EQUATION OF STATE IN A STRONG MAGNETIC-FIELD - FINITE TEMPERATURE AND GRADIENT CORRECTIONS

We construct the equation of state for condensed matter in a strong magnetic field. We treat the regime for which statistical models and spherical Wigner-Seitz lattice cells are valid approximations. First, the equation of state for a free, nonrelativistic, homogeneous electron gas in a uniform magnetic field is examined as a function of temperature. This treatment is then refined by incorporating Coulomb interactions in a magnetic Thomas-Fermi model which allows for finite temperature. This model is characterized by four distinct length scales: the Bohr radius alpha-0 the cyclotron radius r(cyc), the thermal de Broglie wavelength lambda-T, and the lattice cell radius r0. Gradient corrections to the zero-temperature equation of state are next evaluated by constructing a magnetic Thomas-Fermi-Dirac-Weizsacker model. These corrections have a considerable effect on the zero-pressure density for matter in strong magnetic fields. Finally, we integrate the hydrostatic equilibrium equation for the surface structure of a neutron star using our computed equations of state.