Diabatic-state treatment of negative-meson moderation and capture. II. Mixtures of hydrogen and helium

Abstract

Slowing-down and capture cross sections have been consistently calculated for ${\mu }^{-}$, ${\pi }^{-}$, $K^{-}$, and $\overline{p}$ in collisions with hydrogen and helium atoms and isotopic variants. Capture-energy distributions are determined using the differential-energy-loss cross sections in the laboratory frame. Capture is found to occur predominantly at energies near or below the ionization potential of the target. Ratios of capture on different species are given as a function of the mole fraction of each species present in mixtures. For ${\pi }^{-}$ in a He-H mixture the reduced capture ratio obtained is ∼0.73, slightly less than the experimental value of 0.92 for the ${\mathrm{H}\mathrm{e}-\mathrm{H}}_2$ mixture. In contrast with another recent theoretical calculation and in agreement with experimental analysis, it is found that atomic capture of pions in the helium-hydrogen mixture is only slightly nonlinear. It is pointed out that some prior theoretical treatments are in error because of inconsistent calculation of the slowing-down and capture processes and/or subsequent approximate treatment of the energy transport. Use of capture and transfer rates in muon kinetics, e.g., muon-catalyzed fusion, is discussed.