Shell evolution aboveZ,N=50within Skyrme density functional theory: The impact of deformation and tensor interactions

Abstract

Background Recent years have seen considerable effort in associating the shell evolution (SE) for a chain of isotones or isotopes with the underlying nuclear interactions. In particular, it has been fairly well established that the tensor part of the Skyrme interaction is indispensable for understanding certain SE above Z, N =50 shell closures, as a function of nucleon numbers.Purpose The purpose of the present work is twofold: (1) to study the effect of deformation due to blocking, on the SE above Z, N = 50 shell closures; (2) to examine the optimal parameterizations in the tensor part which gives a proper description of the SE above Z, N =50 shell closures.Methods I use Skyrme-Hartree-Fock-Bogoliubov (SHFB) method to compute the even-even vacua of the Z = 50 isotopes and N = 50 isotones. For Sb and odd-A Sn isotopes, I perform calculations with a blocking procedure which accounts for the polarization effects, including deformations.Results The blocking SHFB calculations show that the light odd-A Sb isotopes, with only one valence proton occupying down-sloping Ω = 11/2 − and Ω = 7/2 + Nilsson orbits, assume finite oblate deformations. This reduces the energy differences between 11/2 − and 7/2 + states by about 500 keV for 51Sb56−66, bringing the energy-difference curve closer to the experimental one. With UNE2T1 energy density functional (EDF), which differs from unedf2 parameterization by tensor terms, a better description of the slope of ∆e(π1h 11/2 − π1g 7/2 ) as a function of neutron number has been obtained. However, the trend of ∆e(π1g 7/2 − π2d 5/2 ) curve is worse using UNE2T1 EDF. ∆e(ν3s 1/2 − ν2d 5/2 ), and ∆e(ν1g 7/2 − ν2d 5/2 ) curve for N =50 isotones using UNE2T1 seems to be consistent with experimental data. The neutron SE of ∆e(ν1h 11/2 − ν1g 7/2 ), and ∆e(ν1g 7/2 − ν2d 5/2 ) for Sn isotopes are shown to be sensive to αT tensor parameter.Conclusions Within the Skyrme self-consistent mean-field model, the deformation degree of freedom has to be taken into account for Sb isotopes, N =51 isotones, and odd-A Sn isotopes when discussing variation of quantities like shell gap etc. The tensor terms are important for describing the strong variation of ∆E(Ω π = 11/2 − − 7/2 + ) in Sb isotopes. The SE of 1/2 + , and 7/2 + states in N =51 isotones may show signature for the existence of tensor interaction. The experimental excitation energies of 11/2 − , and 7/2 + states in odd-A Sn isotopes close to 132 Sn give prospects for constraining the αT parameter.

Persistence of magicity in neutron-rich exotic 78Ni in ground as well as excited states

“…31 Furthermore, the sensitivity to the symmetry energy and the role of the continuum in neutron-rich Ni isotopes has been discussed by Piekarewicz et al 32 Shell evolution above Z, N=50 within Skyrme density functional theory has been analyzed with a blocking procedure which accounts for the polarization effects, including deformations. 33 In addition, the signature of fifth island of inversion, i.e., a well-deformed prolate band at low excitation energy in 78 Ni, providing a striking example of shape coexistence far from stability. 34 In a very recent work, the temperature dependence of the symmetry energy and neutron skins in Ni, Sn, and Pb isotopic chains 35 of magic nuclei have indicated the importance of the study of the excited states of the neutron rich doubly magic nuclei.…”

Tensor and pairing interactions within the QMC energy density functional

“…EDFs for magic and semi-magic nuclei [3,5] and using the Gogny interaction for mediummass isotopic chains up to zirconium [25], where results from various parametrisations were compared. In this section we discuss the contribution of the tensor component to nuclear shapes using the QMCπ-III-T functional.…”

“…For some Skyrme parametrizations in Refs. [3,5] the main impact of the tensor component is the disappearance of the deformed minimum of 100 Zr. Note that this is not the case for QMC, where the deformed minimum did not change much along the Zr isotopic chain, even with the inclusion of the tensor component.…”

“…Here the tensor components correspond to the terms of the QMC density functional which are quadratic in the spin-current density (also called spin-tensor) and they arise naturally from the spin dependent part of the QMC effective interaction. They were neglected in previous works for simplicity and we stress that they do not introduce new parameters, contrary to other approaches [1][2][3][4][5].…”

Tensor-force effects on shell-structure evolution in $N = 82$ isotones and $Z = 50$ isotopes in the relativistic Hartree-Fock theory

“…During the last two decades, the tensor-force effects on the single-particle energies have been studied extensively, in both the nuclear density functional theory (DFT) [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] and the shell model [15,21,[40][41][42][43][44].…”