The Bethe approximation: where to draw the line

Modifications of the well known Bethe expression for the asymptotic behaviour of cross sections for electron-impact excitation of optically allowed transitions are derived. Attention is drawn to a simple relation between the coefficient csub(j) of the Bethe expression and the value of energy at which the polarisation of the impact radiation passes through zero. This relation is used to examine experimental data for the Lyman-α line of hydrogen, the 501.6 nm line of helium and the 313 nm line of the beryllium ion. (author)