Multiconfiguration relativistic random-phase approximation. Theory

The relativistic random-phase approximation is generalized to describe excitations of an atomic system having a multiconfiguration ground state. The response of such an atom to an imposed harmonic perturbation is determined by applying the time-dependent variational principle to a multiconfiguration wave function constructed from Dirac orbitals. Terms in the wave function independent of the external field lead to the multiconfiguration Dirac-Fock description of the ground state. Terms proportional to the external field lead to a multiconfiguration generalization of the relativistic random-phase approximation. For the special case of an atom having a ground state with two electrons coupled to $J=0$ outside of closed shells, we write out in detail equations for the configuration weights and for the electronic orbitals. These equations are expanded in a suitable basis to give expressions for the excitation probabilities. An angular momentum analysis is carried out leading to a set of coupled algebraic equations for the configuration weights and a set of radial differential equations for the electronic orbitals.