Mean Field with Tensor Force and Shell Structure of Exotic Nuclei

Abstract

The tensor force is implemented into the mean-field model so that the evolution of nuclear shells can be described for exotic nuclei as well as stable ones. Besides the tensor-force part simulating the meson exchange, the model is an extension of the successful Gogny model. One of the major issues of rareisotope beam physics is a reduced spin-orbit splitting in neutron-rich exotic nuclei. It will be shown that the effect of the tensor force on this splitting is larger than or about equal to the one due to the neutron skin. We will present predictions for stable and exotic nuclei with comparisons to conventional results and experimental data. DOI: 10.1103/PhysRevLett.97.162501 PACS numbers: 21.60.ÿn, 21.10.Pc, 21.30.Fe Like other many-body quantal systems, the mean field governs largely the structure of nuclei. Recently it has been shown, by using the shell model, that the tensor force has a specific, robust, and systematic effect on the single-particle energies of nuclei, even breaking or creating magic numbers in some cases [1]. It is then very interesting to explore what can be seen by including the tensor force into the mean-field calculations. Note that in the shell model, the single-particle wave functions are given a priori and are fixed more or less.The existing successful and systematic mean-field calculations are either of Skyrme-type [2,3] or of Gogny-type [4]. In the former, the interaction is of zero-range nature with derivative couplings, while the tensor terms have been suppressed, probably because the number of free parameters is made as small as possible [5]. In the latter, the interaction is of finite-range nature [4,6,7], while there is no tensor term either.In this Letter, we present a new mean-field model which includes the tensor force explicitly and keeps the merits of the existing models. In exotic nuclei far from stability with large asymmetric ratios between the proton number (Z) and the neutron number (N), the single-particle properties may show distinct characteristic changes from those seen in usual stable nuclei. In particular, in neutron-rich exotic nuclei, the neutron skin can be created [8], which may give rise to a diffuse surface resulting in a reduced spin-orbit splitting [9,10]. The tensor force changes the spin-orbit splitting in a systematic and different way [1]. It should be very important to investigate the neutron-skin effect and the tensor-force effect within a single framework.We introduce a new Gogny-type mean-field model, called GT2. All the terms of the Gogny interaction are kept, while their strength parameters are readjusted. The Gogny interaction contains central interactions with Gaussian-function dependences on the relative distance of nucleons [4,6,7]. Two ranges of Gaussians are included with full four spin-isospin coupling terms, ending up with eight terms. The tensor term is expressed as [1],where 1;2 (s 1;2 ) denotes the isospin (spin) of nucleons 1 and 2, K means the coupling of two operators in the brackets to an angular momentum (or rank) K, and Y d...

Tensor part of the Skyrme energy density functional. III. Time-odd terms at high spin

“…We have seen in Sect. III C 1 that the contributions of E ss and E sT + E sF to J (2) 3 for all parameterizations. In addition, all C s t have been taken independent of density, choosing its value at the saturation density of nuclear matter for the coupling constant that is not varied.…”

Interplay between tensor force and deformation in even–even nuclei

“…Keeping the D1S parameters unchanged the two tensor parameters were adjusted to reproduce the neutron single particle energies 1f 5/2 and 1f 7/2 in 48 Ca. Refitting a nuclear effective interaction in a global procedure as it is done in [24] for the Skyrme plus tensor interaction or in [20] for the Gogny plus a tensor-isospin term interaction represents a considerable amount of work and is far beyond the scope of this study. In the present paper we are interested in the effect of tensor terms in the deformation of the ground state of various nuclei using the D1ST2a interaction.…”

“…A lot of works recently aimed to determine the most reliable tensor term built-in effective interaction. It is now clear that the tensor term modifies the single particle energies [16] and the binding energies [17], the multipoles giant resonances [18,19] and even may affect the magic numbers and the spin-orbit splitting in some cases [20].…”

“…In all cases it rises the problem of the way to fit the parameters. Otsuka et al [20] make the overall fit of the interaction using the properties of the AV8 potential [17] to adjust the tensor strength. Lesinski et al [24] built 36 parametrizations of the zero range Skyrme interaction including a tensor term.…”

“…Alongside a full variational procedure is performed to get the new parametrizations for the Skyrme [24,25] and Gogny [20] interactions. In all cases it rises the problem of the way to fit the parameters.…”