Relativistic spectral random-phase approximation in finite nuclei

A relativistic random-phase approximation (RPA) description of discrete excitations in closed-shell nuclei is presented using a spectral approach, with emphasis on the nature and importance of self-consistency. A functional derivation of self-consistent RPA equations is given, based on a nonrelativistic formalism, and its generalization is discussed. Vacuum polarization is neglected, but consistency demands configuration spaces that include both particle-hole pairs and pairs formed from occupied states and negative-energy states, which ensures current conservation and the decoupling of the spurious state. Results in the Walecka ({σ}-{ω}) model for various isoscalar states in ¹²C, ¹⁶O, and ⁴⁰Ca, are given, including electron scattering form factors.