Computation of K-shell X-ray Fluorescence Cross Section for photons ranging from 5.46keV to 123.6keV using three-dimensional semi-empirical formulae

In this work, we propose a novel three-dimensional semi-empirical formula for the estimation of K-shell X-ray fluorescence cross sections for a wide range of elements $16\le Z\le 92$ based on the database of the experimental values published between 1985 and 2023 for photons spanning from 5.46 to 123.6 keV (over 3300 data). This approach employs an analytical dependent on the atomic number Z and the energy E. Subsequently, the ratio $S_W=\left({\sigma }_{Ki-Exp}\right)/\left({\sigma }_{Ki-W}\right)$ are fitted using a three-dimension polynomial function, in terms of the atomic number Z and energy E. The cross-sections were described as the product of two functions, the first is a polynomial that represents the weighted mean of cross-sections values across different conditions and the second function provides additional fitting to the cross-section based on atomic numbers Z and energy E. The cross-sections expressed as function of these two variables show reasonable agreement with the experimental values.