Abstract
An expression is given for the (${n}_{i}$, ${l}_{i}=0\ensuremath{\rightarrow}{n}_{f}$, ${l}_{f}=0$) excitation cross section in terms of a single one-dimensional integral with the aid of a transformation to prolate spheroidal coordinates. Results are given for the $1s\ensuremath{-}2s$ excitation of arbitrary-$Z$ hydrogenic targets. For our choice of wave functions the cross sections are found to scale as ${Z}^{\ensuremath{-}4}$ at fixed $\frac{{E}_{\mathrm{inc}}}{{Z}^{2}}$. The principal difference between the Coulomb-projected Born-approximation (CPBA) and Born results is in the large-angle portion of the differential cross section. This, however, leads to CPBA and Born momentum-transfer cross sections which differ by less than 20% at high energies for $1s\ensuremath{-}2s$ transitions.
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