Cross section of proton retardation over a broad energy range

Abstract

In describing the cross section of proton retardation three energy ranges are isolated. At high velocities (proton energy greater than 1-2 MeV the Bethe-Bloch formula may be used whereas at low velocities (proton energy less than 50-100 KeV) scattering theory can be employed. The intermediate energy range, where a maximum in the retardation cross section curve occurs as a function of energy, is the most difficult to describe, and requires the use of a combination of empirical and semiempirical expressions. In each of these energy ranges the different parametrization techniques employed make it difficult to cross from one range to another. The purpose of this paper is to modify the Bethe-Bloch formula to make it applicable to the low and intermediate energy ranges and thus eliminate this difficulty.