Lowest energy levels ofH−, He, andLi+in intense magnetic fields

We present rough variational upper-bound estimates of some low-lying bound-state energy levels of two-electron systems, including ${\mathrm{H}}^{-}$, He, and ${\mathrm{Li}}^{+}$, in magnetic fields $B$ above ${10}^{10}$ G, a regime that is relevant to recent astrophysical studies of pulsars. The simple trial wave functions that we use in the Rayleigh-Ritz calculations consist of single antisymmetrized products of single-particle orbitals which are predominantly magnetic in their spatial character. Most importantly, our results indicate that in the regime ${10}^{10}\lesssim B\lesssim {10}^{13}$ G the ${\mathrm{H}}^{-}$ ion has at least one singlet and one triplet bound state; at 2 × ${10}^{12}$ G, e.g., the ionization energy of the triplet ground state of ${\mathrm{H}}^{-}$ is greater than 12 eV. (The number of bound states of ${\mathrm{H}}^{-}$ in this regime of $B$ may be much greater; moreover, the number of levels and their depths is expected to increase monotonically with $B$.) These results appear to contradict a recent indication that there might not be any bound states of ${\mathrm{H}}^{-}$ above ${10}^{10}$ G. For $B\to \infty$ we also present the approximate leading asymptotic terms for the total (nonrelativistic) energies and corresponding ionization energies of some low-lying states of two-electron systems with nuclear charge $Z\ge 2$.