Rapidly Converging Bounds for the Ground-State Energy of Hydrogenic Atoms in Superstrong Magnetic Fields

Abstract

The calculation of rapidly converging lower and upper bounds to the ground-state energy, ${E}_{g}$, of hydrogenic atoms in superstrong magnetic fields ($B\ensuremath{\gtrsim}{10}^{9}$ G) has been an important theoretical problem for the past twenty-five years. Much effort has gone into reconciling the many different estimates for ${E}_{g}$ predicted by an assortment of techniques. On the basis of recently developed eigenvalue moment methods, a precise solution involving rapidly converging bounds to ${E}_{g}$ for arbitrary superstrong magnetic field strengths, is now possible.