Average K-, L-, and M-shell fluorescence yields: A new semi-empirical formulae

Theoretical, experimental, and analytical methods for the calculation of K-, L-, and M-shell fluorescence yields (ω_K,ω_L,andω_M) of different elements are very important because of the large number of their applications in various areas of physical-chemistry, and medical research. In the present work, all the experimental K-, L-, and M-shell fluorescence yields taken from distinctive sources, for elements with atomic number 4≤Z≤99 for the K shell, 23≤Z≤96 for the L shell, and 40≤Z≤92for the M shell, are studied. A detailed analysis of these data, and a table with weighted average values (ω_KW,ω_LW,andω_MW)of these parameters are presented. New recommended values ω_WR are obtained dividing the experimental ratios (ω_EXP) by the weighted ratios (ω_W) and removing out-of-range values (less than 0.9 or greater than 1.1). At that point, new values of average fluorescence yields were deduced using an interpolation that involves the well-known analytical function [ω_WR/(1−ω_WR)]^1/4as function of the atomic number Z, and then semi-empirical data were deduced by fitting the ratio S=ω_EXP/ω_WR, for the three shells. A comparison was made with other theoretical, experimental, and empirical values reported in the literature. An evident correlation was observed between our result and other works.