A generalized Bethe analytic formula. Dipole-excited collision strengths and corresponding rate coefficients in Au50+

A generalized Bethe analytic formula for dipole-excited collision strengths is suggested, in which a cut-off k0 in the momentum transfer, a threshold (via extrapolation) and a thrice threshold of collision strengths for each dipole-excited process are calculated quickly based on the quasi-relativistic plane wave Born (QRPB) and distorted wave (QRDW) methods respectively. The formula can be applied to moderate and low impact electron energies. As a example, dipole collision strengths and corresponding rate coefficients of Au50+ are given at all impact energies, which are in agreement with that of a least-square spline method. Meanwhile the systems of k0 in channel n0l0→n(l0 + 1) are analyzed