Compilation of empirical and semi-empirical Kα1, Kα2, Kβ1′, and Kβ2′ X-ray fluorescence cross-sections by the application of fitting approaches

In this study, empirical and semi-empirical X-ray fluorescence cross-sections are generated for $K{\alpha }_1$, $K{\alpha }_2$, $K\beta {}_1^{\prime },$and $K\beta {}_2^{\prime }$lines. The approach used was the fitting of experimental data by three-dimensional formulae. The empirical values were obtained through a fitting method making use of a three-dimensional function against atomic number Z and excitation energy E, resulting in a three-dimensional plot allowing to estimate empirically $K{\alpha }_1$, $K{\alpha }_2$, $K\beta {}_1^{\prime }$, and $K\beta {}_2^{\prime }$X-ray fluorescence cross sections. Further, new semi-empirical values were derived by fitting the weighted average values using an analytical function against atomic number Z and energy E, and subsequently the ratio $S_W={\left({\sigma }_{K_i}\right)}_{\text{exp}}/{\left({\sigma }_{K_i}\right)}_W$is fitted by a three-dimensional analyzing polynomial function as a function of Z and energy E. For $K{\alpha }_1$ and $K{\alpha }_2$ lines the range of atomic numbers covered was $52\le Z\le 92$ whereas for $K\beta {}_1^{\prime }$ and $K\beta {}_2^{\prime }$ it was$57\le Z\le 79.$ Our findings were compared with selected experimental results, and good agreement was obtained.