Nonrelativistic Mean-field Models Research Articles

Relativistic and nonrelativistic mean field analysis of the shell evolution in 44−52Ar isotopes

The systematic search of axial ground state and the emergence of new gaps in neutron-rich [Formula: see text]Ar isotopes are the challenging of current calculations of relativistic and nonrelativistic mean field models. For this purpose, we have employed the model based on Relativistic Hartree–Bogoliubov (RHB) with the density-dependent effective interaction of point coupling DD-PCX type. However, the nonrelativistic mean field calculations based on Hartree-Fock model were carried out with Skyrme SV-min parametrization. All the present calculations were performed within axial symmetries. The results provide that most of isotopes show an oblate-deformed ground state. In particular, [Formula: see text]Ar and [Formula: see text]Ar display a spherical shape in their ground states with SV-Min calculations. There is a notable signature of the sub-shell closure at neutron number [Formula: see text], whereas [Formula: see text] is expected to be nearly quenched in the spherical ground. Furthermore, coexistence features are predicted in the neutron-rich [Formula: see text]Ar isotope. We have also studied the neutron axial densities and its central depletion in the well-deformed grounds for the first time. In addition to these, the proton single-particle evolution and bubble-like structure at [Formula: see text]Ar are very well reproduced with DD-PCX calculations.

The mean-square radius of the neutron distribution in the relativistic and non-relativistic mean-field models

Abstract It is investigated why the root-mean-square radius of the point neutron distribution is smaller by about 0.1 fm in non-relativistic mean-field models than in relativistic ones. The difference is shown to stem from the different values of the product of the effective mass and the strength of the one-body potential in the two frameworks. The values of those quantities are constrained by the Hugenholtz–Van Hove theorem. The neutron skin is not a simple function of the symmetry potential, but depends on the nucleon effective mass.

Nucleon momentum distribution of 56Fe from the axially deformed relativistic mean-field model with nucleon-nucleon correlations

Nucleon momentum distribution (NMD), particularly its high-momentum components, is essential for understanding the nucleon--nucleon ($ NN $) correlations in nuclei. Herein, we develop the studies of NMD of $^{56}\text{Fe}$ from the axially deformed relativistic mean-field (RMF) model. Moreover, we introduce the effects of $ NN $ correlation into the RMF model from phenomenological models based on deuteron and nuclear matter. For the region $ k<k_{\text{F}} $, the effects of deformation on the NMD of the RMF model are investigated using the total and single-particle NMDs. For the region $ k>k_{\text{F}} $, the high-momentum components of the RMF model are modified by the effects of $ NN $ correlation, which agree with the experimental data. Comparing the NMD of relativistic and non-relativistic mean-field models, the relativistic effects on nuclear structures in momentum space are analyzed. Finally, by analogizing the tensor correlations in deuteron and Jastrow-type correlations in nuclear matter, the behaviors and contributions of $ NN $ correlations in $^{56}\text{Fe}$ are further analyzed, which helps clarify the effects of the tensor force on the NMD of heavy nuclei.

GW170817: Constraining the nuclear matter equation of state from the neutron star tidal deformability

Constraints set on key parameters of the nuclear matter equation of state (EoS) by the values of the tidal deformability, inferred from GW170817, are examined by using a diverse set of relativistic and non-relativistic mean field models. These models are consistent with bulk properties of finite nuclei as well as with the observed lower bound on the maximum mass of neutron star $\sim 2 ~ {\rm M}_\odot$. The tidal deformability shows a strong correlation with specific linear combinations of the isoscalar and isovector nuclear matter parameters associated with the EoS. Such correlations suggest that a precise value of the tidal deformability can put tight bounds on several EoS parameters, in particular, on the slope of the incompressibility and the curvature of the symmetry energy. The tidal deformability obtained from the GW170817 and its UV/optical/infrared counterpart sets the radius of a canonical $1.4~ {\rm M}_{\odot}$ neutron star to be $11.82\leqslant R_{1.4}\leqslant13.72$ km.

Nuclear matter fourth-order symmetry energy in nonrelativistic mean-field models

Background: Nuclear matter fourth-order symmetry energy ${E}_{\text{sym,4}}(\ensuremath{\rho})$ may significantly influence the properties of neutron stars such as the core-crust transition density and pressure as well as the proton fraction at high densities. The magnitude of ${E}_{\text{sym,4}}(\ensuremath{\rho})$ is, however, largely uncertain.Purpose: Based on systematic analyses of several popular nonrelativistic energy density functionals with mean-field approximation, we estimate the value of the ${E}_{\text{sym,4}}(\ensuremath{\rho})$ at nuclear normal density ${\ensuremath{\rho}}_{0}$ and its density dependence, and explore the correlation between ${E}_{\text{sym,4}}({\ensuremath{\rho}}_{0})$ and other macroscopic quantities of nuclear matter properties.Method: We use the empirical values of some nuclear macroscopic quantities to construct model parameter sets by the Monte Carlo method for four different energy density functionals with mean-field approximation, namely, the conventional Skyrme-Hartree-Fock (SHF) model, the extended Skyrme-Hartree-Fock (eSHF) model, the Gogny-Hartree-Fock (GHF) model, and the momentum-dependent interaction (MDI) model. With the constructed samples of parameter sets, we can estimate the density dependence of ${E}_{\text{sym,4}}(\ensuremath{\rho})$ and analyze the correlation of ${E}_{\text{sym,4}}({\ensuremath{\rho}}_{0})$ with other macroscopic quantities.Results: The value of ${E}_{\text{sym,4}}({\ensuremath{\rho}}_{0})$ is estimated to be $1.02\ifmmode\pm\else\textpm\fi{}0.49$ MeV for the SHF model, $1.02\ifmmode\pm\else\textpm\fi{}0.50$ MeV for the eSHF model, $0.70\ifmmode\pm\else\textpm\fi{}0.60$ MeV for the GHF model, and $0.74\ifmmode\pm\else\textpm\fi{}0.63$ MeV for the MDI model. Moreover, our results indicate that the density dependence of ${E}_{\text{sym,4}}(\ensuremath{\rho})$ is model dependent, especially at higher densities. Furthermore, we find that the ${E}_{\text{sym},4}({\ensuremath{\rho}}_{0})$ has strong positive (negative) correlation with isoscalar (isovector) nucleon effective mass ${m}_{s,0}^{*}$ (${m}_{v,0}^{*}$) at ${\ensuremath{\rho}}_{0}$. In particular, for the SHF and eSHF models, the ${E}_{\text{sym,4}}(\ensuremath{\rho})$ is completely determined by the isoscalar and isovector nucleon effective masses ${m}_{s}^{*}(\ensuremath{\rho})$ and ${m}_{v}^{*}(\ensuremath{\rho})$, and the analytical expression is given.Conclusions: In the mean-field models, the magnitude of ${E}_{\text{sym,4}}({\ensuremath{\rho}}_{0})$ is generally less than $2\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$, and its density dependence depends on models, especially at higher densities. ${E}_{\text{sym,4}}({\ensuremath{\rho}}_{0})$ is strongly correlated with ${m}_{s,0}^{*}$ and ${m}_{v,0}^{*}$.

Consistent empirical physical formulas for potential energy curves of 38–66Ti isotopes by using neural networks

Nuclear shape transition has been actively studied in the past decade. In particular, the understanding of this phenomenon from a microscopic point of view is of great importance. Because of this reason, many works have been employed to investigate shape phase transition in nuclei within the relativistic and non-relativistic mean field models by examining potential energy curves (PECs). In this paper, by using layered feed-forward neural networks (LFNNs), we have constructed consistent empirical physical formulas (EPFs) for the PECs of 38-66Ti calculated in Hartree-Fock-Bogoliubov (HFB) method with SLy4 Skyrme forces. It has been seen that the PECs obtained by neural network method are compatible with those of HFB calculations.

Erratum: Multiple band structures inTa169[Phys. Rev. C74, 054314 (2006)

We study the sensitivity of the neutron skin thickness, $S$, in a $^{208}$Pb nucleus to the addition of nucleon-sigma-rho coupling corrections to a selection (PK1, NL3, S271, Z271) of interactions in relativistic mean field model. The PK1 and NL3 effective interactions lead to a minimum value of $S$ = 0.16 fm in comparison with the original value of $S$ = 0.28 fm. The S271 and Z271 effective interactions yield even smaller values of $S$ = 0.11 fm, which are similar to those for nonrelativistic mean field models. A precise measurement of the neutron radius, and therefore $S$, in $^{208}$Pb will place an important constraint on both relativistic and nonrelativistic mean field models. We also study the correlation between the radius of a 1.4 solar-mass neutron star and $S$.

Sensitivity of neutron radii in aPb208nucleus and a neutron star to nucleon-σ-ρ coupling corrections in relativistic mean field theory

We study the sensitivity of the neutron skin thickness S in a Pb-208 nucleus to the addition of nucleon-sigma-rho coupling corrections to a selection (PK1, NL3, S271, and Z271) of interactions in a relativistic mean field model. The PK1 and NL3 effective interactions lead to a minimum value of S= 0.16 fm in comparison with the original value of S= 0.28 fm. The S271 and Z271 effective interactions yield even smaller values of S= 0.11 fm, which are similar to those for nonrelativistic mean field models. A precise measurement of the neutron radius, and therefore S, in Pb-208 will place an important constraint on both relativistic and nonrelativistic mean field models. We also study the correlation between the radius of a 1.4-solar-mass neutron star and S.

Charge density differences near 208Pb in relativistic models.

Charge density differences and cross-section ratios are calculated for $^{206}\mathrm{\ensuremath{-}}^{205}$Tl and $^{206}\mathrm{\ensuremath{-}}^{204}$Hg using relativistic mean-field models of deformed nuclei. Core polarization reduces the pure 3${\mathit{s}}_{1/2}$ component of the densities by about 10%, but the calculations still overpredict the experimental data. The data can be described by assigning fractional level occupancies to the nucleons near the Fermi surface; these occupancies are similar to those needed in calculations using nonrelativistic mean-field models.