Random-phase approximation based on relativistic point-coupling models

The matrix equations of the random-phase approximation (RPA) are derived for the point-coupling Lagrangian of the relativistic mean-field (RMF) model. Fully consistent RMF plus (quasiparticle) RPA illustrative calculations of the isoscalar monopole, isovector dipole, and isoscalar quadrupole response of spherical medium-heavy and heavy nuclei test the phenomenological effective interactions of the point-coupling RMF model. A comparison with experiment shows that the best point-coupling effective interactions accurately reproduce not only ground-state properties but also data on excitation energies of giant resonances.

Figure 1

The isoscalar monopole strength distribution (left panel) and the transition densities (right panel) in ${}^{208}\mathrm{Pb}$, calculated with the PC-F1 interaction. The experimental excitation energy of the ISGMR is denoted by the arrow. The neutron, proton, and total isoscalar transition densities correspond to the peak at $E=14.16\text{MeV}$.

Figure 2

The isovector dipole strength distribution (left panel) in ${}^{208}\mathrm{Pb}$, calculated with the PC-F1, PC-F2, and PC-F4 effective interactions. The experimental excitation energy of the IVGDR is denoted by the arrow. In the right panel we plot the neutron, proton, and total isovector transition densities for the peak at $E=13.0\text{MeV}$ and calculated with PC-F1.

Figure 3

The nuclear matter asymmetry energy as function of the nucleon density, calculated with the PC-F1, PC-F2, and PC-F4 effective interactions.

Figure 4

The isoscalar quadrupole strength distribution (left panel) and the transition densities (right panel) for ${}^{208}\mathrm{Pb}$, calculated with the PC-F1 effective interaction. The experimental excitation energy of the ISGQR is denoted by the arrow. The neutron, proton, and total isoscalar transition densities correspond to the ISGQR peak at $E=11.9\text{MeV}$.