Comparison of the Lindhard-Sorensen and Mott-Bloch corrections to the Bethe stopping formula at moderately relativistic energies

TL;DR

This paper compares two rigorous methods for calculating corrections to the Bethe stopping formula at moderately relativistic energies, showing they agree closely and align well with experimental data, unlike some approximate methods.

Contribution

It demonstrates that the Mott-Bloch and Lindhard-Sorensen corrections, calculated via rigorous methods, are in excellent agreement and superior to approximate methods for stopping power calculations.

Findings

Mott-Bloch and Lindhard-Sorensen corrections agree up to seventh significant digit.

Rigorous methods align well with experimental data.

Approximate methods show less accuracy.

Abstract

The results of numerical calculating the total Mott-Bloch correction to the Bethe stopping formula and the Lindhard-Sorensen correction in the point nucleus approximation, as well as the Mott correction and the difference between the Lindhard-Sorensen and Bloch corrections, which were obtained by some rigorous and approximate methods, are compared for the ranges of a gamma factor of approximately from 1 to 10 and the ion nuclear charge number Z from 6 to 114. It is shown that the accurate calculation of the Mott-Bloch corrections based on the Mott exact cross section using a method previously proposed by one of the authors gives excellent agreement between its values and the values of the Lindhard-Sorensen corrections in the gamma and Z ranges under consideration. In addition, it is demonstrated that the results of stopping power calculations obtained by the two above-mentioned rigorous methods coincide with each other up to the seventh significant digit and provide the best agreement with experimental data in contrast with the results of some approximate methods, such as the methods of Ahlen, Jackson-McCarthy, etc.