Low-lying magnetic excitations of doubly-closed-shell nuclei and nucleon-nucleon effective interactions

Abstract

We have studied the low lying magnetic spectra of 12 C, 16 O, 40 Ca, 48 Ca and 208 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 have first made an investigation by using four phenomenological effective interactions and we have obtained good agreement with the experimental magnetic spectra, and, to a lesser extent, with the electron scattering responses. Then we have made selfconsistent RPA calculations to test the validity of the finite-range D1 Gogny interaction. For all the nuclei under study we have found that this interaction inverts the energies of all the magnetic states forming isospin doublets.PACS numbers:

Tensor interaction in mean-field and density functional theory approaches to nuclear structure

“…where v 6,AV18 (r) is the radial function of the Argonne potential, has been introduced in [49]. We show in Fig.…”

“…It is interesting to notice that the same shortcoming is associated with the D1 Gogny force [107,41]. The calculations of the 1 + states performed, respectively, in [101] with the SLy5 force and in [49] with the D1 force show an inversion of the isospin doublet with respect to experiment. By implicity commenting also the role of the tensor, the authors of Ref.…”

“…(51). Interactions like SLy5 T [55] enlarge the spin-orbit splittings in 48 Ca, 90 Zr and 208 Pb (as compared with the original force SLy5) and push the unperturbed 1 + states upwards; the effect of the residual interaction is not easy to guess from simple arguments but does not tend to alter the positive sign of the shift induced by the change in spin-orbit splittings [for comparison, small residual matrix elements can also be found by using the phenomenological tensor forces that reproduce the experimental findings and that have been introduced in [49] (cf. The key point is that, anyway, simply adding a tunable tensor force does not automatically ensure that one can reproduce the experimental findings.…”

“…4 the Fourier tranform of the bare tensor component of the Argonne potential and of the IV tensor force introduced in Ref. [49]. Although there is a clear resemblance between the effective and bare tensor forces, the quenching is not negligible.…”

“…Although there is a clear resemblance between the effective and bare tensor forces, the quenching is not negligible. [ 49,50] We end this Section by mentioning another class of finite-range tensor forces. In the papers by H. Nakada [51,52,53], semi-realistic interactions derived from the original M3Y interaction [54] have been introduced.…”