Relativistic random-phase approximation with density-dependent meson-nucleon couplings

The matrix equations of the relativistic random-phase approximation (RRPA) are derived for an effective Lagrangian characterized by density-dependent meson-nucleon vertex functions. The explicit density dependence of the meson-nucleon couplings introduces rearrangement terms in the residual two-body interaction. Their contribution is essential for a quantitative description of excited states. Illustrative calculations of the isoscalar monopole, isovector dipole, and isoscalar quadrupole response of ${}^{208}\mathrm{Pb},$ are performed in the fully self-consistent RRPA framework based on effective interactions with a phenomenological density dependence adjusted to nuclear matter and ground-state properties of spherical nuclei. The comparison of the RRPA results on multipole giant resonances with experimental data constrains the parameters that characterize the isoscalar and isovector channel of the density-dependent effective interactions.