The Bloch correction, key to heavy-ion stopping

Abstract

The Bloch correction is known as the link between Bethe’s quantum theory of the stopping of charged particles in matter and Bohr’s classical theory. Less well-known and underestimated in the literature, is its role as the link between the energy loss of heavy vs light ions. At the same time, the role of another key parameter, the ion charge, has been unclear until a few years ago, not the least due to the almost universal use of the competing effective-charge concept. We show that proper account of the Bloch correction and the ion charge forms the key to a qualitative and quantitative description of the electronic energy loss of heavy ions. In the standard textbook versions, neither Bohr nor Bethe stopping provide a valid description below the Bragg maximum, since logarithmic dependencies on the velocity cause the stopping cross section to become negative. Although this obstacle can easily be repaired by more accurate evaluation of the underlying integrals, we found the Bloch correction to be more tightly connected with these logarithms than expected. This requires caution in practical applications.