Pairing in spherical nuclei: Quasiparticle random-phase appropximation calculations with the Gogny interaction

We investigate the effects of the pairing in spherical nuclei. We use the same finite-range interaction of Gogny type in the three steps of our approach, Hartree–Fock, Bardeen, Cooper, and Schrieffer, and quasiparticle random-phase-approximation calculations. We study electric- and magnetic-dipole and quadrupole and octupole excitations in oxygen and calcium isotopes and also in isotones with 20 neutrons. We investigate the pairing effects on single-particle energies and occupation probabilities, on the excitation energies, B values, and collectivity of low-lying states including the isoscalar electric-dipole and magnetic-dipole excitations, and also the giant resonances. The inclusion of the pairing increases the values of the excitation energies in all the cases that we have studied. In general, the effects of the pairing are too small to noticeably improve the agreement with the available experimental data.