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Register a new userThe tensor part of the Skyrme energy density functional. I. Spherical nuclei
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T. Lesinski
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We perform a systematic study of the impact of the J^2 tensor term in the Skyrme energy functional on properties of spherical nuclei. In the Skyrme energy functional, the tensor terms originate both from zero-range central and tensor forces. We build a set of 36 parameterizations, which covers a wide range of the parameter space of the isoscalar and isovector tensor term coupling constants, with a fit protocol very similar to that of the successful SLy parameterizations. We analyze the impact of the tensor terms on a large variety of observables in spherical mean-field calculations, such as the spin-orbit splittings and single-particle spectra of doubly-magic nuclei, the evolution of spin-orbit splittings along chains of semi-magic nuclei, mass residuals of spherical nuclei, and known anomalies of charge radii. Our main conclusion is that the currently used central and spin-orbit parts of the Skyrme energy density functional are not flexible enough to allow for the presence of large tensor terms.
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The tensor force, as an important component of strong nuclear force, generates a variety of intriguing effects ranging from few-body systems to neutron stars. It is responsible for the nucleon-nucleon correlation beyond mean-field approximation, and is accordingly proved to play no role in the standard Skyrme energy density functionals in the present work. Therefore, the Skyrmes original tensor interaction that is extensively-employed presently is invalid. As an alternative strategy, we introduced a central interaction, i.e., the $bm{sigma }_{1}cdot bm{sigma }_{2}$ term, to improve the description of experimental single-particle structure, and to address its effect, we established two Skyrme interactions IMP1 and IMP2 complemented by the calibrated charge-violating interactions. The central $bm{sigma }_{1}cdot bm{sigma }_{2}$ interaction turns out to substantially improve the description of shell evolution in Sn isotopes and $N=82$ isotones.
In a recent paper [Phys. Rev. C 101, 014305 (2020)], Dong and Shang claim that the Skyrme original tensor interaction is invalid. Their conclusion is based on the misconception that the Fourier transform of tensor interaction is difficult or even impossible, so that the Skrme-type tensor interaction was introduced in an unreasonable way. We disagree on their claim. In this note, we show that one can easily get the Skyrme force in momentum space by Fourier transformation if one starts from a general central, spin-orbit or tensor interaction with a radial dependence.
In these proceedings, we report first results for particle-number and angular-momentum projection of self-consistently blocked triaxial one-quasiparticle HFB states for the description of odd-A nuclei in the context of regularized multi-reference energy density functionals, using the entire model space of occupied single-particle states. The SIII parameterization of the Skyrme energy functional and a volume-type pairing interaction are used.
Nuclei in the $Zapprox100$ mass region represent the heaviest systems where detailed spectroscopic information is experimentally available. Although microscopic-macroscopic and self-consistent models have achieved great success in describing the data in this mass region, a fully satisfying precise theoretical description is still missing. By using fine-tuned parametrizations of the energy density functionals, the present work aims at an improved description of the single-particle properties and rotational bands in the nobelium region. Such locally optimized parameterizations may have better properties when extrapolating towards the superheavy region. Skyrme-Hartree-Fock-Bogolyubov and Lipkin-Nogami methods were used to calculate the quasiparticle energies and rotational bands of nuclei in the nobelium region. Starting from the most recent Skyrme parametrization, UNEDF1, the spin-orbit coupling constants and pairing strengths have been tuned, so as to achieve a better agreement with the excitation spectra and odd-even mass differences in $^{251}$Cf and $^{249}$Bk. The quasiparticle properties of $^{251}$Cf and $^{249}$Bk were very well reproduced. At the same time, crucial deformed neutron and proton shell gaps open up at $N=152$ and $Z=100$, respectively. Rotational bands in Fm, No, and Rf isotopes, where experimental data are available, were also fairly well described. To help future improvements towards a more precise description, small deficiencies of the approach were carefully identified. In the $Zapprox100$ mass region, larger spin-orbit strengths than those from global adjustments lead to improved agreement with data. Puzzling effects of particle-number restoration on the calculated moment of inertia, at odds with the experimental behaviour, require further scrutiny.
In the latest version of the QMC model, QMC$pi$-III-T, the density functional is improved to include the tensor component quadratic in the spin-current and a pairing interaction derived in the QMC framework. Traditional pairing strengths are expressed in terms of the QMC parameters and the parameters of the model optimised. A variety of nuclear observables are calculated with the final set of parameters. The inclusion of the tensor component improves the predictions for ground-state bulk properties, while it has a small effect on the single-particle spectra. Further, its effect on the deformation of selected nuclei is found to improve the energies of doubly-magic nuclei at sphericity. Changes in the energy curves along the Zr chain with increasing deformation are investigated in detail. The new pairing functional is also applied to the study of neutron shell gaps, where it leads to improved predictions for subshell closures in the superheavy region.
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