Ordering of cross sections for electron capture from He-like targets by fast projectiles

The continuum-distorted-wave (CDW) method is used to determine total electron-capture cross sections $Q=\Sigma {\mathrm{nl}}^{}\sigma \mathrm{}\left[\mathrm{nl}\right]\mathrm{}$ for proton and $\alpha$-particle projectiles incident on ${\mathrm{Li}}^{+}$ in energy ranges of $100\le E\le 3000$ keV and $100\le E\le 10000$ keV, respectively. A configuration-interaction (CI) wave function is used to describe the ${\mathrm{Li}}^{+}$ electrons; for comparison, capture cross sections for ${\mathrm{H}}^{-}$ and He are examined. For each system the percentage change in $Q$, $\Delta (\mathrm{HF}\to \mathrm{CI})$, is given for progression from a Hartree-Fock (HF) to a CI description of the target electrons. The main emphasis in this work is devoted to a rationalization of the trends observed in the ordering of $Q$ for these three targets. This was achieved by an analysis of the CDW expression for an individual capture cross section $\sigma [nl, n^{\prime }{l}^{\prime }]$, where $\mathrm{nl}$ and $n^{\prime }{l}^{\prime }$ are the states of the "active" (captured) and "passive" electrons, respectively.