Correspondence between the surface integral and linear combination of atomic orbitals methods for ionic-covalent interactions in mutual neutralization processes involving H−/D−

Abstract

The surface integral method for estimating ionic-covalent interactions in diatomic systems been successful in producing cross sections for mutual neutralization (MN) in reasonable agreement with experimental results for branching fractions between final states in systems such as ${\mathrm{O}}^{+}\text{/}{\mathrm{O}}^{\ensuremath{-}}$ and ${\mathrm{N}}^{+}\text{/}{\mathrm{O}}^{\ensuremath{-}}$. However, for simpler cases of MN involving ${\mathrm{H}}^{\ensuremath{-}}$ or ${\mathrm{D}}^{\ensuremath{-}}$, such as ${\mathrm{Li}}^{+}\text{/}{\mathrm{D}}^{\ensuremath{-}}$ and ${\mathrm{Na}}^{+}\text{/}{\mathrm{D}}^{\ensuremath{-}}$, it has not produced results that are in agreement with experiments and other theoretical calculations; in particular, for ${\mathrm{Li}}^{+}\text{/}{\mathrm{D}}^{\ensuremath{-}}$ calculations predict the wrong ordering of importance of final channels, including the incorrect most populated channel. The reason for this anomaly is investigated, and a leading constant to the asymptotic ${\mathrm{H}}^{\ensuremath{-}}$ wave function is found that is different by roughly a factor of $1\text{/}\sqrt{2}$ from that which has been used in previous calculations with the surface integral method involving ${\mathrm{H}}^{\ensuremath{-}}$ or ${\mathrm{D}}^{\ensuremath{-}}$. With this correction, far better agreement with both experimental results and calculations with full quantum and linear combination of atomic orbitals (LCAO) methods is obtained. Further, it is shown that the surface integral method and LCAO methods have the same asymptotic behavior, in contrast to previous claims. This result suggests the surface integral method, which is comparatively easy to calculate, has greater potential for estimating MN processes than earlier comparisons had suggested.