The structure of the Bethe ridge. Relativistic Born and impulse approximations

The ionization of atomic shells by the impact of spin-½ charged particles in collisions involving large momentum transfers is analysed within the framework of the relativistic plane-wave Born approximation. An expression is derived for the double differential cross section based on the impulse approximation, which leads to a relationship between the generalized oscillator strength and the Compton profile. The agreement between the impulse and plane-wave Born approximations is then improved by introducing a Born Compton profile extracted from the numerically evaluated (Born) generalized oscillator strength. Calculations corresponding to the Bethe ridge of different atomic shells demonstrate the usefulness of the present approach for obtaining accurate generalized oscillator strengths at large momentum transfers with a minimum of numerical effort.