Continuous Absorption Coefficient of the Hydrogen and Lithium Negative Ions

Abstract

Previous calculations of the continuous absorption coefficient of ${\mathrm{H}}^{-}$ were based on the use of ground state wave functions obtained through the Ritz variational method. Such functions, although giving good values for the energy, are not in general adequate for the determination of the dipole matrix element needed for the absorption coefficient. Initial and final state functions are constructed for which the following necessary conditions on the true wave functions are satisfied: (1) equality of dipole length, velocity, and acceleration matrix elements and (2) the ${〈r^2〉}_{\mathrm{Av}}$ and $f$ sum rules. The constructed ground state function is also shown to be reasonable on the basis of energy minimization. The resulting absorption coefficient for ${\mathrm{H}}^{-}$ is in substantial agreement with the best previously calculated curves and with experiment. The curve for ${\mathrm{Li}}^{-}$ is also obtained.