We have studied the low-lying magnetic spectra of ${}^{12}\mathrm{C}$, ${}^{16}\mathrm{O}$, ${}^{40}\mathrm{Ca}$, ${}^{48}\mathrm{Ca}$, and ${}^{208}\mathrm{Pb}$ nuclei within the random phase approximation (RPA) theory, finding that the description of low-lying magnetic states of doubly-closed-shell nuclei imposes severe constraints on the spin and tensor terms of the nucleon-nucleon effective interaction. We first used four phenomenological effective interactions, and we obtained good agreement with the experimental magnetic spectra and, to a lesser extent, with the electron scattering responses. Then we made self-consistent RPA calculations to test the validity of the finite-range Gogny D1 interaction. For all the nuclei under study, we found that this interaction inverts the energies of all the magnetic states forming isospin doublets.

• Received 16 January 2009

DOI:https://doi.org/10.1103/PhysRevC.79.044311