Electron Capture fromHe(1s2)by Protons

Abstract

The two equivalent forms of Born's approximation, prior and post, are used to calculate the electron capture cross section for protons incident on $\mathrm{He}\left(1\mathrm{}{s}^2\right)$. These cross sections are calculated for capture into eleven different final states in the energy range 12.5 kev to 1 Mev. Although a rather crude wave function, $\left(\frac{Z^3}{\pi {a_0}^3}\right)\exp [-(\frac{Z}{a_0}\left)\right(r_1+r_2\left)\right](Z=1.6875\mathrm{})\mathrm{}$, is used for He, the prior and post total capture cross sections do not differ by more than twenty percent over the energy range investigated. Estimates of the sum of the cross sections for capture into all $s$ states of the hydrogen atom for the two residual ions, ${\mathrm{He}}^{+}\mathrm{}\left(1s\right)\mathrm{}$ and ${\mathrm{He}}^{+}\mathrm{}\left(2s\right)\mathrm{}$, are obtained from an adaption of the $s$-state sum rule as given in the paper of Jackson and Schiff. As in this work of Jackson and Schiff, it is found that the $s$ states provide the major contribution to the total capture cross section. The calculated cross sections agree fairly well with the experimental values. The cross sections for capture into the state ${\mathrm{He}}^{+}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$, is roughly 2.5 times larger than the values obtained by Bransden, Dalgarno, and King.