Large Atoms in the Magnetic Field of a Neutron Star

Abstract

The asymptotics of the ground state energy of large atoms as $Z \to \infty$ is given exactly by Thomas–Fermi theory. The introduction of a large magnetic field, $B$, changes the situation. If we set $B = cZ^p$ then, as $Z \to \infty$, there are 5 regions: $p < 4/3$, $p = 4/3$, $4/3 < p < 3$, $p = 3$, $p > 3$. The first three are described exactly by a modified TF theory. The fifth is describable exactly by a one-dimensional Hartree like theory. The fourth is describable exactly by a novel density matrix theory. A surprising conclusion is that although the magnetic field has a profound effect on the atomic energy in regions 2, 3, 4 and 5, the atom remains spherical (to leading order) in regions 2 and 3.