Hydrogen and Helium Atoms in Superstrong Magnetic Fields

Abstract

The behaviour of atoms in superstrong magnetic fields of the order of 1012 G is investigated. As a first step, ground-state energies of hydrogen-like and helium-like atoms are calculated and compared with earlier results. Two different approaches are tried for the hydrogen atom; a variational calculation for so-called tightly-bound states and a perturbation-theory approach for so-called hydrogen-like states. In the first case, we make an adiabatic approximation where we neglect effects of the Coulomb interaction in the plane perpendicular to the magnetic field, and in the second case we assume the solution in the direction of the field to correspond to the solution of a one-dimensional Schrödinger equation with a truncated Coulomb potential. For the helium atoms we also try a variational approach where the trial wave functions are products of single-particle "orbitals" which are mainly "magnetic" in their spatial form.Ground-state energies and ionization energies are tabulated for field strengths ranging from 1010 G to 5 × 1013 G. At 1012 G, for instance, the binding energy of a hydrogen atom is changed from - 13.6 eV to approximately - 150 eV, which is in reasonable agreement with other calculations. The corresponding result for the ground-state energy of a helium atom is a change from - 79 eV to approximately - 610 eV, also in reasonable agreement with other calculations. Ionization energies for the "outer" electron are found to be approximately 27 eV for H--atoms and 220 eV for He-atoms in a magnetic field of 1012 G.