Tensor part of the Skyrme energy density functional. II. Deformation properties of magic and semi-magic nuclei

Abstract

We study systematically the impact of the time-even tensor terms of the Skyrme energy density functional, i.e. terms bilinear in the spin-current tensor density, on deformation properties of closed shell nuclei corresponding to 20, 28, 40, 50, 82, and 126 neutron or proton shell closures. We compare results obtained with three different families of Skyrme parameterizations whose tensor terms have been adjusted on properties of spherical nuclei:(i)T IJ interactions proposed in the first paper of this series [T. Lesinski et al., Phys. Rev. C 76, 014312 (2007)] which were constructed through a complete readjustment of the rest of the functional (ii) parameterizations whose tensor terms have been added perturbatively to existing Skyrme interactions, with or without readjusting the spin-orbit coupling constant. We analyse in detail the mechanisms at play behind the impact of tensor terms on deformation properties and how studying the latter can help screen out unrealistic parameterizations. It is expected that findings of the present paperare to a large extent independent of remaining deficiencies of the central and spin-orbit interactions, and will be of great value for the construction of future, improved energy functionals.

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

“…For T62, the deformation energy curve looks like that of a double magic nucleus. For SLy4T and SLy4Tself [38], it is the reduced spin-orbit interaction that reinforces the proton Z = 40 shell closure. The prolate minimum becomes a shoulder around 5 MeV, leading to the coexistence of spherical and oblate minima.…”

“…The protocols for the adopted Skyrme parameter sets can be found in Ref. [38]. This figure is taken from Ref.…”

“…We follow here the notation of [38,39]. The notation T and F will become more transparent by looking at Eq.…”

“…This figure is taken from Ref. [38]. constant α and a vanishing proton-neutron coupling constant β; T44 with a mixture of like-particle and proton-neutron tensor terms, T62 with a large proton-neutron coupling constant β and a vanishing likeparticle coupling constant α; and T66 with large and equal proton-neutron and like-particle tensor-term coupling constants.…”

“…[38] with deformed HF calculations. The main purpose of this work has been to test the forces introduced in [58].…”