Tensor effective interaction in self-consistent random-phase approximation calculations

Abstract

We present a study of the effects of the tensor-isospin term of the effective interaction in Hartree-Fock and random-phase approximation calculations. We used finite-range forces of Gogny type, and we added to them a tensor-isospin term which behaves, at large internucleonic distances, as the analogous term of the microscopic interactions. The strength of this tensor force has been chosen to reproduce the experimental energy of the lowest 0 − excited state in 16 O, which shows large sensitivity to this term of the interaction. With these finite-range interactions, we have studied the effects of the tensor-isospin force in ground and excited states of carbon, oxygen, calcium, nickel, zirconium, tin, and lead isotopes. Our results show that the tensor force affects mainly the nucleon single-particle energies. However, we found some interesting cases where also bulk nuclear properties are sensitive to the tensor interaction.

Tensor and tensor-isospin terms in the effective Gogny interaction

“…To the best of our knowledge, only tensor-isospin terms have been considered up to now for these finite-range We consider the present work as a step forward in the direction of constructing a new parameterization of the Gogny interaction which include tensor terms. We have the perspective of validating these new tensor terms by using them in the description of observables where the particle-like contribution of the tensor force is expected to play a role, for example, in the excitation of unnatural parity states in nuclei with neutron excess and with closed proton shells [36]. Of course, a more accurate fit would require to simultaneously modify all the parameters of the Gogny force, especially the spin-orbit strength which has a strong interplay with the tensor force, in both the s.p.…”

Magnetic excitations in nuclei with neutron excess

“…The D1M force produces a neutron equation of state which has a plausible behavior at high densities, even though it does not reproduce the results of modern microscopic calculations. In addition to these two forces, we also used other two parameterizations of the Gogny force containing a tensor-isospin term, the D1ST and D1MT interactions [20]. In mean-field calculations, the inclusion of the tensor force does not modify the nuclear and neutron matter As last detail regarding our CRPA calculations, it is worth to mention that we found convergence in our results when we included at least 10 expansion coefficients of the Sturm-Bessel basis used in the calculations.…”

“…More recently [19], the D1M parametrization was adjusted to reproduce, together with neutron matter properties, a large number of binding energies and root mean square charge radii within Hartree-Fock-Bogoliubov theory. In our work, together with the D1S and D1M interactions, we also used two new parametrizations, called D1ST and D1MT, which we have recently constructed by adding a finite-range tensor-isospin term to the former two parameterizations [20].…”

Infinite matter properties and zero-range limit of non-relativistic finite-range interactions

“…The inclusion of an explicit tensor term has been proposed by the authors of Refs. [20,28,35]. In the present work we will thus consider such an extended form of the Gogny interaction [36] …”

“…Among the finite-range ones, let us mention the M3Y type effective interaction by Nakada [7,26,27], which includes finite-range spin-orbit and tensor terms, whose parameters are fitted to the Brueckner's G-matrix based on a bare interaction. Much closer to the spirit of an effective interaction, a tensor term was added to a Gogny-type potential to describe the evolution of nuclear shells for exotic nuclei as well as stable ones [20,28]. Concerning Skyrme interactions, zero-range tensor terms as originally proposed by Skyrme have been either included perturbatively to existing central ones or with a complete refit of the parameters [19].…”