H2+ dipole strengths by asymptotic techniques

Asymptotic expansions in the internuclear separation R-n of the dipole transition moments Q(R)=( psi (r mod R) mod r mod psi '(r mod R)) involving the electronic Born-Oppenheimer states of H2+ are presented. The four leading terms of all non-zero dipole transition moments involving the 20 states correlating to a proton and a hydrogen atom with principal quantum number n=1, 2, and 3 are given. Numerical calculations indicate the expansions are useful beyond R=10a0 for transitions involving only the n=1 states. The useful range decreases with increasing n, as expected. The coefficients of the charge transfer transitions can be related to the permanent dipole and polarizability of the hydrogen atom in the field of a proton. A perturbative approach due to Coulson, usable for larger systems, was found to give the same asymptotic coefficients.