Collision quenching of the metastable2Sstate of muonic hydrogen and the muonic helium ion

We present calculations of the cross section for quenching of the metastable $2S$ state of muonic hydrogen (${\mu }^{-}p$) in collisions with a hydrogen atom, at collision energies below the threshold for inelastic $2S-2P$ excitation. A quantum mechanical approach based on the adiabatic approximation is used with phase shifts evaluated in the WKB approximation. Below threshold, the dominant quenching process involves Stark admixture of $2S$ and $2P$ states of ${\mu }^{-}p$ during the collision, which is accompanied by a $2P-1S$ radiative transition also during the collision, and consequently the cross section is reduced by several orders of magnitude compared with the inelastic cross section. These results are important to considerations of the possibility of measuring the $n=2\mathrm{}$ fine and hyperfine structures of ${\mu }^{-}p$. We also present quenching cross section results based on this same approach for collisions of the muonic helium ion, ${\left({\mu }^{-}\alpha \right)}^{+}$, on He, relevant to lifetime and fine-structure measurements of ${\left({\mu }^{-}\alpha \right)}^{+}$. Our theoretical results for ${\left({\mu }^{-}\alpha \right)}^{+}$ differ from available experimental lifetime results for ${\left({\mu }^{-}\alpha \right)}^{+}$. We attribute the discrepancy to uncertainties in the values of the interatomic potential used in the calculations.