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ATTENUATION COEFFICIENTS OF VARIOUS ELEMENTS
APPENDIX 1
GAMMA-RAY ATTENUATION COEFFICIENTS C. M. DAVISSON (A) ATTENUATION COEFFICIENTS OF VARIOUS ELEMENTS The attenuation coefficients given in this set of tables have for the most part been calculated from theories concerning the interaction of y-radiation with matter as discussed in Chapter II. 1 The scattering coefficients have been taken directly from the Grodstein report . The values in the column headed 'With coherent' are the sum of coherent scattering and of incoherent scattering from the Klein-Nishina formula corrected for binding effects. Those in the column headed 'Without coherent' are for incoherent scattering as given by the Klein-Nishina formula for free electrons. 2 The photoelectric values at low energies were taken from the experimental values listed by McGinnies . For values at higher energies three sets of values were ob tained. (1) The values of the Grodstein tables were reduced to K-shell coefficients using the reciprocal of Grodstein's conversion coefficients. They were then converted to atomic3coefficients using the experimental values of (τ α/τκ)κ edge as obtained from Kirchner and given in Table 3. (2) The Pratt values of Table 2, Chapter II were used to obtain K-shell coefficients for the energies between 0.4 and 2.0 MeV. These were converted to atomic coefficients using the conversion constants of Table 3. (3) The Pratt values of Table 3, Chapter II were used to obtain K-shell coefficients for energies between 1 and 100 MeV. These were converted to atomic coefficients using the same conversion constants. All three sets of atomic photoelectric coefficients were plotted and the values given in the present table were obtained from a smooth curve connecting the high energy Pratt values with the low energy Grodstein values, the shape at the intermediate values of 0.4 to 2.0 MeV being guided by the intermediate Pratt values. The largest difference from the Grodstein values is found at the high energy, high-Z values, where the Hall formula used by Grodstein gave values which were too large. The values for pair production in the field of the nucleus were taken directly from the 1 Grodstein report. However, for pair production in the field of an electron, the G. White Grodstein, X-ray attenuation coefficients from 10 keV to 100 M e V , Natl. Bur. Standards
2 Circular 583 (1957).
R. T. McGinnies, X-ray attenuation coefficients from l O k e V to 100 M e V , Natl. Bur. Standards
3 Supplement to Circular 583 (1959).
F. Kirchner, H a n d b u c h der Experimentalphysik 24/1 (ed. W. Wien and F. H a r m s ; A k a d e m i s c h e
4 Verlagsgesellschaft, Leipzig, 1930) p. 265.
G. R. White, X-ray attenuation coefficients from l O k e V to 100 M e V , unpublished Natl. Bur.
5 Standards Report N o . 1003 (1952).
Beta- and gamma-ray spectroscopy (ed. K. Siegbahn; N o r t h - H o l l a n d Publ. C o . , Amsterdam, 1955). 827 K. Siegbahn, Editor, Alpha-, Beta- and Gamma-Ray
Spectroscopy
828
C. M. DAVISSON
APP.
1
values from the Borsellino4 theory were used. That is, the5 values were taken from the tables given by White and republished in Siegbahn . Due to approximations in the theories, and the applicability of different theories to different ranges of energy and atomic number, the accuracy of the values tabulated here is not the same throughout. Interpolations and extrapolations made between different ranges of energy and atomic number have been such that all the values fall on a smooth curve within about 1 %. However, in some ranges, the true accuracy may not be better than 5% or 10%. - 42tables 2 the cross sections 2 are given in units of barns/atom,2which is the same-1 In the as 1 0 cm /atom, and in cm /g. These can be converted to cm /electron or c m by the use of the following relationships : Άμ = Ζβμ
μ/ρ =
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μ=ρΝ(Ζ/Α)6μ (3) 2 2 -1 Here μβ is the value in om /electron, μΆ is in cm /atom, and μ is in c m . Ζ is the atomic number, A the atomic weight, Ν Avogadro's number, and ρ the density in g/cc.
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GAMMA-RAY ATTENUATION COEFFICIENTS C. M. DAVISSON (A) ATTENUATION COEFFICIENTS OF VARIOUS ELEMENTS The attenuation coefficients given in this set of tables have for the most part been calculated from theories concerning the interaction of y-radiation with matter as discussed in Chapter II. 1 The scattering coefficients have been taken directly from the Grodstein report . The values in the column headed 'With coherent' are the sum of coherent scattering and of incoherent scattering from the Klein-Nishina formula corrected for binding effects. Those in the column headed 'Without coherent' are for incoherent scattering as given by the Klein-Nishina formula for free electrons. 2 The photoelectric values at low energies were taken from the experimental values listed by McGinnies . For values at higher energies three sets of values were ob tained. (1) The values of the Grodstein tables were reduced to K-shell coefficients using the reciprocal of Grodstein's conversion coefficients. They were then converted to atomic3coefficients using the experimental values of (τ α/τκ)κ edge as obtained from Kirchner and given in Table 3. (2) The Pratt values of Table 2, Chapter II were used to obtain K-shell coefficients for the energies between 0.4 and 2.0 MeV. These were converted to atomic coefficients using the conversion constants of Table 3. (3) The Pratt values of Table 3, Chapter II were used to obtain K-shell coefficients for energies between 1 and 100 MeV. These were converted to atomic coefficients using the same conversion constants. All three sets of atomic photoelectric coefficients were plotted and the values given in the present table were obtained from a smooth curve connecting the high energy Pratt values with the low energy Grodstein values, the shape at the intermediate values of 0.4 to 2.0 MeV being guided by the intermediate Pratt values. The largest difference from the Grodstein values is found at the high energy, high-Z values, where the Hall formula used by Grodstein gave values which were too large. The values for pair production in the field of the nucleus were taken directly from the 1 Grodstein report. However, for pair production in the field of an electron, the G. White Grodstein, X-ray attenuation coefficients from 10 keV to 100 M e V , Natl. Bur. Standards
2 Circular 583 (1957).
R. T. McGinnies, X-ray attenuation coefficients from l O k e V to 100 M e V , Natl. Bur. Standards
3 Supplement to Circular 583 (1959).
F. Kirchner, H a n d b u c h der Experimentalphysik 24/1 (ed. W. Wien and F. H a r m s ; A k a d e m i s c h e
4 Verlagsgesellschaft, Leipzig, 1930) p. 265.
G. R. White, X-ray attenuation coefficients from l O k e V to 100 M e V , unpublished Natl. Bur.
5 Standards Report N o . 1003 (1952).
Beta- and gamma-ray spectroscopy (ed. K. Siegbahn; N o r t h - H o l l a n d Publ. C o . , Amsterdam, 1955). 827 K. Siegbahn, Editor, Alpha-, Beta- and Gamma-Ray
Spectroscopy
828
C. M. DAVISSON
APP.
1
values from the Borsellino4 theory were used. That is, the5 values were taken from the tables given by White and republished in Siegbahn . Due to approximations in the theories, and the applicability of different theories to different ranges of energy and atomic number, the accuracy of the values tabulated here is not the same throughout. Interpolations and extrapolations made between different ranges of energy and atomic number have been such that all the values fall on a smooth curve within about 1 %. However, in some ranges, the true accuracy may not be better than 5% or 10%. - 42tables 2 the cross sections 2 are given in units of barns/atom,2which is the same-1 In the as 1 0 cm /atom, and in cm /g. These can be converted to cm /electron or c m by the use of the following relationships : Άμ = Ζβμ
μ/ρ =
Ν(Ζ/Α)6μ
d)
(2)
μ=ρΝ(Ζ/Α)6μ (3) 2 2 -1 Here μβ is the value in om /electron, μΆ is in cm /atom, and μ is in c m . Ζ is the atomic number, A the atomic weight, Ν Avogadro's number, and ρ the density in g/cc.
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