Comparison of the Lindhard–Sørensen and Mott–Bloch Corrections to the Bethe Stopping Formula at Moderately Relativistic Energies

Abstract

The results of numerical calculating the total Mott−Bloch correction to the Bethe stopping formula and the Lindhard−Sørensen correction in the point nucleus approximation, as well as the Mott correction and the difference between the Lindhard−Sørensen and Bloch corrections, which were obtained by some rigorous and approximate methods, are compared for the ranges of a gamma factor 1 ≲ 𝛾 ≲ 10 and the ion nuclear charge number 6 ≤ Z ≤ 114. It is shown that the accurate calculation of the Mott−Bloch correction 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−Sørensen correction in the 𝛾 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.