Stark mixing of 2Smuonic helium. I. Collisions with hydrogen atoms

The transitions between the 2S and 2P states of the muonic helium atom (αμ or ${}_{}{}^3{}_{}{}^{}\mathit{\mu }$) in collisions with hydrogen atoms are examined using the rectilinear-trajectory coupled-equation method. The 2S level shift is included semiempirically and the target atom is approximated using the frozen ground-state charge density. Partial decoupling of the coupled equations is achieved, and some simple approximations for the 2S-to-2P transition probability are derived and compared with the exact solution of the coupled equations. The cross section obtained is fit by ${\sigma }_{2S\mathrm{-}2P}$≃5.5×${10}^{\mathrm{-}3}$/ $v^{1.8}$ $a_0^2$ for v≳1, with the velocity v in atomic units, and muon-catalyzed fusion parameters are reevaluated using this expression.