ASYMPTOTICS OF HEAVY-ATOMS IN HIGH MAGNETIC-FIELDS .1. LOWEST LANDAU BAND REGIONS

The ground state energy of an atom of nuclear charge Ze in a magnetic field B is evaluated exactly to leading order as Z --> infinity. In th is and a companion work (see [28]) we show that there are five regions as Z --> infinity: B << Z4/3, B approximately Z4/3, Z4/3 << B << Z3, B approximately Z3, B >> Z3. Regions 1, 2, 3, and 4 (and conceivably 5 ) are relevant for neutron stars. Different regions have different phy sics and different asymptotic theories. Regions 1, 2, and 3 are descri bed by a simple density functional theory of the semiclassical Thomas- Fermii form. Here we concentrate mainly on regions 4 and 5 which canno t be so described, although 3, 4, and 5 have the common feature (as sh own here) that essentially all electrons are in the lowest Landau band . Region 5 does have, however, a simple non-classical density function al theory (which can be solved exactly). Region 4 does not, but, surpr isingly, it can be described by a novel density matrix functional theo ry! (C) 1994 John Wiley & Sons, Inc.