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Register a new userSpin-orbit splitting and the tensor component of the Skyrme interaction
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G. Colo
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We study the role of the tensor term of the Skyrme effective interactions on the spin-orbit splittings in the N=82 isotones and Z=50 isotopes. The different role of the triplet-even and triplet-odd tensor forces is pointed out by analyzing the spin-orbit splittings in these nuclei. The experimental isospin dependence of these splittings cannot be described by Hartree-Fock calculations employing the usual Skyrme parametrizations, but is very well accounted for when the tensor interaction is introduced. The capability of the Skyrme forces to reproduce binding energies and charge radii in heavy nuclei is not destroyed by the introduction of the tensor term. Finally, we also discuss the effect of the tensor force on the centroid of the Gamow-Teller states.
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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.
We derive the nucleon-nucleon isoscalar spin-orbit potential from the Skyrme model and find good agreement with the Paris potential. This solves a problem that has been open for more than thirty years and gives a new geometric understanding of the spin-orbit force. Our calculation is based on the dipole approximation to skyrmion dynamics and higher order perturbation theory.
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.
Single particle spin-orbit interaction energy problem in nuclear shell structure is solved through negative harmonic oscillator in the self-similar-structure shell model (SSM) [4] and considering quarks contributions on single particle spin and orbit momentum. The paper demonstrates that single particle motion in normal nuclei is described better by SSM negative harmonic oscillator than conventional shell model positive harmonic oscillator[1][2][3]. The proposed theoretical formula for spin orbit interaction energy agrees well to experiment measurements.
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