Lowest energy levels of H-, He, and Li+ in intense magnetic fields

We present rough variational upper-bound estimates of some low-lying bound-state energy levels of two-electron systems, including H-, He, and Li+, in magnetic fields B above 1010 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 1010B 1013G the H- ion has at least one singlet and one triplet bound state; at 2 × 1012 G, e.g., the ionization energy of the triplet ground state of H- is greater than 12 eV. (The number of bound states of 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 H- above 1010 G. For B→ 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 Z2. © 1975 The American Physical Society