Atomic fine structure in a space of constant curvature

Abstract

As a contribution to a tentative formulation of atomic physics in a curved space, the determination of atomic fine structure energies in a space of constant curvature is investigated. Starting from the Dirac equation in a curved space-time, the analogue of the Pauli equation in a general coordinate system is derived. When particularising these results to the model of a spherical three-space with a Coulombic field, one obtains the 'curved' form of the one-electron fine structure Hamiltonian, i.e. the curved form of the Lande spin-orbit interaction and of the relativistic correction of the kinetic energy as well as some additional terms which vanish at the traditional flat limit. The theoretical curvature induced shifts and splittings of the fine structure energy levels are put in evidence and examined for the particular case of the hydrogenic n=2 levels.