Electron capture by fast protons and α-particles in hydrogen

Abstract

Cross-sections are calculated for the accidental resonance reaction, $\mathrm{He}^{2+} + \mathrm{H}(1s) \rightarrow \mathrm{He}^+(2s \text{or} 2p) + H^+,$ and the non-resonance reaction, $\mathrm{H}^+ + \mathrm{H}(1s) \rightarrow \mathrm{H}(2s \text{or} 2p) + \mathrm{H}^+,$ by means of the method due to Bates in which account is taken of the non-orthogonality of the wave functions describing the initial and final states. Proper allowance is made for the effects of distortion and of momentum transfer. The calculations are carried out for incident ion energies in the range 25 to 800 keV. In the accidental resonance case, the cross-section is small at low velocities of relative motion, and tends rapidly towards zero as the velocity is decreased in accordance with the prediction of Bates & Lynn. In all processes investigated the effect of distortion is considerable. Using the results of McCarroll & McElroy and of McCarroll for capture into the ground states of He$^+$ and H, the cross-sections for capture into all states are estimated. Comparisons are made with the experimental data of Fite, Smith & Stebbings for the incident alpha particle case and with that of Fite, Stebbings, Hummer & Brackman for the incident proton case. The highest energy for which cross-sections are measured in either case is however only 40 keV.