Accurate Analytic Static and Dynamic Polarizabilities forH−via the Asymptotic Approximation

Abstract

Accurate closed analytic expressions for certain properties of ${\mathrm{H}}^{\ensuremath{-}}$ that strongly depend on the long-range tail of its wave function are given. These properties are $〈{{\mathcal{r}}_{1}}^{n}+{{\mathcal{r}}_{2}}^{n}〉$, the static electric multipole polarizabilities, and the dynamic dipole polarizability. From the last, the ${\mathrm{H}}^{\ensuremath{-}}$ photodetachment cross section is calculated and the simple but accurate result obtained by Armstrong is recovered. The only assumption made is that the exact wave function can be replaced by its rigorous asymptotic form, for the purpose of calculating these properties. No model potentials or arbitrary cutoffs are introduced. The results for the dipole polarizabilities agree to better than 5% with the extensive recent calculations of Chung. For $〈{\mathcal{r}}_{1}^{n}+{\mathcal{r}}_{2}^{n}〉$, $n\ensuremath{\ge}2$, the formula obtained agrees to within 0.5% with values obtained from large calculations. For all these quantities, the Hartree-Fock results are far inferior.