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

• Received 8 October 1973

DOI:https://doi.org/10.1103/PhysRevA.9.1013