Modified Kramers’ law for bremsstrahlung produced by complete beta particle absorption in thick targets and compounds

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External bremsstrahlung spectra produced by the complete absorption of beta particles from the decay of 32P in compounds, some of them used as nuclear radiation detectors including CdO, NaI, CsI, BiI3, HgI2, PbI2, and HgO, and in thick targets of Ni, Cu, Mo, Cd, Ta, and Pb, are measured using a NaI(T1) detector. The bremsstrahlung energy yields are calculated using the unfolded bremsstrahlung spectra. The effective atomic numbers of compounds for the bremsstrahlung process are interpolated from the energy yield data of elements and compounds. Although the experimental effective atomic numbers of compounds are consistently lower than the theoretical ones, the overall agreement between the experimental values and those derived from the Markwich and Van Greiken expression for the modified effective atomic number [A. A. Markowicz and R. E. Van Grieken, Anal. Chem. 56, 2049 (1984)] and from the expression for the mean atomic number, which has commonly been used for samples composed of more than one element, is good within experimental uncertainties. However, the experimentally derived effective atomic numbers are closer to the modified atomic numbers than to the mean atomic numbers. The linear relationship between the total energy yield and the atomic number Z does not strictly hold, and hence the equation of Kramers for total bremsstrahlung intensity is approximately valid. The exponent of the atomic number in the Kramers equation is found to be 1.08. The Kramers law is modified to give a better description of the experimental observations.