Extended asymptotic model for the alkali-anion photodetachment cross sections and multipole polarizabilities

An analytically tractable extended asymptotic model for the response properties of weakly bound anions (small detachment energy $E$) is proposed and the $2^l$-pole polarizability, the sum rules, and the photodetachment cross section determined by the model are computed analytically. The model is based on the following two assumptions: (1) The alkali-anion valence orbital ${\Psi }_{0,\gamma }\mathrm{}\left(r\right)\mathrm{}$ may be approximated by its asymptotic form ${\Psi }_{0,\gamma }\mathrm{}\left(r\right)\mathrm{}\sim {\mathrm{Nr}}^{-1\mathrm{}}{e}^{-\gamma r}$, as $r\to \infty$, where $N$ is a normalization factor and $\gamma ={\mathrm{}\left(2E\right)\mathrm{}}^{\frac{1}{2}}$. (2) The alkali-anion $l$-wave continuum states are approximated by analytic eigenstates determined by a one-parameter $r^{-2\mathrm{}}$-type pseudopotential. The pseudopotential parameter $\lambda$ is chosen to reproduce an appropriately defined representative $l$-wave electron-alkali phase shift. For the case of zero pseudopotential ($\lambda =l$), the model reduces to one successfully applied to the hydride anion. Dipole polarizabilities and photodetachment cross sections determined from the model for ${\mathrm{Li}}^{-}$, ${\mathrm{Na}}^{-}$, and ${\mathrm{K}}^{-}$ are compared with the numerical results of Moores and Norcross. Agreement is typically within 10-15% if the pseudopotential ($\lambda \ne l$) is included.