Variational ground state for relativistic ions in strong magnetic fields

Abstract

The lowest bound state of a one-electron ion in a constant magnetic field $\mathbf{B}$ is calculated from the pseudorelativistic no-pair Brown-Ravenhall operator. The variational wave function is chosen as the product of a Landau function (in the transverse direction) and a hydrogenic state (in the longitudinal direction). The dependence of the ground-state energy on the nuclear charge $Z$ as well as on the magnetic field strength is investigated, and a scaling with $B∕{Z}^{2}$ is observed. Relativistic effects are shown to be important both for large $B$ and large $Z$. When $B\ensuremath{\rightarrow}\ensuremath{\infty}$, a decrease of the ground-state energy with $\sqrt{B}$ is found in contrast to the $\mathrm{ln}\phantom{\rule{0.2em}{0ex}}B$ behavior of the Pauli operator.