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 (\ensuremath{\sigma}-\ensuremath{\omega}) model for various isoscalar states in $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, and $^{40}\mathrm{Ca}$, are given, including electron scattering form factors.