Theory of the Quenching of Metastable Hydrogen Atoms by Helium

In this article we analyze the quenching of metastable hydrogen atoms by helium in the energy range below roughly 250 eV. Two methods are discussed. In one, a perturbation-theory approach is used; in the other, a pseudopotential is employed which attempts to relate the quenching matrix elements to low-energy-electron elastic scattering data. At thermal energies, both methods predict very large quenching cross sections. The pseudopotential approach gives a result of about $80\pi a_0^2$ while the perturbation analysis yields $40\pi a_0^2$. As one goes to higher energies, the cross sections decrease, with the pseudopotential result falling off much less rapidly than the perturbation-theory result. Reasonable agreement between experiment and the pseudopotential method is found at about 300 eV, which is the lowest energy experimentally available at present.