Electron loss by atomic and molecular hydrogen in collisions with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mrow/><mml:mrow><mml:mo>+</mml:mo><mml:mo>+</mml:mo></mml:mrow><mml:mrow/><mml:mrow/><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mrow/><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mrow/><mml:mrow/><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>

Total cross sections for single-electron capture by $^{4}\mathrm{He}^{+}$ and $^{4}\mathrm{He}^{++}$ incident on atomic and molecular hydrogen have been measured in the velocity range (1-6)\ifmmode\times\else\texttimes\fi{}${10}^{8}$ cm/sec. A classical-trajectory Monte Carlo method was also used to calculate the electron-capture and impact-ionization cross sections for ${\mathrm{He}}^{++}$ on H in this velocity range. The theoretical electron-capture cross sections are found to be in good agreement with the present experimental values at velocities above 2.5\ifmmode\times\else\texttimes\fi{}${10}^{8}$ cm/sec, but tend to underestimate the experimental values by roughly 25% at the lowest velocities. The experimental ${\mathrm{He}}^{++}$ + H electron-capture cross sections are in excellent agreement with the measurements of Shah and Gilbody in the velocity region where the two experiments overlap. No significant isotope effect ($^{4}\mathrm{He}^{++}$ versus $^{3}\mathrm{He}^{++}$) could be discerned on the theoretical cross sections as a function of relative velocity.

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