Relativistic electrons in a rotating spherical magnetic dipole: Localized three-dimensional states

Paralleling a previous paper, we examine single- and many-body states of re lativistic electrons in an intense, rotating magnetic dipole field. Single- body orbitals are derived semiclassically and then applied to the many-body case via the Thomas-Fermi approximation. The many-body case is reminiscent of the quantum Hall state. Electrons in a realistic neutron star crust are considered with both fixed density profiles and constant Fermi energy. In the first case, applicable to young neutron star crusts, the varying magnet ic field and relativistic Coriolis correction lead to a varying Fermi energ y and macroscopic currents. In the second, relevant to older crusts, the el ectron density is redistributed by the magnetic field.