\alpha }] 2.210E−02 5.49E+03 5.89E+03 6.29E+03 6.73E+03 7.20E+03 7.69E+03 8.17E+03 8.72E+03
Pd K[\bar {\alpha }] 2.112E−02 6.20E+03 6.63E+03 7.11E+03 7.62E+03 8.14E+03 8.69E+03 9.23E+03 9.84E+03
Rh K[\bar {\alpha }] 2.017E−02 7.03E+03 7.69E+03 8.07E+03 8.62E+03 9.22E+03 9.84E+03 1.05E+04 1.11E+04
Mo K[\beta _1] 1.961E−02 7.59E+03 8.12E+03 8.70E+03 9.29E+03 9.94E+03 1.06E+04 1.13E+04 1.20E+04
Mo K[\bar {\alpha }] 1.744E−02 1.04E+04 1.11E+04 1.19E+04 1.27E+04 1.36E+04 1.44E+04 1.54E+04 1.63E+04
Zn K[\beta _1] 9.572E−03 5.10E+04 5.42E+04 5.78E+04 6.15E+04 6.57E+04 6.97E+04 9.93E+04 7.83E+04
Cu K[\beta _1] 8.905E−03 6.14E+04 6.56E+04 7.00E+04 7.42E+04 7.90E+04 8.36E+04 8.88E+04 9.40E+04
Zn K[\bar {\alpha }] 8.631E−03 6.67E+04 7.12E+04 7.58E+04 8.04E+04 8.44E+04 9.06E+04 9.59E+04 1.02E+05
Ni K[\beta _1] 8.265E−03 7.47E+04 7.96E+04 8.49E+04 9.00E+04 9.56E+04 1.01E+05 1.07E+05 9.84E+04
Cu K[\bar {\alpha }] 8.041E−03 8.03E+04 8.56E+04 9.12E+04 9.68E+04 1.03E+05 1.08E+05 1.02E+05 1.05E+05
Co K[\beta _1] 7.649E−03 9.11E+04 9.70E+04 1.03E+05 1.09E+05 1.16E+05 1.07E+05 1.21E+05 8.75E+04
Ni K[\bar {\alpha }] 7.472E−03 9.68E+04 1.03E+05 1.09E+05 1.16E+05 1.23E+05 1.14E+05 8.70E+04 9.29E+04
Fe K[\beta _1] 7.058E−03 1.11E+05 1.19E+05 1.26E+05 1.18E+05 1.22E+05 9.56E+04 1.03E+05 3.99E+04
Co K[\bar {\alpha }] 6.925E−03 1.17E+05 1.24E+05 1.32E+05 1.21E+05 9.63E+04 9.89E+04 4.04E+04 4.20E+04
Mn K[\beta _1] 6.490E−03 1.38E+05 1.27E+05 1.39E+05 1.05E+05 1.13E+05 4.39E+04 4.67E+04 4.93E+04
Fe K[\bar {\alpha }] 6.400E−03 1.43E+05 1.31E+05 1.02E+05 1.09E+05 4.19E+04 4.59E+04 4.87E+04 5.09E+04
Cr K[\beta _1] 5.947E−03 1.48E+05 1.15E+05 1.22E+05 4.74E+04 5.01E+04 5.52E+04 5.65E+04 6.14E+04
Mn K[\bar {\alpha }] 5.895E−03 1.50E+05 1.19E+05 4.52E+04 4.86E+04 5.18E+04 5.64E+04 6.03E+04 6.29E+04
Cr K[\bar {\alpha }] 5.412E−03 5.19E+04 5.54E+04 5.57E+04 6.01E+04 6.43E+04 6.97E+04 7.54E+04 7.78E+04
Ti K[\beta _1] 4.932E−03 6.55E+04 6.98E+04 7.02E+04 7.52E+04 8.11E+04 8.74E+04 9.34E+04 9.76E+04
Ti K[\bar {\alpha }] 4.509E−03 8.19E+04 8.31E+04 8.77E+04 9.51E+04 1.02E+05 1.09E+05 1.16E+05 1.22E+05

RadiationEnergy (MeV)6566676869707172
TerbiumDysprosiumHolmiumErbiumThuliumYtterbiumLutetiumHafnium
Ag K[\beta _1] 2.494E−02 6.66E+03 7.15E+03 7.59E+03 8.05E+03 8.52E+03 9.02E+03 9.53E+03 1.01E+04
Pd K[\beta _1] 2.382E−02 7.52E+03 8.07E+03 8.57E+03 9.08E+03 9.62E+03 1.02E+04 1.08E+04 1.14E+04
Rh K[\beta _1] 2.272E−02 8.15E+03 9.15E+03 9.69E+03 1.03E+04 1.08E+04 1.15E+04 1.22E+04 1.29E+04
Ag K[\bar {\alpha }] 2.210E−02 9.16E+03 9.85E+03 1.01E+04 1.11E+04 1.17E+04 1.24E+04 1.31E+04 1.38E+04
Pd K[\bar {\alpha }] 2.112E−02 1.03E+04 1.11E+04 1.18E+04 1.25E+04 1.32E+04 1.40E+04 1.48E+04 1.56E+04
Rh K[\bar {\alpha }] 2.017E−02 1.17E+04 1.26E+04 1.33E+04 1.41E+04 1.50E+04 1.58E+04 1.67E+04 1.76E+04
Mo K[\beta _1] 1.961E−02 1.26E+04 1.35E+04 1.43E+04 1.52E+04 1.61E+04 1.70E+04 1.80E+04 1.90E+04
Mo K[\bar {\alpha }] 1.744E−02 1.72E+04 1.84E+04 1.95E+04 2.07E+04 2.19E+04 2.31E+04 2.44E+04 2.57E+04
Zn K[\beta _1] 9.572E−03 8.20E+04 8.74E+04 9.20E+04 8.53E+04 6.59E+04 6.90E+04 7.26E+04 7.70E+04
Cu K[\beta _1] 8.905E−03 9.87E+04 9.31E+04 7.17E+04 7.42E+04 8.27E+04 3.10E+04 3.52E+04 3.56E+04
Zn K[\bar {\alpha }] 8.631E−03 9.29E+04 1.02E+05 7.78E+04 7.97E+04 3.28E+04 3.36E+04 3.81E+04 3.85E+04
Ni K[\beta _1] 8.265E−03 1.08E+05 8.53E+04 8.60E+04 3.42E+04 3.67E+04 3.76E+04 4.24E+04 4.30E+04
Cu K[\bar {\alpha }] 8.041E−03 8.38E+04 9.23E+04 3.53E+04 3.67E+04 3.93E+04 4.08E+04 4.53E+04 4.59E+04
Co K[\beta _1] 7.649E−03 9.40E+04 3.72E+04 4.00E+04 4.14E+04 4.46E+04 4.57E+04 5.17E+04 5.21E+04
Ni K[\bar {\alpha }] 7.472E−03 3.89E+04 3.94E+04 4.24E+04 4.39E+04 4.47E+04 4.86E+04 5.49E+04 5.54E+04
Fe K[\beta _1] 7.058E−03 4.22E+04 4.53E+04 4.87E+04 5.05E+04 5.50E+04 5.63E+04 6.33E+04 6.40E+04
Co K[\bar {\alpha }] 6.925E−03 4.43E+04 4.75E+04 5.12E+04 5.30E+04 5.78E+04 5.92E+04 6.65E+04 6.73E+04
Mn K[\beta _1] 6.490E−03 5.22E+04 5.59E+04 6.02E+04 6.22E+04 6.82E+04 7.01E+04 7.84E+04 7.91E+04
Fe K[\bar {\alpha }] 6.400E−03 5.44E+04 5.77E+04 6.24E+04 6.44E+04 7.10E+04 7.21E+04 8.13E+04 8.21E+04
Cr K[\beta _1] 5.947E−03 6.46E+04 6.93E+04 7.45E+04 7.75E+04 8.55E+04 8.73E+04 9.85E+04 9.90E+04
Mn K[\bar {\alpha }] 5.895E−03 6.68E+04 7.07E+04 7.67E+04 7.92E+04 8.75E+04 8.94E+04 1.01E+05 1.01E+05
Cr K[\bar {\alpha }] 5.412E−03 8.29E+04 8.77E+04 9.51E+04 9.78E+04 1.08E+05 1.11E+05 1.25E+05 1.26E+05
Ti K[\beta _1] 4.932E−03 1.05E+05 1.11E+05 1.20E+05 1.23E+05 1.39E+05 1.41E+05 1.59E+05 1.60E+05
Ti K[\bar {\alpha }] 4.509E−03 1.31E+05 1.39E+05 1.50E+05 1.54E+05 1.73E+05 1.78E+05 2.00E+05 2.01E+05

RadiationEnergy (MeV)7374757677787980
TantalumTungstenRheniumOsmiumIridiumPlatinumGoldMercury
Ag K[\beta _1] 2.494E−02 1.17E+04 1.24E+04 1.30E+04 1.37E+04 1.44E+04 1.52E+04 1.60E+04 1.68E+04
Pd K[\beta _1] 2.382E−02 1.20E+04 1.27E+04 1.34E+04 1.41E+04 1.48E+04 1.56E+04 1.64E+04 1.72E+04
Rh K[\beta _1] 2.272E−02 1.35E+04 1.45E+04 1.52E+04 1.59E+04 1.69E+04 1.78E+04 1.77E+04 1.94E+04
Ag K[\bar {\alpha }] 2.210E−02 1.46E+04 1.54E+04 1.62E+04 1.71E+04 1.80E+04 1.89E+04 1.99E+04 2.09E+04
Pd K[\bar {\alpha }] 2.112E−02 1.65E+04 1.74E+04 1.83E+04 1.93E+04 2.02E+04 2.13E+04 2.24E+04 2.35E+04
Rh K[\bar {\alpha }] 2.017E−02 1.86E+04 1.96E+04 2.07E+04 2.17E+04 2.28E+04 2.40E+04 2.52E+04 2.65E+04
Mo K[\beta _1] 1.961E−02 2.00E+04 2.11E+04 2.22E+04 2.34E+04 2.46E+04 2.58E+04 2.71E+04 2.84E+04
Mo K[\bar {\alpha }] 1.744E−02 2.72E+04 2.86E+04 3.01E+04 3.16E+04 3.31E+04 3.48E+04 3.65E+04 3.82E+04
Zn K[\beta _1] 9.572E−03 3.30E+04 3.29E+04 3.67E+04 3.73E+04 4.01E+04 4.08E+04 4.24E+04 4.29E+04
Cu K[\beta _1] 8.905E−03 3.76E+04 3.97E+04 4.43E+04 4.48E+04 4.83E+04 4.89E+04 5.08E+04 5.18E+04
Zn K[\bar {\alpha }] 8.631E−03 4.05E+04 4.26E+04 4.78E+04 4.84E+04 5.20E+04 5.28E+04 5.58E+04 5.58E+04
Ni K[\beta _1] 8.265E−03 4.41E+04 4.80E+04 5.34E+04 5.41E+04 5.81E+04 5.66E+04 6.14E+04 6.20E+04
Cu K[\bar {\alpha }] 8.041E−03 4.85E+04 5.13E+04 5.72E+04 5.80E+04 6.24E+04 6.34E+04 6.69E+04 6.68E+04
Co K[\beta _1] 7.649E−03 5.39E+04 5.83E+04 6.50E+04 6.55E+04 7.09E+04 6.87E+04 7.49E+04 6.91E+04
Ni K[\bar {\alpha }] 7.472E−03 5.84E+04 6.19E+04 6.88E+04 6.97E+04 7.51E+04 7.62E+04 8.03E+04 8.02E+04
Fe K[\beta _1] 7.058E−03 6.60E+04 7.15E+04 7.95E+04 8.03E+04 8.68E+04 8.45E+04 9.17E+04 9.14E+04
Co K[\bar {\alpha }] 6.925E−03 6.92E+04 7.51E+04 8.33E+04 8.44E+04 9.11E+04 9.20E+04 9.71E+04 9.71E+04
Mn K[\beta _1] 6.490E−03 8.16E+04 8.82E+04 9.83E+04 9.94E+04 1.07E+05 1.04E+05 1.14E+05 1.09E+05
Fe K[\bar {\alpha }] 6.400E−03 8.46E+04 9.15E+04 1.02E+05 1.02E+05 1.11E+05 1.12E+05 1.18E+05 1.19E+05
Cr K[\beta _1] 5.947E−03 1.01E+05 1.10E+05 1.22E+05 1.23E+05 1.34E+05 1.31E+05 1.41E+05 1.36E+05
Mn K[\bar {\alpha }] 5.895E−03 1.06E+05 1.12E+05 1.25E+05 1.27E+05 1.37E+05 1.34E+05 1.45E+05 1.42E+05
Cr K[\bar {\alpha }] 5.412E−03 1.31E+05 1.40E+05 1.55E+05 1.57E+05 1.70E+05 1.66E+05 1.79E+05 1.80E+05
Ti K[\beta _1] 4.932E−03 1.64E+05 1.77E+05 1.96E+05 1.99E+05 2.15E+05 2.11E+05 2.23E+05 2.33E+05
Ti K[\bar {\alpha }] 4.509E−03 2.60E+05 2.18E+05 2.46E+05 2.49E+05 2.65E+05 2.66E+05 2.80E+05 2.98E+05

RadiationEnergy (MeV)8182838485868788
ThalliumLeadBismuthPoloniumAstatineRadonFranciumRadium
Ag K[\beta _1] 2.494E−02 1.76E+04 1.84E+04 1.93E+04 2.02E+04 2.11E+04 2.20E+04 2.30E+04 2.41E+04
Pd K[\beta _1] 2.382E−02 1.80E+04 1.89E+04 1.98E+04 2.07E+04 2.16E+04 2.26E+04 2.36E+04 2.46E+04
Rh K[\beta _1] 2.272E−02 1.99E+04 2.05E+04 2.27E+04 2.37E+04 2.49E+04 2.55E+04 2.60E+04 2.68E+04
Ag K[\bar {\alpha }] 2.210E−02 2.19E+04 2.29E+04 2.40E+04 2.51E+04 2.62E+04 2.73E+04 2.85E+04 2.98E+04
Pd K[\bar {\alpha }] 2.112E−02 2.46E+04 2.58E+04 2.70E+04 2.82E+04 2.94E+04 3.07E+04 3.20E+04 3.34E+04
Rh K[\bar {\alpha }] 2.017E−02 2.78E+04 2.91E+04 3.04E+04 3.18E+04 3.31E+04 3.45E+04 3.60E+04 3.76E+04
Mo K[\beta _1] 1.961E−02 2.98E+04 3.12E+04 3.27E+04 3.41E+04 3.56E+04 3.71E+04 3.87E+04 4.03E+04
Mo K[\bar {\alpha }] 1.744E−02 4.01E+04 4.19E+04 4.38E+04 4.58E+04 4.07E+04 3.98E+04 3.22E+04 3.30E+04
Zn K[\beta _1] 9.572E−03 4.83E+04 5.11E+04 5.42E+04 5.66E+04 5.56E+04 6.22E+04 6.55E+04 6.56E+04
Cu K[\beta _1] 8.905E−03 5.81E+04 6.15E+04 6.51E+04 6.80E+04 6.68E+04 7.48E+04 7.87E+04 7.80E+04
Zn K[\bar {\alpha }] 8.631E−03 6.29E+04 6.66E+04 7.04E+04 7.35E+04 7.21E+04 8.11E+04 8.92E+04 8.55E+04
Ni K[\beta _1] 8.265E−03 7.03E+04 7.44E+04 7.86E+04 8.22E+04 8.04E+04 9.06E+04 9.94E+04 9.53E+04
Cu K[\bar {\alpha }] 8.041E−03 7.54E+04 7.98E+04 8.43E+04 8.81E+04 8.65E+04 9.72E+04 1.02E+05 1.02E+05
Co K[\beta _1] 7.649E−03 8.58E+04 9.01E+04 9.57E+04 1.00E+05 9.82E+04 1.11E+05 1.16E+05 1.16E+05
Ni K[\bar {\alpha }] 7.472E−03 9.11E+04 9.64E+04 1.02E+05 1.06E+05 1.04E+05 1.17E+05 1.23E+05 1.23E+05
Fe K[\beta _1] 7.058E−03 1.05E+05 1.12E+05 1.17E+05 1.22E+05 1.20E+05 1.36E+05 1.42E+05 1.43E+05
Co K[\bar {\alpha }] 6.925E−03 1.11E+05 1.17E+05 1.23E+05 1.29E+05 1.26E+05 1.43E+05 1.49E+05 1.49E+05
Mn K[\beta _1] 6.490E−03 1.31E+05 1.39E+05 1.46E+05 1.51E+05 1.49E+05 1.69E+05 1.77E+05 1.76E+05
Fe K[\bar {\alpha }] 6.400E−03 1.36E+05 1.48E+05 1.51E+05 1.57E+05 1.54E+05 1.75E+05 1.82E+05 1.83E+05
Cr K[\beta _1] 5.947E−03 1.64E+05 1.74E+05 1.82E+05 1.89E+05 1.86E+05 2.11E+05 2.21E+05 2.19E+05
Mn K[\bar {\alpha }] 5.895E−03 1.68E+05 1.78E+05 1.86E+05 1.93E+05 1.91E+05 2.16E+05 2.23E+05 2.25E+05
Cr K[\bar {\alpha }] 5.412E−03 2.22E+05 2.22E+05 2.32E+05 1.99E+05 2.37E+05 2.70E+05 2.82E+05 2.79E+05
Ti K[\beta _1] 4.932E−03 2.66E+05 2.82E+05 2.94E+05 2.88w+05 2.99E+05 3.43E+05 3.56E+05 3.53E+05
Ti K[\bar {\alpha }] 4.509E−03 3.36E+05 3.56E+05 3.67E+05 3.17E+05 3.78E+05 4.33E+05 4.49E+05 4.99E+05

RadiationEnergy (MeV)8990919293949596
ActiniumThoriumProtactiniumUraniumNeptuniumPlutoniumAmericiumCurium
Ag K[\beta _1] 2.494E−02 2.51E+04 2.62E+04 2.73E+04 2.84E+04 2.95E+04 3.07E+04 3.18E+04 2.89E+04
Pd K[\beta _1] 2.382E−02 2.57E+04 2.68E+04 2.79E+04 2.90E+04 3.02E+04 3.14E+04 3.26E+04 2.96E+04
Rh K[\beta _1] 2.272E−02 2.83E+04 3.09E+04 3.00E+04 3.54E+04 3.42E+04 3.03E+04 3.34E+04 2.36E+04
Ag K[\bar {\alpha }] 2.210E−02 3.11E+04 3.23E+04 3.42E+04 3.50E+04 2.99E+04 2.27E+04 2.50E+04 2.46E+04
Pd K[\bar {\alpha }] 2.112E−02 3.48E+04 3.62E+04 3.77E+04 3.40E+04 4.08E+04 4.24E+04 4.39E+04 4.05E+04
Rh K[\bar {\alpha }] 2.017E−02 3.92E+04 4.07E+04 4.24E+04 2.74E+04 4.58E+04 4.76E+04 4.93E+04 4.57E+04
Mo K[\beta _1] 1.961E−02 3.42E+04 3.80E+04 4.55E+04 2.96E+04 4.91E+04 5.10E+04 5.29E+04 4.92E+04
Mo K[\bar {\alpha }] 1.744E−02 5.40E+04 3.70E+04 3.87E+04 4.03E+04 2.57E+04 1.62E+04 1.89E+04 2.01E+04
Zn K[\beta _1] 9.572E−03 1.07E+05 6.57E+04 6.74E+04 7.11E+04 7.47E+04 7.29E+04 7.63E+04 7.95E+04
Cu K[\beta _1] 8.905E−03 1.14E+05 8.70E+04 8.11E+04 8.54E+04 8.92E+04 8.75E+04 9.27E+04 9.51E+04
Zn K[\bar {\alpha }] 8.631E−03 1.16E+05 9.84E+04 8.78E+04 9.23E+04 9.67E+04 9.48E+04 1.01E+05 1.03E+05
Ni K[\beta _1] 8.265E−03 1.19E+05 1.10E+05 9.82E+04 1.03E+05 1.08E+05 1.06E+05 1.14E+05 1.15E+05
Cu K[\bar {\alpha }] 8.041E−03 1.43E+05 1.18E+05 1.06E+05 1.12E+05 1.23E+05 1.13E+05 1.44E+05 1.38E+05
Co K[\beta _1] 7.649E−03 1.50E+05 1.34E+05 1.19E+05 1.26E+05 1.32E+05 1.28E+05 1.46E+05 1.41E+05
Ni K[\bar {\alpha }] 7.472E−03 1.67E+05 1.42E+05 1.27E+05 1.33E+05 1.40E+05 1.36E+05 1.48E+05 1.47E+05
Fe K[\beta _1] 7.058E−03 1.47E+05 1.54E+05 1.46E+05 1.54E+05 1.61E+05 1.57E+05 1.73E+05 1.73E+05
Co K[\bar {\alpha }] 6.925E−03 1.74E+05 1.72E+05 1.53E+05 1.61E+05 1.69E+05 1.65E+05 1.81E+05 1.79E+05
Mn K[\beta _1] 6.490E−03 1.96E+05 1.87E+05 1.81E+05 1.90E+05 1.98E+05 1.94E+05 2.15E+05 2.11E+05
Fe K[\bar {\alpha }] 6.400E−03 2.00E+05 1.96E+05 1.88E+05 1.97E+05 2.17E+05 2.02E+05 2.43E+05 2.42E+05
Cr K[\beta _1] 5.947E−03 2.32E+05 2.35E+05 2.27E+05 2.37E+05 2.48E+05 2.43E+05 2.72E+05 2.62E+05
Mn K[\bar {\alpha }] 5.895E−03 2.37E+05 2.40E+05 2.31E+05 2.43E+05 2.53E+05 2.48E+05 2.78E+05 2.68E+05
Cr K[\bar {\alpha }] 5.412E−03 2.79E+05 2.96E+05 2.88E+05 3.03E+05 3.14E+05 3.08E+05 3.49E+05 3.33E+05
Ti K[\beta _1] 4.932E−03 3.32E+05 3.77E+05 3.83E+05 3.82E+05 3.97E+05 3.90E+05 4.47E+05 4.22E+05
Ti K[\bar {\alpha }] 4.509E−03 3.95E+05 4.76E+05 4.84E+05 4.88E+05 3.79E+05 3.65E+05 4.26E+05 4.03E+05

RadiationEnergy (MeV)9798
BerkeliumCalifornium
Ag K[\beta _1] 2.494E−02 2.13E+04 3.06E+04
Pd K[\beta _1] 2.382E−02 2.18E+04 3.44E+04
Rh K[\beta _1] 2.272E−02 2.41E+04 3.86E+04
Ag K[\bar {\alpha }] 2.210E−02 2.50E+04 2.89E+04
Pd K[\bar {\alpha }] 2.112E−02 2.98E+04 4.62E+04
Rh K[\bar {\alpha }] 2.017E−02 3.37E+04 5.21E+04
Mo K[\beta_1] 1.961E−02 3.64E+04 5.59E+04
Mo K[\bar {\alpha }] 1.744E−02 2.01E+04 2.09E+04
Zn K[\beta_1] 9.572E−03 7.63E+04 8.67E+04
Cu K[\beta _1] 8.905E−03 9.27E+04 1.04E+04
Zn K[\bar {\alpha }] 8.631E−03 1.01E+05 1.13E+05
Ni K[\beta _1] 8.265E−03 1.13E+05 1.26E+05
Cu K[\bar {\alpha }] 8.041E−03 1.43E+05 1.50E+05
Co K[\beta _1] 7.649E−03 1.46E+05 1.52E+05
Ni K[\bar {\alpha }] 7.472E−03 1.48E+05 1.61E+05
Fe K[\beta _1] 7.058E−03 1.73E+05 1.87E+05
Co K[\bar {\alpha }] 6.925E−03 1.82E+05 1.96E+05
Mn K[\beta _1] 6.490E−03 2.16E+05 2.30E+05
Fe K[\bar {\alpha }] 6.400E−03 2.43E+05 2.53E+05
Cr K[\beta _1] 5.947E−03 2.72E+05 2.86E+05
Mn K[\bar {\alpha }] 5.895E−03 2.78E+05 2.93E+05
Cr K[\bar {\alpha }] 5.412E−03 3.49E+05 3.63E+05
Ti K[\beta _1] 4.932E−03 4.47E+05 4.59E+05
Ti K[\bar {\alpha }] 4.509E−03 4.26E+05 4.38E+05

Table 4.2.4.3| top | pdf |
Mass attenuation coefficients (cm2 g−1)

RadiationEnergy (MeV)12345678
HydrogenHeliumLithiumBerylliumBoronCarbonNitrogenOxygen
Ag K[\beta _1] 2.494E−02 3.63E−01 1.89E−01 1.72E−01 1.95E−01 2.37E−01 3.15E−01 4.04E−01 3.29E−01
Pd K[\beta _1] 2.382E−02 3.65E−01 1.90E−01 1.74E−01 2.00E−01 2.47E−01 3.35E−01 4.37E−01 5.82E−01
Rh K[\beta _1] 2.272E−02 3.66E−01 1.92E−01 1.77E−01 2.05E−01 2.59E−01 3.58E−01 4.77E−01 6.44E−01
Ag K[\bar {\alpha }] 2.210E−02 3.67E−01 1.93E−01 1.79E−01 2.09E−01 2.67E−01 3.74E−01 5.03E−01 6.85E−01
Pd K[\bar {\alpha }] 2.112E−02 3.68E−01 1.94E−01 1.82E−01 2.16E−01 2.81E−01 4.02E−01 5.51E−01 7.60E−01
Rh K[\bar {\alpha }] 2.017E−02 3.69E−01 1.96E−01 1.85E−01 2.24E−01 2.98E−01 4.35E−01 6.07E−01 8.48E−01
Mo K[\beta _1] 1.961E−02 3.70E−01 1.97E−01 1.87E−01 2.29E−01 3.09E−01 4.58E−01 6.45E−01 9.08E−01
Mo K[\bar {\alpha }] 1.744E−02 3.73E−01 2.02E−01 1.98E−01 2.56E−01 3.68E−01 5.76E−01 8.45E−01 1.22E+00
Zn K[\beta _1] 9.572E−03 3.86E−01 2.55E−01 3.64E−01 7.16E−01 1.41E+00 2.69E+00 4.42E+00 6.78E+00
Cu K[\beta _1] 8.905E−03 3.88E−01 2.68E−01 4.12E−01 8.53E−01 1.73E+00 3.33E+00 5.48E+00 8.42E+00
Zn K[\bar {\alpha }] 8.631E−03 3.89E−01 2.74E−01 4.36E−01 9.23E−01 1.89E+00 3.65E+00 6.01E+00 9.25E+00
Ni K[\beta _1] 8.265E−03 3.90E−01 2.85E−01 4.73E−01 1.03E+00 2.14E+00 4.15E+00 6.85E+00 1.05E+01
Cu K[\bar {\alpha }] 8.041E−03 3.91E−01 2.92E−01 5.00E−01 1.11E+00 2.31E+00 4.51E+00 7.44E+00 1.15E+01
Co K[\beta _1] 7.649E−03 3.93E−01 3.07E−01 5.55E−01 1.27E+00 2.67E+00 5.24E+00 8.66E+00 1.33E+01
Ni K[\bar {\alpha }] 7.472E−03 3.94E−01 3.14E−01 5.84E−01 1.35E+00 2.87E+00 5.62E+00 9.29E+00 1.43E+01
Fe K[\beta _1] 7.058E−03 3.96E−01 3.35E−01 6.63E−01 1.58E+00 3.39E+00 6.68E+00 1.10E+01 1.70E+01
Co K[\bar {\alpha }] 6.925E−03 3.97E−01 3.43E−01 6.93E−01 1.67E+00 3.59E+00 7.07E+00 1.17E+01 1.80E+01
Mn K[\beta _1] 6.490E−03 4.00E−01 3.74E−01 8.10E−01 2.01E+00 4.37E+00 8.62E+00 1.42E+01 2.19E+01
Fe K[\bar {\alpha }] 6.400E−03 4.00E−01 3.81E−01 8.39E−01 2.09E+00 4.55E+00 8.99E+00 1.49E+01 2.28E+01
Cr K[\beta _1] 5.947E−03 4.05E−01 4.25E−01 1.01E+00 2.59E+00 5.69E+00 1.12E+01 1.86E+01 2.84E+01
Mn K[\bar {\alpha }] 5.895E−03 4.05E−01 4.31E−01 1.03E+00 2.66E+00 5.84E+00 1.16E+01 1.91E+01 2.92E+01
Cr K[\bar {\alpha }] 5.412E−03 4.12E−01 4.98E−01 1.30E+00 3.44E+00 7.59E+00 1.50E+01 2.47E+01 3.78E+01
Ti K[\beta _1] 4.932E−03 4.21E−01 5.92E−01 1.68E+00 4.56E+00 1.01E+01 1.99E+01 3.28E+01 4.99E+01
Ti K[\bar {\alpha }] 4.509E−03 4.33E−01 7.12E−01 2.18E+00 6.00E+00 1.33E+01 2.62E+01 4.30E+01 6.52E+01

RadiationEnergy (MeV)910111213141516
FluorineNeonSodiumMagnesiumAluminiumSiliconPhosphorusSulfur
Ag K[\beta _1] 2.494E−02 6.60E−01 9.06E−01 1.13E+00 1.50E+00 1.85E+00 2.38E+00 2.84E+00 3.55E+00
Pd K[\beta _1] 2.382E−02 7.35E−01 1.02E+00 1.28E+00 1.70E+00 2.10E+00 2.71E+00 3.24E+00 4.05E+00
Rh K[\beta _1] 2.272E−02 8.22E−01 1.15E+00 1.45E+00 1.93E+00 2.39E+00 3.09E+00 3.70E+00 4.64E+00
Ag K[\bar {\alpha }] 2.210E−02 8.79E−01 1.23E+00 1.56E+00 2.09E+00 2.59E+00 3.35E+00 4.01E+00 5.02E+00
Pd K[\bar {\alpha }] 2.112E−02 9.84E−01 1.39E+00 1.77E+00 2.37E+00 2.94E+00 3.81E+00 4.57E+00 5.72E+00
Rh K[\bar {\alpha }] 2.017E−02 1.11E+00 1.57E+00 2.01E+00 2.70E+00 3.36E+00 4.36E+00 5.23E+00 6.55E+00
Mo K[\beta _1] 1.961E−02 1.19E+00 1.69E+00 2.17E+00 2.92E+00 3.64E+00 4.73E+00 5.67E+00 7.11E+00
Mo K[\bar {\alpha }] 1.744E−02 1.63E+00 2.35E+00 3.03E+00 4.09E+00 5.11E+00 6.64E+00 7.97E+00 9.99E+00
Zn K[\beta _1] 9.572E−03 9.35E+00 1.36E+01 1.77E+01 2.40E+01 2.98E+01 3.85E+01 4.58E+01 5.68E+01
Cu K[\beta _1] 8.905E−03 1.16E+01 1.69E+01 2.20E+01 2.96E+01 3.68E+01 4.75E+01 5.64E+01 6.98E+01
Zn K[\bar {\alpha }] 8.631E−03 1.28E+01 1.86E+01 2.41E+01 3.25E+01 4.03E+01 5.20E+01 6.17E+01 7.63E+01
Ni K[\beta_1] 8.265E−03 1.45E+01 2.11E+01 2.74E+01 3.69E+01 4.58E+01 5.89E+01 6.98E+01 8.63E+01
Cu K[\bar {\alpha }] 8.041E−03 1.58E+01 2.29E+01 2.97E+01 4.00E+01 4.96E+01 6.37E+01 7.55E+01 9.33E+01
Co K[\beta _1] 7.649E−03 1.83E+01 2.66E+01 3.45E+01 4.63E+01 5.73E+01 7.36E+01 8.70E+01 1.07E+02
Ni K[\bar {\alpha }] 7.472E−03 1.97E+01 2.85E+01 3.69E+01 4.96E+01 6.13E+01 7.87E+01 9.30E+01 1.15E+02
Fe K[\beta _1] 7.058E−03 2.33E+01 3.38E+01 4.37E+01 5.85E+01 7.23E+01 9.27E+01 1.09E+02 1.35E+02
Co K[\bar {\alpha }] 6.925E−03 2.47E+01 3.58E+01 4.62E+01 6.19E+01 7.64E+01 9.78E+01 1.15E+02 1.42E+02
Mn K[\beta _1] 6.490E 03 3.00E+01 4.34E+01 5.59E+01 7.47E+01 9.21E+01 1.18E+02 1.39E+02 1.70E+02
Fe K[\bar {\alpha }] 6.400E−03 3.13E+01 4.52E+01 5.82E+01 7.78E+01 9.59E+01 1.22E+02 1.44E+02 1.77E+02
Cr K[\beta _1] 5.947E−03 3.89E+01 5.61E+01 7.21E+01 9.62E+01 1.18E+02 1.51E+02 1.77E+02 2.17E+02
Mn K[\bar {\alpha }] 5.895E−03 3.99E+01 5.76E+01 7.40E+01 9.87E+01 1.21E+02 1.54E+02 1.81E+02 2.22E+02
Cr K[\bar {\alpha }] 5.412E−03 5.15E+01 7.41E+01 9.49E+01 1.26E+02 1.55E+02 1.96E+02 2.30E+02 2.81E+02
Ti K[\beta _1] 4.932E−03 6.78E+01 9.72E+01 1.24E+02 1.65E+02 2.01E+02 2.55E+02 2.97E+02 3.62E+02
Ti K[\bar {\alpha }] 4.509E−03 8.84E+01 1.26E+02 1.61E+02 2.12E+02 2.59E+02 3.27E+02 3.79E+02 4.60E+02

RadiationEnergy (MeV)1718192021222324
ChlorineArgonPotassiumCalciumScandiumTitaniumVanadiumChromium
Ag K[\beta _1] 2.494E−02 4.09E+00 4.56E+00 5.78E+00 6.92E+00 7.47E+00 8.43E+00 9.42E+00 1.09E+01
Pd K[\beta _1] 2.382E−02 4.67E+00 5.21E+00 6.60E+00 7.90E+00 8.53E+00 9.61E+00 1.07E+01 1.24E+01
Rh K[\beta _1] 2.272E−02 5.35E+00 5.96E+00 7.56E+00 9.04E+00 9.76E+00 1.10E+01 1.23E+01 1.42E+01
Ag K[\bar {\alpha }] 2.210E−02 5.79E+00 6.46E+00 8.19E+00 9.79E+00 1.06E+01 1.19E+01 1.33E+01 1.54E+01
Pd K[\bar {\alpha }] 2.112E−02 6.61E+00 7.37E+00 9.33E+00 1.12E+01 1.20E+01 1.36E+01 1.51E+01 1.75E+01
Rh K[\bar {\alpha }] 2.017E−02 7.55E+00 8.42E+00 1.07E+01 1.27E+01 1.38E+01 1.55E+01 1.73E+01 1.99E+01
Mo K[\beta _1] 1.961E−02 8.20E+00 9.14E+00 1.16E+01 1.38E+01 1.49E+01 1.68E+01 1.87E+01 2.15E+01
Mo K[\bar {\alpha }] 1.744E−02 1.15E+01 1.28E+01 1.62E+01 1.93E+01 2.08E+01 2.34E+01 2.60E+01 2.99E+01
Zn K[\beta _1] 9.572E−03 6.48E+01 7.14E+01 8.94E+01 1.05E+02 1.12E+02 1.25E+02 1.37E+02 1.55E+02
Cu K[\beta _1] 8.905E−03 7.95E+01 8.75E+01 1.09E+02 1.29E+02 1.37E+02 1.52E+02 1.66E+02 1.85E+02
Zn K[\bar {\alpha }] 8.631E−03 8.69E+01 9.55E+01 1.19E+02 1.40E+02 1.49E+02 1.66E+02 1.81E+02 2.01E+02
Ni K[\beta _1] 8.265E−03 9.81E+01 1.08E+02 1.34E+02 1.58E+02 1.67E+02 1.86E+02 2.03E+02 2.27E+02
Cu K[\bar {\alpha }] 8.041E−03 1.06E+02 1.16E+02 1.45E+02 1.70E+02 1.80E+02 2.00E+02 2.19E+02 2.47E+02
Co K[\beta _1] 7.649E−03 1.22E+02 1.34E+02 1.66E+02 1.95E+02 2.06E+02 2.27E+02 2.50E+02 2.93E+02
Ni K[\bar {\alpha }] 7.472E−03 1.30E+02 1.43E+02 1.77E+02 2.08E+02 2.20E+02 2.40E+02 2.66E+02 3.18E+02
Fe K[\beta _1] 7.058E−03 1.52E+02 1.67E+02 2.07E+02 2.42E+02 2.56E+02 2.77E+02 3.09E+02 3.85E+02
Co K[\bar {\alpha }] 6.925E−03 1.61E+02 1.76E+02 2.18E+02 2.55E+02 2.69E+02 2.91E+02 3.25E+02 4.08E+02
Mn K[\beta _1] 6.490E−03 1.92E+02 2.10E+02 2.60E+02 3.03E+02 3.19E+02 3.45E+02 3.85E+02 4.80E+02
Fe K[\bar {\alpha }] 6.400E−03 2.00E+02 2.18E+02 2.70E+02 3.14E+02 3.32E+02 3.58E+02 3.99E+02 4.92E+02
Cr K[\beta _1] 5.947E−03 2.44E+02 2.66E+02 3.28E+02 3.82E+02 4.03E+02 4.44E+02 4.79E+02 6.70E+01
Mn K[\bar {\alpha }] 5.895E−03 2.50E+02 2.72E+02 3.36E+02 3.91E+02 4.12E+02 4.57E+02 4.89E+02 6.86E+01
Cr K[\bar {\alpha }] 5.412E−03 3.16E+02 3.42E+02 4.21E+02 4.90E+02 5.16E+02 5.90E+02 7.47E+01 8.68E+01
Ti K[\beta _1] 4.932E−03 4.04E+02 4.38E+02 5.38E+02 6.24E+02 6.52E+02 8.54E+01 9.65E+01 1.12E+02
Ti K[\bar {\alpha }] 4.509E−03 5.11E+02 5.56E+02 6.80E+02 7.81E+02 8.08E+02 1.09E+02 1.23E+02 1.43E+02

RadiationEnergy (MeV)2526272829303132
ManganeseIronCobaltNickelCopperZincGalliumGermanium
Ag K[\beta _1] 2.494E−02 1.21E+01 1.38E+01 1.51E+01 1.74E+01 1.83E+01 2.02E+01 2.14E+01 2.31E+01
Pd K[\beta _1] 2.382E−02 1.37E+01 1.57E+01 1.72E+01 1.98E+01 2.08E+01 2.30E+01 2.43E+01 2.62E+01
Rh K[\beta _1] 2.272E−02 1.57E+01 1.79E+01 1.96E+01 2.26E+01 2.38E+01 2.62E+01 2.77E+01 2.98E+01
Ag K[\bar {\alpha }] 2.210E−02 1.70E+01 1.94E+01 2.12E+01 2.44E+01 2.56E+01 2.82E+01 2.98E+01 3.21E+01
Pd K[\bar {\alpha }] 2.112E−02 1.93E+01 2.20E+01 2.41E+01 2.77E+01 2.91E+01 3.20E+01 3.38E+01 3.64E+01
Rh K[\bar {\alpha }] 2.017E−02 2.20E+01 2.51E+01 2.74E+01 3.15E+01 3.30E+01 3.63E+01 3.84E+01 4.13E+01
Mo K[\beta _1] 1.961E−02 2.38E+01 2.71E+01 2.96E+01 3.40E+01 3.57E+01 3.93E+01 4.15E+01 4.46E+01
Mo K[\bar {\alpha }] 1.744E−02 3.31E+01 3.76E+01 4.10E+01 4.69E+01 4.91E+01 5.40E+01 5.70E+01 6.12E+01
Zn K[\beta _1] 9.572E−03 1.70E+02 1.92E+02 2.06E+02 2.33E+02 2.40E+02 3.59E+01 3.85E+01 4.22E+01
Cu K[\beta _1] 8.905E−03 2.07E+02 2.32E+02 2.48E+02 2.79E+02 3.92E+01 4.38E+01 4.70E+01 5.14E+01
Zn K[\bar {\alpha }] 8.631E 03 2.24E+02 2.52E+02 2.69E+02 3.02E+02 4.27E+01 4.77E+01 5.12E+01 5.59E+01
Ni K[\beta _1] 8.265E−03 2.51E+02 2.81E+02 3.00E+02 4.53E+01 4.80E+01 5.37E+01 5.76E+01 6.30E+01
Cu K[\bar {\alpha }] 8.041E 03 2.70E+02 3.02E+02 3.21E+02 4.88E+01 5.18E+01 5.79E+01 6.21E+01 6.79E+01
Co K[\beta _1] 7.649E−03 3.06E+02 3.42E+02 4.81E+01 5.60E+01 5.94E+01 6.64E+01 7.12E+01 7.78E+01
Ni K[\bar {\alpha }] 7.472E−03 3.25E+02 3.62E+02 5.13E+01 5.97E+01 6.33E+01 7.08E+01 7.59E+01 8.29E+01
Fe K[\beta _1] 7.058E−03 3.75E+02 5.43E+01 6.00E+01 6.98E+01 7.40E+01 8.27E+01 8.86E+01 9.69E+01
Co K[\bar {\alpha }] 6.925E−03 3.93E+02 5.72E+01 6.32E+01 7.35E+01 7.80E+01 8.71E+01 9.34E+01 1.02E+02
Mn K[\beta _1] 6.490E−03 5.92E+01 6.84E+01 7.55E+01 8.78E+01 9.31E+01 1.04E+02 1.11E+02 1.22E+02
Fe K[\bar {\alpha }] 6.400E−03 6.16E+01 7.10E+01 7.85E+01 9.13E+01 9.68E+01 1.08E+02 1.16E+02 1.27E+02
Cr K[\beta _1] 5.947E−03 7.53E+01 8.69E+01 9.60E+01 1.12E+02 1.18E+02 1.32E+02 1.42E+02 1.55E+02
Mn K[\bar {\alpha }] 5.895E−03 7.72E+01 8.90E+01 9.83E+01 1.14E+02 1.21E+02 1.35E+02 1.45E+02 1.58E+02
Cr K[\bar {\alpha }] 5.412E−03 9.75E+01 1.13E+02 1.24E+02 1.44E+02 1.53E+02 1.71E+02 1.83E+02 1.99E+02
Ti K[\beta _1] 4.932E−03 1.26E+02 1.45E+02 1.60E+02 1.86E+02 1.97E+02 2.20E+02 2.35E+02 2.56E+02
Ti K[\bar {\alpha }] 4.509E−03 1.61E+02 1.85E+02 2.04E+02 2.37E+02 2.51E+02 2.80E+02 2.99E+02 3.26E+02

RadiationEnergy (MeV)3334353637383940
ArsenicSeleniumBromineKryptonRubidiumStrontiumYttriumZirconium
Ag K[\beta _1] 2.494E−02 2.50E+01 2.65E+01 2.91E+01 3.07E+01 3.32E+01 3.56E+01 3.84E+01 4.07E+01
Pd K[\beta _1] 2.382E−02 2.84E+01 3.00E+01 3.29E+01 3.48E+01 3.76E+01 4.03E+01 4.34E+01 4.60E+01
Rh K[\beta _1] 2.272E−02 3.23E+01 3.41E+01 3.74E+01 3.95E+01 4.27E+01 4.57E+01 4.91E+01 5.20E+01
Ag K[\bar {\alpha }] 2.210E−02 3.48E+01 3.68E+01 4.03E+01 4.25E+01 4.59E+01 4.91E+01 5.29E+01 5.59E+01
Pd K[\bar {\alpha }] 2.112E−02 3.93E+01 4.16E+01 4.55E+01 4.80E+01 5.18E+01 5.54E+01 5.95E+01 6.29E+01
Rh K[\bar {\alpha }] 2.017E−02 4.46E+01 4.71E+01 5.15E+01 5.43E+01 5.85E+01 6.25E+01 6.71E+01 6.25E+01
Mo K[\beta _1] 1.961E−02 4.82E+01 5.08E+01 5.55E+01 5.84E+01 6.30E+01 6.72E+01 7.21E+01 7.61E+01
Mo K[\bar {\alpha }] 1.744E−02 6.61E+01 6.95E+01 7.56E+01 7.93E+01 8.51E+01 9.06E+01 9.70E+01 1.63E+01
Zn K[\beta _1] 9.572E−03 4.64E+01 4.97E+01 5.53E+01 5.92E+01 6.49E+01 7.06E+01 7.73E+01 8.35E+01
Cu K[\beta _1] 8.905E−03 5.65E+01 6.05E+01 6.74E+01 7.21E+01 7.90E+01 8.59E+01 9.40E+01 1.01E+02
Zn K[\bar {\alpha }] 8.631E−03 6.15E+01 6.59E+01 7.33E+01 7.85E+01 8.60E+01 9.35E+01 1.02E+02 1.10E+02
Ni K[\beta _1] 8.265E−03 6.93E+01 7.42E+01 8.26E+01 8.83E+01 9.68E+01 1.05E+02 1.15E+02 1.24E+02
Cu K[\bar {\alpha }] 8.041E−03 7.47E+01 8.00E+01 8.90E+01 9.52E+01 1.04E+02 1.13E+02 1.24E+02 1.39E+02
Co K[\beta _1] 7.649E−03 8.55E+01 9.16E+01 1.02E+02 1.09E+02 1.19E+02 1.30E+02 1.42E+02 1.54E+02
Ni K[\bar {\alpha }] 7.472E−03 9.11E+01 9.76E+01 1.09E+02 1.16E+02 1.27E+02 1.38E+02 1.51E+02 1.63E+02
Fe K[\beta _1] 7.058E−03 1.06E+02 1.14E+02 1.27E+02 1.35E+02 1.48E+02 1.61E+02 1.76E+02 1.91E+02
Co K[\bar {\alpha }] 6.925E−03 1.12E+02 1.20E+02 1.33E+02 1.42E+02 1.56E+02 1.70E+02 1.85E+02 2.00E+02
Mn K[\beta _1] 6.490E−03 1.34E+02 1.43E+02 1.59E+02 1.70E+02 1.86E+02 2.02E+02 2.21E+02 2.38E+02
Fe K[\bar {\alpha }] 6.400E−03 1.39E+02 1.49E+02 1.65E+02 1.76E+02 1.93E+02 2.10E+02 2.29E+02 2.47E+02
Cr K[\beta _1] 5.947E−03 1.70E+02 1.82E+02 2.02E+02 2.15E+02 2.36E+02 2.56E+02 2.79E+02 3.00E+02
Mn K[\bar {\alpha }] 5.895E−03 1.74E+02 1.86E+02 2.06E+02 2.20E+02 2.41E+02 2.62E+02 2.86E+02 3.08E+02
Cr K[\bar {\alpha }] 5.412E−03 2.19E+02 2.34E+02 2.60E+02 2.77E+02 3.03E+02 3.28E+02 3.58E+02 3.86E+02
Ti K[\beta _1] 4.932E−03 2.81E+02 3.00E+02 3.33E+02 3.55E+02 3.88E+02 4.21E+02 4.59E+02 4.93E+02
Ti K[\bar {\alpha }] 4.509E−03 3.57E+02 3.81E+02 4.23E+02 4.50E+02 4.92E+02 5.32E+02 5.80E+02 6.22E+02

RadiationEnergy (MeV)4142434445464748
NiobiumMolybdenumTechnetiumRutheniumRhodiumPalladiumSilverCadmium
Ag K[\beta _1] 2.494E−02 4.36E+01 5.25E+01 4.84E+01 5.06E+01 5.35E+01 5.55E+01 1.01E+01 1.06E+01
Pd K[\beta _1] 2.382E−02 4.92E+01 6.03E+01 5.45E+01 5.69E+01 6.01E+01 1.06E+01 1.15E+01 1.20E+01
Rh K[\beta _1] 2.272E−02 5.56E+01 6.80E+01 6.15E+01 7.00E+01 1.14E+01 1.21E+01 1.30E+01 1.36E+01
Ag K[\bar {\alpha }] 2.210E−02 5.98E+01 7.20E+01 6.60E+01 1.14E+01 1.23E+01 1.30E+01 1.40E+01 1.46E+01
Pd K[\bar {\alpha }] 2.112E−02 6.71E+01 7.71E+01 7.41E+01 1.29E+01 1.39E+01 1.47E+01 1.58E+01 1.66E+01
Rh K[\bar {\alpha }] 2.017E−02 7.55E+01 7.95E+01 1.38E+01 1.47E+01 1.58E+01 1.67E+01 1.79E+01 1.88E+01
Mo K[\beta _1] 1.961E−02 8.10E+01 1.38E+01 1.49E+01 1.58E+01 1.70E+01 1.80E+01 1.94E+01 2.02E+01
Mo K[\bar {\alpha }] 1.744E−02 1.77E+01 1.88E+01 2.04E+01 2.17E+01 2.33E+01 2.47E+01 2.65E+01 2.78E+01
Zn K[\beta _1] 9.572E−03 9.04E+01 9.65E+01 1.04E+02 1.10E+02 1.18E+02 1.25E+02 1.34E+02 1.40E+02
Cu K[\beta _1] 8.905E−03 1.10E+02 1.17E+02 1.26E+02 1.34E+02 1.44E+02 1.51E+02 1.63E+02 1.69E+02
Zn K[\bar {\alpha }] 8.631E−03 1.20E+02 1.27E+02 1.37E+02 1.46E+02 1.56E+02 1.65E+02 1.77E+02 1.84E+02
Ni K[\beta _1] 8.265E−03 1.34E+02 1.43E+02 1.54E+02 1.63E+02 1.75E+02 1.85E+02 1.98E+02 2.07E+02
Cu K[\bar {\alpha }] 8.041E−03 1.45E+02 1.54E+02 1.66E+02 1.76E+02 1.89E+02 1.99E+02 2.13E+02 2.22E+02
Co K[\beta _1] 7.649E−03 1.66E+02 1.76E+02 1.90E+02 2.01E+02 2.16E+02 2.27E+02 2.43E+02 2.53E+02
Ni K[\bar {\alpha }] 7.472E−03 1.76E+02 1.88E+02 2.02E+02 2.14E+02 2.29E+02 2.41E+02 2.59E+02 2.69E+02
Fe K[\beta _1] 7.058E−03 2.05E+02 2.19E+02 2.35E+02 2.49E+02 2.67E+02 2.81E+02 3.01E+02 3.13E+02
Co K[\bar {\alpha }] 6.925E−03 2.16E+02 2.30E+02 2.47E+02 2.62E+02 2.80E+02 2.95E+02 3.16E+02 3.29E+02
Mn K[\beta _1] 6.490E−03 2.57E+02 2.73E+02 2.94E+02 3.11E+02 3.33E+02 3.50E+02 3.75E+02 3.90E+02
Fe K[\bar {\alpha }] 6.400E−03 2.67E+02 2.84E+02 3.05E+02 3.23E+02 3.46E+02 3.63E+02 3.89E+02 4.05E+02
Cr K[\beta _1] 5.947E−03 3.25E+02 3.45E+02 3.70E+02 3.92E+02 4.20E+02 4.41E+02 4.72E+02 4.90E+02
Mn K[\bar {\alpha }] 5.895E 03 3.32E+02 3.53E+02 3.79E+02 4.01E+02 4.29E+02 4.51E+02 4.83E+02 5.02E+02
Cr K[\bar {\alpha }] 5.412E−03 4.16E+02 4.42E+02 4.74E+02 5.01E+02 5.36E+02 5.63E+02 6.02E+02 6.26E+02
Ti K[\beta _1] 4.932E−03 5.32E+02 5.65E+02 6.04E+02 6.39E+02 6.83E+02 7.16E+02 7.65E+02 7.95E+02
Ti K[\bar {\alpha }] 4.509E−03 6.71E+02 7.12E+02 7.61E+02 8.04E+02 8.60E+02 9.01E+02 9.61E+02 9.95E+02

RadiationEnergy (MeV)4950515253545556
IndiumTinAntimonyTelluriumIodineXenonCaesiumBarium
Ag K[\beta _1] 2.494E−02 1.13E+01 1.18E+01 1.25E+01 1.29E+01 1.40E+01 1.46E+01 1.56E+01 1.62E+01
Pd K[\beta _1] 2.382E−02 1.27E+01 1.34E+01 1.41E+01 1.46E+01 1.59E+01 1.65E+01 1.76E+01 1.83E+01
Rh K[\beta _1] 2.272E−02 1.45E+01 1.52E+01 1.60E+01 1.66E+01 1.80E+01 1.88E+01 2.00E+01 2.08E+01
Ag K[\bar {\alpha }] 2.210E−02 1.56E+01 1.64E+01 1.73E+01 1.79E+01 1.94E+01 2.02E+01 2.15E+01 2.24E+01
Pd K[\bar {\alpha }] 2.112E−02 1.76E+01 1.85E+01 1.96E+01 2.02E+01 2.19E+01 2.29E+01 2.43E+01 2.54E+01
Rh K[\bar {\alpha }] 2.017E−02 2.00E+01 2.10E+01 2.22E+01 2.29E+01 2.18E+01 2.27E+01 2.42E+01 2.52E+01
Mo K[\beta _1] 1.961E−02 2.16E+01 2.26E+01 2.39E+01 2.47E+01 2.68E+01 2.80E+01 2.98E+01 3.10E+01
Mo K[\bar {\alpha }] 1.744E−02 2.95E+01 3.10E+01 3.27E+01 3.38E+01 3.67E+01 3.82E+01 4.07E+01 4.23E+01
Zn K[\beta _1] 9.572E−03 1.48E+02 1.55E+02 1.64E+02 1.68E+02 1.82E+02 1.90E+02 2.01E+02 2.09E+02
Cu K[\beta _1] 8.905E−03 1.80E+02 1.88E+02 1.98E+02 2.04E+02 2.20E+02 2.29E+02 2.43E+02 2.52E+02
Zn K[\bar {\alpha }] 8.631E−03 1.95E+02 2.04E+02 2.15E+02 2.21E+02 2.39E+02 2.49E+02 2.63E+02 2.73E+02
Ni K[\beta _1] 8.265E−03 2.19E+02 2.29E+02 2.41E+02 2.48E+02 2.68E+02 2.78E+02 2.95E+02 3.06E+02
Cu K[\bar {\alpha }] 8.041E−03 2.36E+02 2.47E+02 2.59E+02 2.67E+02 2.88E+02 2.99E+02 3.17E+02 3.25E+02
Co K[\beta _1] 7.649E−03 2.69E+02 2.81E+02 2.96E+02 3.04E+02 3.30E+02 3.43E+02 3.63E+02 3.76E+02
Ni K[\bar {\alpha }] 7.472E−03 2.86E+02 2.99E+02 3.14E+02 3.23E+02 3.49E+02 3.62E+02 3.83E+02 3.96E+02
Fe K[\beta _1] 7.058E−03 3.32E+02 3.47E+02 3.65E+02 3.74E+02 4.08E+02 4.22E+02 4.46E+02 4.61E+02
Co K[\bar {\alpha }] 6.925E−03 3.49E+02 3.64E+02 3.83E+02 3.94E+02 4.25E+02 4.40E+02 4.65E+02 4.80E+02
Mn K[\beta _1] 6.490E−03 4.13E+02 4.31E+02 4.54E+02 4.66E+02 5.03E+02 5.20E+02 5.49E+02 5.66E+02
Fe K[\bar {\alpha }] 6.400E−03 4.28E+02 4.47E+02 4.71E+02 4.83E+02 5.22E+02 5.40E+02 5.69E+02 5.86E+02
Cr K[\beta _1] 5.947E−03 5.19E+02 5.42E+02 5.70E+02 5.85E+02 6.31E+02 6.52E+02 6.86E+02 6.45E+02
Mn K[\bar {\alpha }] 5.895E−03 5.31E+02 5.54E+02 5.82E+02 5.98E+02 6.45E+02 6.66E+02 7.00E+02 6.60E+02
Cr K[\bar {\alpha }] 5.412E−03 6.63E+02 6.91E+02 7.23E+02 7.40E+02 7.96E+02 7.21E+02 7.60E+02 5.70E+02
Ti K[\beta _1] 4.932E−03 8.41E+02 8.76E+02 9.15E+02 9.32E+02 1.00E+03 1.03E+03 2.60E+02 3.14E+02
Ti K[\bar {\alpha }] 4.509E−03 1.05E+03 1.09E+03 9.91E+02 7.51E+02 2.83E+02 2.65E+02 3.30E+02 3.34E+02

RadiationEnergy (MeV)5758596061626364
LanthanumCeriumPraseodymiumNeodymiumPromethiumSamariumEuropiumGadolinium
Ag K[\beta _1] 2.494E−02 1.72E+01 1.83E+01 1.95E+01 2.04E+01 2.17E+01 2.23E+01 2.35E+01 2.42E+01
Pd K[\beta _1] 2.382E−02 1.95E+01 2.07E+01 2.20E+01 2.30E+01 2.45E+01 2.52E+01 2.66E+01 2.74E+01
Rh K[\beta _1] 2.272E−02 2.21E+01 2.35E+01 2.50E+01 2.61E+01 2.78E+01 2.86E+01 3.01E+01 3.10E+01
Ag K[\bar {\alpha }] 2.210E−02 2.38E+01 2.53E+01 2.69E+01 2.81E+01 2.99E+01 3.08E+01 3.24E+01 3.34E+01
Pd K[\bar {\alpha }] 2.112E−02 2.69E+01 2.86E+01 3.04E+01 3.18E+01 3.38E+01 3.48E+01 3.66E+01 3.77E+01
Rh K[\bar {\alpha }] 2.017E−02 3.05E+01 3.24E+01 3.45E+01 3.60E+01 3.83E+01 3.94E+01 4.15E+01 4.27E+01
Mo K[\beta _1] 1.961E−02 3.29E+01 3.49E+01 3.72E+01 3.88E+01 4.13E+01 4.24E+01 4.47E+01 4.60E+01
Mo K[\bar {\alpha }] 1.744E−02 4.49E+01 4.77E+01 5.07E+01 5.30E+01 5.63E+01 5.78E+01 6.09E+01 6.26E+01
Zn K[\beta _1] 9.572E−03 2.21E+02 2.33E+02 2.47E+02 2.57E+02 2.73E+02 2.79E+02 2.93E+02 3.00E+02
Cu K[\beta _1] 8.905E−03 2.66E+02 2.82E+02 2.99E+02 3.10E+02 3.28E+02 3.35E+02 3.52E+02 3.60E+02
Zn K[\bar {\alpha }] 8.631E−03 2.89E+02 3.06E+02 3.24E+02 3.36E+02 3.55E+02 3.63E+02 3.80E+02 3.89E+02
Ni K[\beta _1] 8.265E−03 3.24E+02 3.43E+02 3.63E+02 3.76E+02 3.97E+02 4.05E+02 4.24E+02 4.33E+02
Cu K[\bar {\alpha }] 8.041E−03 3.48E+02 3.68E+02 3.90E+02 4.04E+02 4.26E+02 4.34E+02 4.34E+02 4.03E+02
Co K[\beta _1] 7.649E−03 3.95E+02 4.17E+02 4.41E+02 4.57E+02 4.82E+02 3.54E+02 4.80E+02 3.35E+02
Ni K[\bar {\alpha }] 7.472E−03 4.19E+02 4.42E+02 4.68E+02 4.84E+02 5.11E+02 3.71E+02 3.75E+02 3.56E+02
Fe K[\beta _1] 7.058E−03 4.83E+02 5.10E+02 5.39E+02 4.92E+02 5.88E+02 1.63E+02 4.08E+02 1.53E+02
Co K[\bar {\alpha }] 6.925E−03 5.07E+02 5.35E+02 5.65E+02 5.05E+02 4.00E+02 1.76E+02 4.19E+02 1.61E+02
Mn K[\beta _1] 6.490E−03 5.97E+02 5.47E+02 6.16E+02 4.39E+02 4.68E+02 1.66E+02 1.95E+02 1.89E+02
Fe K[\bar {\alpha }] 6.400E−03 6.18E+02 5.61E+02 4.48E+02 4.55E+02 1.94E+02 2.04E+02 2.03E+02 1.95E+02
Cr K[\beta _1] 5.947E−03 7.44E+02 4.94E+02 1.88E+02 1.98E+02 2.32E+02 2.21E+02 2.44E+02 2.35E+02
Mn K[\bar {\alpha }] 5.895E−03 7.60E+02 5.12E+02 1.93E+02 2.03E+02 2.37E+02 2.25E+02 2.49E+02 2.41E+02
Cr K[\bar {\alpha }] 5.412E−03 2.25E+02 2.38E+02 2.38E+02 2.51E+02 2.94E+02 2.79E+02 3.09E+02 2.98E+02
Ti K[\beta _1] 4.932E−03 2.84E+02 3.00E+02 3.00E+02 3.14E+02 3.69E+02 3.50E+02 3.90E+02 3.74E+02
Ti K[\bar {\alpha }] 4.509E−03 3.55E+02 3.57E+02 3.75E+02 3.97E+02 4.62E+02 4.35E+02 4.88E+02 4.69E+02

RadiationEnergy (MeV)6566676869707172
TerbiumDysprosiumHolmiumErbiumThuliumYtterbiumLutetiumHafnium
Ag K[\beta _1] 2.494E−02 2.55E+01 2.65E+01 2.77E+01 2.90E+01 3.04E+01 3.14E+01 3.28E+01 3.40E+01
Pd K[\beta _1] 2.382E−02 2.88E+01 2.99E+01 3.13E+01 3.27E+01 3.43E+01 3.54E+01 3.71E+01 3.84E+01
Rh K[\beta _1] 2.272E−02 3.26E+01 3.39E+01 3.54E+01 3.71E+01 3.89E+01 4.01E+01 4.20E+01 4.35E+01
Ag K[\bar {\alpha }] 2.210E−02 3.51E+01 3.65E+01 3.81E+01 3.99E+01 4.18E+01 4.32E+01 4.51E+01 4.67E+01
Pd K[\bar {\alpha }] 2.112E−02 3.96E+01 4.12E+01 4.30E+01 4.50E+01 4.71E+01 4.87E+01 5.09E+01 5.27E+01
Rh K[\bar {\alpha }] 2.017E−02 4.49E+01 4.66E+01 4.87E+01 5.09E+01 5.33E+01 5.50E+01 5.75E+01 5.95E+01
Mo K[\beta _1] 1.961E−02 4.83E+01 5.02E+01 5.24E+01 5.48E+01 5.74E+01 5.93E+01 6.19E+01 6.41E+01
Mo K[\bar {\alpha }] 1.744E−02 6.58E+01 6.83E+01 7.13E+01 7.44E+01 7.79E+01 8.04E+01 8.40E+01 8.69E+01
Zn K[\beta _1] 9.572E−03 3.14E+02 3.24E+02 3.36E+02 3.49E+02 3.65E+02 3.75E+02 3.91E+02 1.00E+02
Cu K[\beta _1] 8.905E−03 3.76E+02 3.87E+02 4.02E+02 4.17E+02 1.08E+02 1.08E+02 1.21E+02 1.20E+02
Zn K[\bar {\alpha }] 8.631E−03 4.06E+02 4.19E+02 3.98E+02 2.87E+02 1.17E+02 1.17E+02 1.31E+02 1.30E+02
Ni K[\beta _1] 8.265E−03 4.52E+02 3.36E+02 4.44E+02 1.23E+02 1.31E+02 1.31E+02 1.46E+02 1.45E+02
Cu K[\bar {\alpha }] 8.041E−03 3.21E+02 3.62E+02 1.29E+02 1.32E+02 1.40E+02 1.42E+02 1.56E+02 1.55E+02
Co K[\beta _1] 7.649E−03 3.60E+02 1.38E+02 1.46E+02 1.49E+02 1.59E+02 1.59E+02 1.78E+02 1.76E+02
Ni K[\bar {\alpha }] 7.472E−03 1.49E+02 1.46E+02 1.55E+02 1.58E+02 1.69E+02 1.69E+02 1.89E+02 1.87E+02
Fe K[\beta _1] 7.058E−03 1.71E+02 1.68E+02 1.78E+02 1.82E+02 1.96E+02 1.96E+02 2.18E+02 2.16E+02
Co K[\bar {\alpha }] 6.925E−03 1.80E+02 1.76E+02 1.87E+02 1.91E+02 2.06E+02 2.06E+02 2.29E+02 2.27E+02
Mn K[\beta _1] 6.490E−03 2.11E+02 2.07E+02 2.20E+02 2.24E+02 2.43E+02 2.44E+02 2.70E+02 2.67E+02
Fe K[\bar {\alpha }] 6.400E−03 2.19E+02 2.14E+02 2.28E+02 2.32E+02 2.53E+02 2.51E+02 2.80E+02 2.77E+02
Cr K[\beta _1] 5.947E−03 2.63E+02 2.57E+02 2.72E+02 2.78E+02 3.05E+02 3.04E+02 3.39E+02 3.34E+02
Mn K[\bar {\alpha }] 5.895E−03 2.69E+02 2.62E+02 2.80E+02 2.85E+02 3.12E+02 3.11E+02 3.47E+02 3.41E+02
Cr K[\bar {\alpha }] 5.412E−03 3.32E+02 3.25E+02 3.47E+02 3.52E+02 3.86E+02 3.87E+02 4.31E+02 4.25E+02
Ti K[\beta _1] 4.932E−03 4.19E+02 4.10E+02 4.38E+02 4.43E+02 4.94E+02 4.92E+02 5.47E+02 5.39E+02
Ti K[\bar {\alpha }] 4.509E−03 5.24E+02 5.15E+02 5.47E+02 5.54E+02 6.21E+02 6.19E+02 6.88E+02 6.78E+02

RadiationEnergy (MeV)7374757677787980
TantalumTungstenRheniumOsmiumIridiumPlatinumGoldMercury
Ag K[\beta _1] 2.494E−02 3.54E+01 3.68E+01 3.83E+01 3.95E+01 4.11E+01 4.26E+01 4.44E+01 4.58E+01
Pd K[\beta _1] 2.382E−02 4.00E+01 4.15E+01 4.32E+01 4.45E+01 4.64E+01 4.80E+01 5.00E+01 5.16E+01
Rh K[\beta _1] 2.272E−02 4.53E+01 4.70E+01 4.89E+01 5.04E+01 5.24E+01 5.43E+01 5.65E+01 5.83E+01
Ag K[\bar {\alpha }] 2.210E−02 4.87E+01 5.05E+01 5.25E+01 5.41E+01 5.63E+01 5.83E+01 6.07E+01 6.26E+01
Pd K[\bar {\alpha }] 2.112E−02 5.48E+01 5.69E+01 5.92E+01 6.10E+01 6.34E+01 6.57E+01 6.83E+01 7.04E+01
Rh K[\bar {\alpha }] 2.017E−02 6.20E+01 6.43E+01 6.69E+01 6.89E+01 7.16E+01 7.41E+01 7.71E+01 7.95E+01
Mo K[\beta _1] 1.961E−02 6.67E+01 6.92E+01 7.19E+01 7.41E+01 7.70E+01 7.97E+01 8.29E+01 8.54E+01
Mo K[\bar {\alpha }] 1.744E−02 9.04E+01 9.38E+01 9.74E+01 1.00E+02 1.04E+02 1.07E+02 1.12E+02 1.15E+02
Zn K[\beta _1] 9.572E−03 1.02E+02 1.08E+02 1.19E+02 1.18E+02 1.23E+02 1.21E+02 1.30E+02 1.16E+02
Cu K[\beta _1] 8.905E−03 1.22E+02 1.30E+02 1.43E+02 1.42E+02 1.48E+02 1.45E+02 1.55E+02 1.41E+02
Zn K[\bar {\alpha }] 8.631E−03 1.32E+02 1.41E+02 1.55E+02 1.54E+02 1.60E+02 1.57E+02 1.68E+02 1.54E+02
Ni K[\beta _1] 8.265E−03 1.47E+02 1.57E+02 1.72E+02 1.71E+02 1.78E+02 1.75E+02 1.88E+02 1.74E+02
Cu K[\bar {\alpha }] 8.041E−03 1.58E+02 1.68E+02 1.87E+02 1.84E+02 1.91E+02 1.88E+02 2.01E+02 1.88E+02
Co K[\beta _1] 7.649E−03 1.79E+02 1.91E+02 2.09E+02 2.09E+02 2.16E+02 2.14E+02 2.29E+02 2.16E+02
Ni K[\bar {\alpha }] 7.472E−03 1.90E+02 2.03E+02 2.22E+02 2.21E+02 2.30E+02 2.27E+02 2.43E+02 2.30E+02
Fe K[\beta _1] 7.058E−03 2.20E+02 2.34E+02 2.57E+02 2.55E+02 2.65E+02 2.61E+02 2.79E+02 2.60E+02
Co K[\bar {\alpha }] 6.925E−03 2.31E+02 2.46E+02 2.68E+02 2.68E+02 2.78E+02 2.76E+02 2.95E+02 2.73E+02
Mn K[\beta _1] 6.490E−03 2.73E+02 2.88E+02 3.16E+02 3.14E+02 3.30E+02 3.25E+02 3.48E+02 3.27E+02
Fe K[\bar {\alpha }] 6.400E−03 2.83E+02 3.01E+02 3.27E+02 3.27E+02 3.40E+02 3.57E+02 3.61E+02 3.39E+02
Cr K[\beta _1] 5.947E−03 3.39E+02 3.61E+02 3.94E+02 3.92E+02 4.11E+02 4.23E+02 4.34E+02 4.16E+02
Mn K[\bar {\alpha }] 5.895E−03 3.46E+02 3.69E+02 4.05E+02 4.03E+02 4.18E+02 4.34E+02 4.45E+02 4.27E+02
Cr K[\bar {\alpha }] 5.412E−03 4.32E+02 4.57E+02 5.01E+02 4.99E+02 5.20E+02 5.41E+02 5.51E+02 5.41E+02
Ti K[\beta _1] 4.932E−03 5.46E+02 5.79E+02 6.33E+02 6.31E+02 6.59E+02 6.83E+02 6.99E+02 6.99E+02
Ti K[\bar {\alpha }] 4.509E−03 6.85E+02 7.25E+02 7.94E+02 7.92E+02 8.26E+02 8.19E+02 8.76E+02 8.97E+02

RadiationEnergy (MeV)8182838485868788
ThalliumLeadBismuthPoloniumAstatineRadonFranciumRadium
Ag K[\beta _1] 2.494E−02 4.72E+01 4.88E+01 5.06E+01 5.30E+01 5.51E+01 5.45E+01 5.67E+01 5.84E+01
Pd K[\beta _1] 2.382E−02 5.31E+01 5.49E+01 5.70E+01 5.96E+01 6.20E+01 6.12E+01 6.37E+01 6.56E+01
Rh K[\beta _1] 2.272E−02 6.00E+01 6.20E+01 6.44E+01 6.73E+01 7.00E+01 6.90E+01 7.18E+01 7.40E+01
Ag K[\bar {\alpha }] 2.210E−02 6.45E+01 6.66E+01 6.91E+01 7.23E+01 7.51E+01 7.21E+01 7.70E+01 7.93E+01
Pd K[\bar {\alpha }] 2.112E−02 7.25E+01 7.49E+01 7.77E+01 8.12E+01 8.43E+01 8.32E+01 8.64E+01 8.90E+01
Rh K[\bar {\alpha }] 2.017E−02 8.18E+01 8.45E+01 8.76E+01 9.15E+01 9.50E+01 9.36E+01 9.72E+01 1.00E+02
Mo K[\beta _1] 1.961E−02 8.79E+01 9.08E+01 9.41E+01 9.83E+01 1.02E+02 1.01E+02 1.04E+02 1.08E+01
Mo K[\bar {\alpha }] 1.744E−02 1.18E+02 1.22E+02 1.26E+02 1.32E+02 1.17E+02 1.08E+02 8.70E+01 8.80E+01
Zn K[\beta _1] 9.572E−03 1.45E+02 1.51E+02 1.57E+02 1.63E+02 1.71E+02 1.71E+02 1.77E+02 1.75E+02
Cu K[\beta _1] 8.905E−03 1.75E+02 1.81E+02 1.88E+02 1.96E+02 1.86E+02 2.05E+02 2.13E+02 2.10E+02
Zn K[\bar {\alpha }] 8.631E−03 1.89E+02 1.96E+02 2.04E+02 2.12E+02 2.07E+02 2.23E+02 2.30E+02 2.28E+02
Ni K[\beta _1] 8.265E−03 2.11E+02 2.16E+02 2.28E+02 2.37E+02 2.31E+02 2.49E+02 2.57E+02 2.54E+02
Cu K[\bar {\alpha }] 8.041E−03 2.26E+02 2.35E+02 2.44E+02 2.54E+02 2.48E+02 2.67E+02 2.77E+02 2.73E+02
Co K[\beta _1] 7.649E−03 2.57E+02 2.67E+02 2.76E+02 2.88E+02 2.82E+02 3.04E+02 3.12E+02 3.10E+02
Ni K[\bar {\alpha }] 7.472E−03 2.71E+02 2.83E+02 2.95E+02 3.05E+02 2.99E+02 3.21E+02 3.32E+02 3.29E+02
Fe K[\beta _1] 7.058E−03 3.14E+02 3.27E+02 3.39E+02 3.54E+02 3.45E+02 3.73E+02 3.84E+02 3.80E+02
Co K[\bar {\alpha }] 6.925E−03 3.31E+02 3.43E+02 3.55E+02 3.70E+02 3.63E+02 3.92E+02 4.03E+02 3.98E+02
Mn K[\beta _1] 6.490E−03 3.90E+02 4.06E+02 4.21E+02 4.35E+02 4.26E+02 4.60E+02 4.77E+02 4.70E+02
Fe K[\bar {\alpha }] 6.400E−03 4.03E+02 4.20E+02 4.34E+02 4.52E+02 4.44E+02 4.77E+02 4.93E+02 4.87E+02
Cr K[\beta _1] 5.947E−03 4.87E+02 5.07E+02 5.24E+02 5.44E+02 5.33E+02 5.76E+02 5.97E+02 5.85E+02
Mn K[\bar {\alpha }] 5.895E−03 5.00E+02 5.18E+02 5.35E+02 5.58E+02 5.45E+02 5.89E+02 6.02E+02 5.99E+02
Cr K[\bar {\alpha }] 5.412E−03 5.97E+02 6.43E+02 6.66E+02 6.91E+02 6.80E+02 7.34E+02 7.58E+02 7.43E+02
Ti K[\beta _1] 4.932E−03 7.15E+02 8.15E+02 8.44E+02 8.30E+02 8.60E+02 9.32E+02 9.61E+02 9.41E+02
Ti K[\bar {\alpha }] 4.509E−03 9.89E+02 1.03E+03 1.06E+03 1.10E+03 1.08E+03 1.18E+03 1.21E+03 1.33E+03

RadiationEnergy (MeV)8990919293949596
ActiniumThoriumProtactiniumUraniumNeptuniumPlutoniumAmericiumCurium
Ag K[\beta _1] 2.494E−02 6.07E+01 6.19E+01 6.48E+01 6.55E+01 6.84E+01 7.05E+01 7.20E+01 7.35E+01
Pd K[\beta _1] 2.382E−02 6.82E+01 6.95E+01 7.27E+01 7.35E+01 7.67E+01 7.91E+01 8.08E+01 8.24E+01
Rh K[\beta _1] 2.272E−02 7.68E+01 7.82E+01 8.19E+01 8.27E+01 8.63E+01 8.89E+01 9.08E+01 6.00E+01
Ag K[\bar {\alpha }] 2.210E−02 8.24E+01 8.39E+01 8.78E+01 8.86E+01 9.25E+01 5.60E+01 5.95E+01 6.43E+01
Pd K[\bar {\alpha }] 2.112E−02 9.24E+01 9.41E+01 9.84E+01 9.93E+01 1.04E+02 1.07E+02 1.09E+02 1.11E+02
Rh K[\bar {\alpha }] 2.017E−02 1.04E+02 1.06E+02 1.11E+02 1.12E+02 1.16E+02 1.20E+02 1.22E+02 1.10E+02
Mo K[\beta _1] 1.961E−02 1.10E+02 9.87E+01 1.19E+02 7.49E+01 1.25E+02 1.29E+02 1.31E+02 1.34E+02
Mo K[\bar {\alpha }] 1.744E−02 9.08E+01 9.65E+01 1.01E+02 1.02E+02 4.22E+01 3.99E+01 4.81E+01 4.90E+01
Zn K[\beta _1] 9.572E−03 2.49E+02 1.70E+02 1.73E+02 1.85E+02 1.90E+02 1.80E+02 1.89E+02 1.94E+02
Cu K[\beta _1] 8.905E−03 2.85E+02 2.19E+02 2.08E+02 2.22E+02 2.27E+02 2.16E+02 2.27E+02 2.32E+02
Zn K[\bar {\alpha }] 8.631E−03 3.03E+02 2.55E+02 2.25E+02 2.40E+02 2.46E+02 2.34E+02 2.41E+02 2.51E+02
Ni K[\beta _1] 8.265E−03 3.09E+02 2.85E+02 2.52E+02 2.68E+02 2.75E+02 2.62E+02 2.73E+02 2.80E+02
Cu K[\bar {\alpha }] 8.041E−03 3.17E+02 3.06E+02 2.71E+02 2.88E+02 3.14E+02 2.80E+02 3.22E+02 3.38E+02
Co K[\beta _1] 7.649E−03 3.81E+02 3.48E+02 3.06E+02 3.26E+02 3.35E+02 3.17E+02 3.33E+02 3.43E+02
Ni K[\bar {\alpha }] 7.472E−03 3.99E+02 3.69E+02 3.25E+02 3.47E+02 3.55E+02 3.36E+02 3.52E+02 3.60E+02
Fe K[\beta _1] 7.058E−03 4.44E+02 3.89E+02 3.75E+02 4.00E+02 4.10E+02 3.89E+02 4.07E+02 4.21E+02
Co K[\bar {\alpha }] 6.925E−03 4.61E+02 4.06E+02 3.94E+02 4.20E+02 4.30E+02 4.08E+02 4.26E+02 4.37E+02
Mn K[\beta _1] 6.490E−03 5.21E+02 4.46E+02 4.65E+02 4.96E+02 5.05E+02 4.08E+02 5.03E+02 5.15E+02
Fe K[\bar {\alpha }] 6.400E−03 5.30E+02 4.85E+02 4.82E+02 5.28E+02 5.52E+02 4.98E+02 5.81E+02 5.90E+02
Cr K[\beta _1] 5.947E−03 6.18E+02 5.09E+02 5.82E+02 6.17E+02 6.30E+02 6.00E+02 6.27E+02 6.40E+02
Mn K[\bar {\alpha }] 5.895E−03 6.29E+02 6.23E+02 5.93E+02 6.32E+02 6.45E+02 6.12E+02 6.42E+02 6.55E+02
Cr K[\bar {\alpha }] 5.412E−03 7.39E+02 7.68E+02 7.38E+02 7.66E+02 8.00E+02 7.60E+02 7.95E+02 8.12E+02
Ti K[\beta _1] 4.932E−03 8.83E+02 9.78E+02 9.83E+02 9.66E+02 1.01E+03 9.62E+02 1.03E+03 1.03E+03
Ti K[\bar {\alpha }] 4.509E−03 1.05E+03 1.23E+03 1.24E+03 1.23E+03 9.65E+02 9.00E+02 9.55E+02 9.84E+02

RadiationEnergy (MeV)9798
BerkeliumCalifornium
Ag K[\beta _1] 2.494E−02 6.66E+01 7.35E+01
Pd K[\beta _1] 2.382E−02 7.52E+01 8.24E+01
Rh K[\beta _1] 2.272E−02 8.51E+01 9.26E+01
Ag K[\bar {\alpha }] 2.210E−02 6.10E+01 6.92E+01
Pd K[\bar {\alpha }] 2.112E−02 1.03E+02 1.11E+02
Rh K[\bar {\alpha }] 2.017E−02 1.02E+02 1.25E+02
Mo K[\beta _1] 1.961E−02 1.25E+02 1.34E+02
Mo K[\bar {\alpha }] 1.744E−02 4.90E+01 5.00E+01
Zn K[\beta _1] 9.572E−03 1.86E+02 2.08E+02
Cu K[\beta _1] 8.905E−03 2.26E+02 2.49E+02
Zn K[\bar{\alpha}] 8.631E−03 2.46E+02 2.70E+02
Ni K[\beta _1] 8.265E−03 2.77E+02 3.01E+02
Cu K[\bar {\alpha }] 8.041E−03 3.52E+02 3.60E+02
Co K[\beta _1] 7.649E−03 3.57E+02 3.66E+02
Ni K[\bar {\alpha }] 7.472E−03 3.62E+02 3.86E+02
Fe K[\beta _1] 7.058E−03 4.22E+02 4.48E+02
Co K[\bar {\alpha }] 6.925E−03 4.43E+02 4.69E+02
Mn K[\beta _1] 6.490E−03 5.26E+02 5.52E+02
Fe K[\bar {\alpha }] 6.400E−03 5.92E+02 6.07E+02
Cr K[\beta _1] 5.947E−03 6.64E+02 6.87E+02
Mn K[\bar {\alpha }] 5.895E−03 6.78E+02 7.03E+02
Cr K[\bar {\alpha }] 5.412E−03 8.52E+02 8.71E+02
Ti K[\beta _1] 4.932E−03 1.09E+03 1.10E+03
Ti K[\bar {\alpha }] 4.509E−03 1.04E+03 1.05E+03

Users of these tables should be aware of three important facts.

  • (i) The values given in the tables are derived for the case of isolated atoms, and cooperative effects may become important in condensed phases (Section 4.2.3[link]).

  • (ii) The values are based solely on theoretical calculations.

  • (iii) The limits to the reliability of the data when compared with experimental values are shown in Fig. 4.2.4.4[link].

The linear attenuation coefficient [\mu_l] in units of cm−1 can be defined operationally as [\mu _l= \bigg({\rm ln} {I_o\over I}\bigg)\bigg/t \eqno (4.2.4.1)]from the exponential attenuation relationship [{I \over I_0} = \exp (- \mu_lt) \eqno (4.2.4.2)]in which an idealized plane-parallel slab of material is interposed normally into a parallel beam of monoenergetic X-rays initially of intensity [I_0], attenuated by the interposed slab to a reduced intensity I.

The linear attenuation coefficient [\mu_l] for multi-element substances may be obtained in two ways. Through the mass absorption coefficients, we have [\mu _l = \rho\textstyle \sum\limits_i g_i (\mu _m)_i, \eqno (4.2.4.3)]where [g_i] is the mass fraction of the element i for which the mass attenuation coefficient [(\mu_m)_i] is in units of cm2 g−1, and ρ is the density of the material in units of g cm−3. The summation is over all the constituent elements. The mass attenuation coefficient [\mu _m] is sometimes written as [(\mu _l/\rho).]

For a crystal with unit-cell volume [V_c], [\mu _l = {1 \over V_c} \sum _i \sigma _i, \eqno (4.2.4.4)]where the summation is over all the atoms in the cell. If [\sigma _i] is in barns/atom and [V_c] is in Å3, then [\mu_l] is in cm−1.

These tables list total interaction cross sections and mass attenuation coefficients for isolated atoms calculated for characteristic X-ray photon emissions ranging from Ti Kα to Ag Kβ.

The total interaction cross section is defined by [\sigma = \sigma _{\rm pe} + \sigma _R + \sigma _C, \eqno (4.2.4.5)]where [\sigma _{\rm pe}] is the photo-effect cross section; [\sigma _R] is the Rayleigh (unmodified, elastic) cross section; [\sigma _C] is the Compton (modified, inelastic) cross section.

The reader's attention is drawn to the fact that in the neighbourhood of an absorption edge for aggregations of atoms significant deviations may be found because of cooperative effects (XAFS and XANES). A discussion of these effects is given in Section 4.2.3[link].

4.2.4.2. Sources of information

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4.2.4.2.1. Theoretical photo-effect data: σpe

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Of the many theoretical data sets in existence, those of Storm & Israel (1970[link]), Cromer & Liberman (1970[link]), and Scofield (1973[link]) have often been used as bench marks against which both experimental and theoretical data have been compared. In particular, theoretical data produced using the S-matrix approach have been compared with these values. See, for example, Kissel, Roy & Pratt (1980[link]). Some indication of the extent to which agreement exists between the different theoretical data sets is given in §4.2.6.2.4[link] (Tables 4.2.6.3[link](b) and 4.2.6.5[link]). These tables show that the values of [f'(\omega,0)], which is proportional to σ, calculated using modern relativistic quantum mechanics, agree to better than 1%. It has also been demonstrated by Creagh & Hubbell (1987[link], 1990[link]) in their analysis of the results of the IUCr X-ray Attenuation Project that there appears to be no rational basis for preferring one of these data sets over the other.

These tables do not list separately photo-effect cross sections. However, should these be required, the data can be found using Table 4.2.6.8[link]. The cross section in barns/atom is related to [f'(\omega,0)] expressed in electrons/atom by σ = 5636λ[\,f'(\omega, 0),] where λ is expressed in ångströms.

The values for [\sigma_{\rm pe}] used in this compilation are derived from recent tabulations based on relativistic Hartree–Fock–Dirac–Slater calculations by Creagh. The extent to which this data set differs from other theoretical and experimental data sets has been discussed by Creagh (1990[link]).

4.2.4.2.2. Theoretical Rayleigh scattering data: σR

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If each of the atoms gives rise to scattering in which momentum but not energy changes occur, and if each of the atoms can be considered to scatter as if it were an isolated atom, the cross section may be written as [\sigma _R = \pi r ^2_e \textstyle\int\limits^1_{-1} (1 + \cos ^2 \varphi) \,f^2(q,Z) \,{\rm d} (\cos \varphi), \eqno (4.2.4.6)]where

  • [r_e] is the classical radius of the electron;

  • [\varphi] is the angle of scattering ([=2 \theta] if [\theta] is the Bragg angle);

  • [2 \pi \,{\rm d} (\cos \varphi)] is the solid angle between cones with angles [\varphi] and [\varphi + {\rm d} \varphi];

  • [f(q,Z)] is the atomic scattering factor as defined by Cromer & Waber (1974[link]);

  • q is [ [\sin (\varphi /2) / \lambda],] the momentum transfer parameter. Here λ is expressed in ångströms.

Reliable tables of f(q, Z) exist and have been reviewed recently by Kane, Kissel, Pratt & Roy (1986[link]). The most recent schematic tabulations of f(q, Z) are those of Hubbell & Øverbø (1979[link]) and Schaupp et al. (1983[link]). The data used in these tables have been derived from the tabulation for q = 0.02 to 109 Å−1, for all Z's from 1 to 100 by Hubbell & Øverbø (1979[link]) based on the exact formula of Pirenne (1946[link]) for H, and relativistic calculations by Doyle & Turner (1968[link]), Cromer & Waber (1974[link]), Øverbø (1977[link], 1978[link]), and high-q extensions using the Bethe–Levinger expression in Levinger (1952[link]).

As mentioned in Creagh & Hubbell (1987[link]), the atoms in highly ordered single crystals do not scatter as though they are isolated atoms. Rather, cooperative effects become important. In this case, the Rayleigh scattering cross section must be replaced by two cross sections:

  • the Laue–Bragg cross section [\sigma _{\rm LB}],

  • and the thermal diffuse scattering cross section [\sigma _{\rm TD}].

That is, [\sigma _R] is replaced by [\sigma _{\rm LB} + \sigma _{\rm TD}].

These effects are discussed elsewhere (Subsection 4.2.3.2[link]). Briefly, [\sigma _{\rm LB} = (r^2_e \lambda ^2 / 2 NV_c) \textstyle\sum\limits _H [C_p md | F | {}^2 \exp (-2M)]_H. \eqno (4.2.4.7)]In equation (4.2.4.7)[link], which is due to De Marco & Suortti (1971[link]),

  • [C_p= \textstyle {1 \over 2}(1+ \cos ^2 \varphi)];

  • [d_H] is the spacing of the (hkl) planes in the crystal;

  • [m_H] is the multiplicity of the hkl Bragg reflection;

  • [F_H] is the geometrical structure factor for the crystal structure that contains N atoms in a cell of volume [V_c];

  • [\exp (-2M)_H] is the Debye–Waller temperature factor.

It is assumed that the total thermal diffuse scattering is equal to the scattering lost from Laue–Bragg scattering because of thermal vibrations. [\sigma _{\rm TD} = (r^2_e \lambda ^2/2NV_c) \textstyle\sum\limits _H \{ C_p md | F | {}^2 [1- \exp (-2 M)] \} _H. \eqno (4.2.4.8)]This equation is not in a convenient form for computation and the alternative formalism presented by Sano, Ohtaka & Ohtsuki (1969[link]) is often used in calculations. In this formalism, [\sigma _{\rm TD}= 2 \pi r ^2 _e \textstyle\int \limits^1 _{-1} C _p\,f^2 (q,Z) \{ 1 - \exp [-2M (q)] \} \,{\rm d} (\cos \varphi). \eqno (4.2.4.9)]

The values of f(q, Z) are those of Cromer & Waber (1974[link]).

Cross sections calculated using equation (4.2.4.8)[link] tend to oscillate at low energy and this corresponds to the inclusion of Bragg peaks in the summation or integration. Eventually, these oscillations abate and [\sigma _{\rm TD}] becomes a smoothly varying function of energy.

Creagh & Hubbell (1987[link]) and Creagh (1987a[link]) have stressed that, before cross sections are calculated for a given ensemble of atoms, care should be taken to ascertain whether single-atom or single-crystal scattering is appropriate for that ensemble.

4.2.4.2.3. Theoretical Compton scattering data: σC

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The bound-electron Compton scattering cross section is given by [\eqalignno{ \sigma _C = {}&\pi r \,^2_e \textstyle\int\limits^1_{-1} [1 + k (1 - \cos \varphi)] ^{-2}\cr &\times \{ + \cos ^2 \varphi + k ^2 (1 - \cos \varphi) ^2\cr &\times [1 + k (1 - \cos \varphi)] ^{-1} \} I (q,z)\, {\rm d} (\cos \varphi). &(4.2.4.10)}]Here [k = \hbar \omega /mc^2] and [I (q, z)] is the incoherent scattering intensity expressed in electron units. The other symbols have the meanings defined in §§4.2.4.2.1[link] and 4.2.4.2.2[link].

Values of [\sigma _C] incorporated into the tables of total cross section σ have been computed using the incoherent scattering intensities from the tabulation by Hubbell et al. (1975[link]) based on the calculations by Cromer & Mann (1967[link]) and Cromer (1969[link]).

4.2.4.3. Comparison between theoretical and experimental data sets

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Saloman & Hubbell (1986[link]) and Saloman et al. (1988[link]) have published an extensive comparison of the experimental database with the theoretical values of Scofield (1973[link], 1986[link]) for photon energies between 0.1 and 100 keV. Some examples taken from Saloman & Hubbell (1986[link]) are shown in Figs. 4.2.4.1[link] , 4.2.4.2[link] , and 4.2.4.3[link] .

[Figure 4.2.4.1]

Figure 4.2.4.1 | top | pdf |

Agreement between theory and experiment for oxygen (Z = 8) in the `soft' X-ray region. The solid line is for the Scofield (1973[link]) values without renormalization and the dotted line is for the semi-empirical data of Henke et al. (1982[link]).

[Figure 4.2.4.2]

Figure 4.2.4.2 | top | pdf |

The total cross section for silicon (Z = 14) compared with the unrenormalized Scofield values. The measured and theoretical attenuation coefficients show systematic differences of several percent for the photon energy range 10 to 100 keV.

[Figure 4.2.4.3]

Figure 4.2.4.3 | top | pdf |

The total cross section for uranium (Z = 92): The theoretical values (solid line) are partially obscured by the high density of available measurements. Deviations of the measured values from the theoretical predictions are mostly of the order of 5%, although a few data sets deviate by more than 30%.

Comparisons between theory and experiment exist for about 80 elements and space does not permit reproduction of all the available information. This information has been summarized in Fig. 4.2.4.4[link]. Superimposed on the Periodic Table of the elements are two sets of data. The upper set corresponds to the average percent deviation between experiment and theory for the photon energy range 10 to 100 keV. The lower set corresponds to the average percent deviation between experiment and theory for the photon energy range 1 to 10 keV. An upwards pointing arrow [\uparrow] means that [(\sigma _{\exp}- \sigma _{\rm theor}) \,\gt \, 0] . No arrow implies that [(\sigma _{\exp} - \sigma _{\rm theor})=0.] A downwards pointing arrow [\downarrow] means that [(\sigma _{\exp} - \sigma _{\rm theor}) \lt 0.] An asterisk means no experimental data set was available.

[Figure 4.2.4.4]

Figure 4.2.4.4 | top | pdf |

Comparison between this tabulation and experimental data contained in Saloman & Hubbell (1986[link]). The upper set corresponds to the average percent deviation between the experimental data and this tabulation for the energy range 10 to 100 keV. The lower set corresponds to the energy range 1 to 10 keV. For explanation of symbols see text.

For example: for tin (Z = 50), the experimental data are on average 5% higher than the theoretical predictions for the range of photon energies from 10 to 100 keV. For the range 1 to 10 keV, the experimental data are on average 7% higher than the theoretical predictions.

Fig. 4.2.4.4[link] is given as a rapid means of comparing theory and experiment. For more detailed information, see Saloman & Hubbell (1986[link]), Saloman et al. (1988[link]), and Creagh (1990[link]).

4.2.4.4. Uncertainty in the data tables

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It is not possible to generalize on the accuracy of the experimental data sets. Creagh & Hubbell (1987[link]) have shown that many experiments for which the precision quoted by the author is high differ from other accurate measurements by a considerable amount. It must be stressed that the experimental apparatus has to be chosen so that it is appropriate for the atomic system being investigated. Details concerning the proper choice of measuring system are given in Section 4.2.3[link]. Within about 200 eV of an absorption edge, deviations of up to 200% may be observed between theory and experiment. This is the region in which XAFS and XANES oscillations occur.

With respect to the theoretical data: the detailed agreement between the several methods for calculating the photo-effect cross sections is quite remarkable and it is estimated that the reliability of these data is to within 2% for the energy range considered in this compilation. Some problems may exist, however, close to the absorption edges. Errors in the calculation of the Rayleigh and the Compton scattering cross sections are assessed to be of the order of 5%. Because the greater proportion of total attenuation is photoelectric, the accuracy of the total scattering cross section should be much better than 5% and usually close to 2%.

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