The stopping power of atomic matter for relativistic ions, mesons, electrons and positrons

Abstract

The Born-approximation energy-loss formulas are derived for fast charged particles traversing matter and losing energy by excitation and ionization of atomic species. Bethe's results are obtained in an elementary, but more rigorous, derivation which also makes use of some recent work by the author on the corresponding stopping-power problem for a plasma. The formulas for the atomic and plasma problems are compared and the effects of magnetic interactions, retardation, and electron spin are discussed briefly. It is shown that in the computation of the stopping power, it is necessary to introduce and sum contributions from three momentum-transfer domains (“very small”, “small”, and “large”). In Bethe's formula for heavy ions, half of the additive (to the logarithmic factor) term -β 2 results from the very small momentum transfers and arises from essentially classical effects (retardation and magnetic interactions not involving spin); the other half arises from the contribution of the largest momentum transfers and is due to electron spin. In the stopping-power formulas for electrons and positrons the results are given in terms of an arbitrary maximum fractional energy loss.