Nonspectral Dirac random-phase approximation for finite nuclei

We present a version of the random-phase approximation for the description of nuclear excitations which is a consistent extension of the QHD1 mean-field theory of the ground states of doubly magic nuclei. This approach includes correlations induced by the isoscalar σ and ω mesons of QHD1. Our method employs a nonspectral single particle propagator in such a way that we avoid any basis truncation and automatically include the escape widths implied by the theory. Our calculations yield exactly conserved random-phase approximation transition currents as well as correct treatment of spuriosity for $1^{\mathrm{-}}$T=0 excitations. Because of the flexibility of our numerical method, we can treat discrete excitations, giant resonances, and the continuum response in general—including quasielastic scattering—in a unified way. We compare our results with experimental (e,e’) form factors for various discrete excitations in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ as well as with the quasielastic Coulomb response functions for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. Agreement with transition charge densities is typically quite good and in some cases superior to comparable nonrelativistic random-phase approximation calculations. Transition current densities are less well described. The question of sum rules in the relativistic random-phase approximation is also addressed.