The quantum mechanical two-Coulomb-centre problem in the Dirac equation framework

The asymptotic expansions (at small and large internuclear distances R) of the eigenvalues (potential curves) E(R) of the two-Coulomb-centre problem are obtained. The Dirac equation with an axially symmetrical potential, not allowing complete separation of variables, is solved analytically by the Wentzel-Kramers-Brillouin approach and boundary-layer method. In the framework of this scheme, the relativistic two-Coulomb-centre wavefunction is constructed. The first two terms of the asymptotic (at large internuclear distance) behaviour of the exchange interaction potential for an ion with an atom are calculated.