Electron capture from He(1s2) by protons. III

The prior (i), post (f), and distorted wave (dw) forms of the first Born approximation, and a one-parameter approximate helium wave function, are used to calculate cross sections for electron capture from $\mathrm{He}(1{s}^{2})$ by protons. These cross sections are calculated for capture into $\mathrm{H}(3lm)$, $l=1, 2$; $\ensuremath{-}1\ensuremath{\le}m\ensuremath{\le}1$, for impact energies, $10\ensuremath{\le}E\ensuremath{\le}1000$ keV, leaving the residual ion ${\mathrm{He}}^{+}(1s)$. The associated polarizations $P$ are calculated for the axis of quantization of H parallel to the direction of incidence, and the apparent cross sections ${Q}_{A}=3Q{(3\ensuremath{-}P)}^{\ensuremath{-}1}$ are obtained from $P$ and the calculated cross sections $Q=\ensuremath{\Sigma}{m=\ensuremath{-}l}^{l}{Q}_{m}$. The $Q$ used to determine ${Q}_{A}$ are $Q(\mathrm{dw})$ and the arithmetic average of $Q(\mathrm{i})$ and $Q(\mathrm{f})$. Of these two sets, ${Q}_{A}(\mathrm{dw})$ predicts the measured ${Q}_{A}(3p)$ more successfully for $E<250$ keV, and the measured ${Q}_{A}(3d)$ better for $E<200$ keV. For larger values of $E$ both sets predict the measured values equally well. In the range $15\ensuremath{\le}E\ensuremath{\le}60$ keV, the effect of $P(\mathrm{dw})$ is more marked for capture into $\mathrm{H}(3p)$ than into $\mathrm{H}(3d)$.