Spin-polarised relativistic exchange energies and potentials

Expressions for the exchange energy of a relativistic polarised electron gas have been derived. These expressions have been evaluated numerically over a wide range of densities and polarisations. The leading-order relativistic corrections for the transverse exchange energy, which are of most importance in practice, have been evaluated analytically. The numerical results have been fitted to a simple form, suggested by the analytic leading-order-correction expressions, which should be useful for local-density-approximation applications.