Hydrogen negative ion: Semiclassical quantization and weak-magnetic-field effect

We report the results of semiclassical quantization of the hydrogen negative ion using the Gutzwiller trace formula and the unstable periodic orbits of the classically chaotic repeller of the collinear configuration with the two electrons on opposite sides of the nucleus. The energies of the ${}_{}{}^1{}_{}{}^{}$ ${\mathit{S}}^{\mathit{e}}$ and ${}_{}{}^3{}_{}{}^{}$ ${\mathit{S}}^{\mathit{e}}$ autoionizing states have been calculated for principal quantum numbers up to N=16 and 12, respectively. We also report the results of a semiclassical study of the quadratic effect of a weak magnetic field on the autoionizing states of ${\mathrm{H}}^{\mathrm{-}}$.