Some approaches to the calculation of the normalized Mott cross section, displacement cross section, and the Mott correction to the Bethe formula

Abstract

A new exact representation for the normalized Mott cross section is obtained. Some earlier exact and approximate methods for its calculation are compared with the method proposed in this work. It is demonstrated that applying the suggested rigorous method, along with the approximate method of Lijian et al., is most preferable for the above calculations. Some modifications of Lijian’s method are proposed. Based on these modifications and the Lijian method itself, new analytical expressions are obtained for the Mott corrections to the Bethe stopping formula and the primary displacement cross section by fast electrons. It is shown that the highest fitting accuracy of the displacement cross sections is provided by the twice modified Lijian method.