Variational ground state for relativistic ions in strong magnetic fields

The lowest bound state of a one-electron ion in a constant magnetic field 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 -> infinity, a decrease of the ground-state energy with root B is found in contrast to the ln B behavior of the Pauli operator.