Abstract
Relativistic virial relations are first discussed for a homogeneous electron liquid. The chemical potential is involved in such virial relations, and the approximate effects of electron correlation are studied, using the Quantum Monte Carlo (QMC) data of Kenny et al. (S.D. Kenny, G. Rajagopal, R.J. Needs, W.-K. Leung, M.J. Godfrey, A.J. Williamson and W.M.C. Foulkes (1996). Phys. Rev. Lett., 77, 1099). Attention is then shifted to inhomogeneous electron liquids. Based on Dirac's relativistic wave equation, an approximate propagator solution using a WKB-like treatment of this equation by Linderberg for central fields is a focal point. This approach, it is demonstrated here, leads back to the exact single-particle kinetic energy of the uniform electron gas and hence to the virial relations referred to above when the central field is switched off. Virial relations are then referred to for the finite central field case. Finally, a local density approximation applied to heavy atoms in intense magnetic fields is briefly treated, and another approximate virial relation is exhibited.
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