Energy-loss spectra of swift ions: Beyond the Landau approximation

Abstract

The paper revises the well-known simple approximation for the energy-loss spectrum of swift charged particles. The original formula by Landau is restricted to the range of path lengths where the energy loss straggling Ω 2≪T m 2 , T m being the maximum energy transfer in a collision; this is a severe limitation in the case of penetrating ions. The present work eliminates the restriction by means of a general relationship between the energy-loss spectra for true and extended collision cross-sections. Improving accuracy, this also delivers a straight generalization of Landau's argument based upon plain equivalence of the two spectra for Ω 2/T m 2→0 . Arising expressions for the spectrum remain sufficiently simple roughly up to Ω 2∼T m 2 , thus complementing existing approximations applicable for Ω 2≳T m 2 and eliminating the notorious gap at moderately small Ω 2/T m 2 . For the range Ω 2/T m 2≲1/5 , 1/3, especially simple accurate formulae arise for the peak energy loss, the half-widths, and related parameters of the spectrum. Analytical formulae are tested against numerical results confirming good accuracy and wide applicability of the former.