Skyrme Hartree Fock Model Research Articles

Impurity effects of the Λ hyperon in the hypernuclear systems and

Based on the beyond-mean-field Skyrme–Hartree–Fock model, impurity effects of the Λ hyperon in the hypernuclear systems Mg and Si are investigated, respectively. Four cases, in which the Λ hyperon occupies the single-particle orbitals [000], [110], [101] and [101], are focused. In each case, the potential energy surface and the energy curves projected on certain angular momenta are employed to show the influence of the Λ hyperon on the nuclear core. Beside the shrinkage effect that is induced by the Λ hyperon occupying the s Λ orbital, it is found that the Λ hyperon on the p Λ orbital, [110], drives the nuclear core toward a prolate shape, while the ones on the other two p Λ orbitals, [101] and [101], drive the nuclear core toward an oblate shape. The energy spectra and the corresponding intra-band E2 transition rates for the rotational bands are given as a prediction for future experiments.

Initialization effects of nucleon profile on the π yields in heavy-ion collisions at medium energies

We study the problem of π production in heavy-ion collisions in the context of the isospin-dependent Boltzmann–Uehling–Uhlenbeck transport model. We generated nucleon densities using two different models, the Skyrme–Hartree–Fock (SHF) model and the configuration interaction shell model (SM). Indeed, inter-nucleon correlations are explicitly taken into account in SM, while they are averaged in the SHF model. As an application of our theoretical frameworks, we calculated the π − and π + yields in collisions of nuclei with A = 30–40 nucleons. We used different harmonic oscillator lengths b HO to generate the harmonic oscillator basis for SM in order to study both theoretical and experimental cases. It is found that the SM framework with b HO = 2.5 fm and SHF can be distinguished by the yield of π mesons, in this case the density distribution calculated by the SM produces more π in the collision. In comparison, SM with b HO = 2.0 fm is distinguished from SHF by the double π −/π + ratios with different large impact parameters, from which one can find that the double π −/π + ratios of SM change smoother and are less than those of SHF.

Neutron–proton interaction, bubble structure and neutron skin properties of Co in a Supernova

In the present paper, we investigated the neutron skin properties, central depletion effects, residual and average neutron–proton interactions for Co in a Type II Supernova 1987A. The neutron skin thicknesses performed by Skyrme–Hartree–Fock model for the isotopic chain of Co $$(17\le N\le 82)$$ are obtained with different methods to investigate the bulk and surface contributions to neutron skin thicknesses as a function of neutron number N and relative neutron excess I = (N-Z)/A. For this purpose, two-parameter Fermi (2pF) distributions for each nucleus are obtained by the proton and neutron density distributions. Since the neutron skin thickness demonstrates the dependency on the symmetry pressure of neutron matter and sensitive to the symmetry energy at the sub-saturation density, the neutron skin properties lead to the investigation on the formation and composition of the crusts in Supernova and neutron stars. For a proper understanding of surface effects of nuclei, the central depletion (or bubble structure) effects on neutron skin of nuclei in the Supernova are explained by calculating the bubble parameters b and b′. Furthermore, in order to illustrate accuracy of theoretical model used in the current work, the mass model approach is also analyzed by the calculating residual and average neutron–proton interactions, where the fluctuations in the mass model approaches have also been compared with the experimental and theoretical results in the literature. In order to evaluate more nuclear properties, we also analyzed the charge form factors and the single- particle energy levels for Co isotopes in the Supernova for providing nuclear data for electron-nucleus scattering experimental processes.

Study of the nuclear structure of some exotic nuclei using nonrelativistic and relativistic mean-field methods

The nuclear shell model with the Skyrme–Hartree–Fock (SHF), as a nonrelativistic approach, and the Relativistic Hartree–Fock–Bogoliubov (RHFB) methods have been used to study the nuclear structure of some exotic nuclei at the proton and neutron drip lines. Different Skyrme parametrizations, in particular SkM*, SkX, SkO, SLy4, Skxs25 and Z, have been used in the nonrelativistic region. In the relativistic region, the density-dependence meson-exchange models and density-dependence point-coupling models are used. Both methods are used to study ground state properties such as binding energy, mass radial density distribution and the corresponding root mean square (rms) mass radii. The fragmentation reaction cross-section is used as an important property to investigate the halo structure. Strong evidence for existence of a neutron halo in [Formula: see text]Li and [Formula: see text]Be and proton halo in [Formula: see text]Ne, [Formula: see text]Al and [Formula: see text]P are found using the SHF model and reaction cross-section. The ability of the SHF model to study the exotic structure with shell model occupation probability is confirmed.

Deformed K− nuclei in the Skyrme–Hartree–Fock approach

Abstract The properties of kaonic nuclei are studied using a two-dimensional Skyrme–Hartree–Fock model with a $KN$ Skyrme force. We focus in particular on the instability of the solutions for a too strong $KN$ interaction, which determines a maximum value of the kaon binding in this approach. We then analyze the change of the deformation properties of several core-deformed nuclei caused by the added kaon, and find a shrinking of the core and in some cases a complete loss of deformation.

Systematic Study of the Nuclear Structure for Some Exotic Nuclei Using Skyrme–Hartree–Fock Method

The ground state charge, neutron, proton and matter densities, the associated nuclear radii and the binding energy per nucleon of 8B, 17Ne, 23Al and 27P halo nuclei have been investigated using the Skyrme–Hartree–Fock (SHF) model with the new SKxs25 parameters. According to the calculated results, it is found that the SHF model with these Skyrme parameters provides a good description on the nuclear structure of above proton-rich halo nuclei. The elastic charge form factors of 8B and 17Ne halo nuclei and those of their stable isotopes 10B and 20Ne are calculated using plane-wave Born approximation with the charge density distributions obtained by SHF model to investigate the effect of the extended charge distributions of proton-rich nuclei on the elastic electron scattering. Calculations show that the major difference between the elastic charge form factors of halo nuclei and those of their stable isotopes is caused by the variation in the charge density distributions, especially the details of the outer parts.

Impact parameter dependence of the yield ratios of light particles as a probe of neutron skin

The yield ratios of neutron/proton (R(n/p)) and $${^3}\hbox {H}/{^3}{\text{He}}$$ ( $$R(t/{^3}{\mathrm{He}})$$ ) with reduced rapidity from 0 to 0.5 are investigated for 50 MeV/u $${^{42,44,46,48,50,52,54,56}}{\text{Ca}} + {^{40}}{\text{Ca}}$$ . This was conducted at whole reduced impact parameters using the isospin-dependent quantum-molecular-dynamics model in which the initial neutron and proton densities are sampled within the Skyrme–Hartree–Fock model, using which the neutron skin thickness ( $$\Delta {R_{\rm{np}}}$$ ) is determined for different neutron-rich Ca isotopes. The results show that both R(n/p) and $$R(t/{^3}{\mathrm{He}})$$ have strong linear correlations with $$\Delta {R_{\rm{np}}}$$ of different Ca isotopic projectiles from five different centralities. It is suggested that R(n/p) and $$R(t/{^3}{\mathrm{He}})$$ , from the same centrality, could be treated as possible experimental observables to extract the neutron skin or halo thickness for neutron-rich isotopic nuclei, including the nuclei near the neutron drip line.

Evolution of the Position of Single-particle Levels in Neutron-rich Cerium and Neodymium Isotopes

Different Skyrme functional parametrizations were tested for Ce and Nd isotopes for N > 82. The method employed in the study is the axial Skyrme–Hartree–Fock model+BCS. For selected parametrizations, ground-state deformations β2,β3 and β4 have been found and the evolution of single-neutron and single-proton states around the Fermi level along the chain of Ce and Nd isotopes has been investigated. These results were then compared to the existing experimental data.

Nuclear density-functional theory and fission of super-heavy elements

We review the prediction of fission properties of super-heavy elements (SHE) by self-consistent mean-field models thereby concentrating on the widely used Skyrme-Hartree-Fock (SHF) approach. We explain briefly the theoretical tools: the SHF model, the calibration of model parameters together with statistical analysis of uncertainties and correlations, and the involved computation of fission lifetimes. We present an overview of fission stability in comparison to other decay channels over the whole landscape of SHE reaching deep into the $r$-process domain. The main emphasis lies on a detailed discussion of the various ingredients determining eventually the fission properties. The main result is that fission is an involved process which explores many different influences with almost equal share, basic bulk properties (also known as liquid-drop model parameters), pairing strengths, and shell effects. %

Exotic structure of medium-heavy hypernuclei in the Skyrme Hartree-Fock model

We study exotic structure of medium heavy hypernuclei with core nuclei of Ar isotopes and $^{40}\mathrm{Ca}$. Particulary, the superdeformed (SD) states and the corresponding hypernuclei are calculated in the frame of the Skyrme Hartree-Fock (SHF) + BCS model together with a microscopic $\mathrm{\ensuremath{\Lambda}}N$ interaction. We found that the $\mathrm{\ensuremath{\Lambda}}$ separation energy of the ground state is larger than that of the SD state. The result is consistent with the antisymmetrized molecular dynamics (AMD) calculation, but inconsistent with that of relativistic mean field (RMF). The similarity between SHF and AMD and the difference of $\mathrm{\ensuremath{\Lambda}}$ separation energy between SHF and RMF both come from the density distribution in the core nuclei and the corresponding hypernuclei.

The structure of hypernuclei and hyperon mixing in neutron-star matter

We review our recent studies of the structure of Λ hypernuclei within the framework of the Gaussian expansion method for s- and p-shell hypernuclei and the mean-field approach for sd-shell hypernuclei. Specifically, we focus on the structures of (i) the energy splittings of the – and – levels in Be and within the framework of and , three- and four-body cluster models for the hyperon–nucleon (Y–N) spin–orbit force; (ii) the system for coupling; (iii) the weakly bound states or resonant states of neutron-rich Λ hypernuclei such as and He within the framework of and four-body models; and (iv) the tensor correlation effect and super-deformation structure of Λ hypernuclei based on sd-shell nuclei with mass using the deformed Skyrme–Hartree–Fock model and the antisymmetrized molecular dynamics model. As an extreme limit of nuclei including multiple hyperons, we review hyperon effects in neutron-star matter in the high-density region using recent Y–N interactions.

Investigating a suitable equation of state for an infinite system of nucleons

In this paper, the average energy variation with respect to the density of a system of nucleons is theoretically studied. A new formula is proposed for the nuclear equation of state. This formula is related to an infinite system of protons and neutrons with relatively small thermal excitation. It is shown that the presented formulation for the nuclear equation of state reproduces the results obtained in the Skyrme–Hartree–Fock (SHF) and Relativistic Mean-Field (RMF) models of nuclear matter. It should be realized that the consistency of the obtained results for nuclear matter with the predictions of the well-known SHF and RMF models for symmetric and asymmetric system of nucleons indicates the reliability of this formulation for various types of nuclear matter in large scales such as neutron stars.

Error estimates for the Skyrme–Hartree–Fock model

There are many complementary strategies to estimate the extrapolation errors of a model calibrated in least-squares fits. We consider the Skyrme–Hartree–Fock model for nuclear structure and dynamics and exemplify the following five strategies: uncertainties from statistical analysis, covariances between observables, trends of residuals, variation of fit data, and dedicated variation of model parameters. This gives useful insight into the impact of the key fit data as they consist of binding energies, charge rms radii, and charge formfactor. Amongst others, we check in particular the predictive value for observables in the stable nucleus 208Pb, the super-heavy element 266Hs, r-process nuclei, and neutron stars.

A region of high-spin toroidal isomers

The combined considerations of both the bulk liquid-drop-type behavior and the quantized angular momentum reveal that high-spin toroidal isomeric states may have general occurrences for light nuclei with 28⩽A⩽52. High-spin N=Z toroidal isomers in this mass region have been located theoretically using cranked self-consistent constraint Skyrme–Hartree–Fock model calculations.

Tensor force and shape evolution of Si isotopes in the Skyrme–Hartree–Fock model

Much interest has recently been devoted to the shape evolution of neutron-rich Si isotopes both experimentally and theoretically. We present our study of |$^{28-42}$|Si using the Skyrme–Hartree–Fock model with the Bardeen-Cooper-Schrieffer approximation for the pairing channel. We use an empirical pairing parameter deduced from the experimental binding energy data for each nucleus and each Skyrme parametrization. The recent highlight of the deformation change from the prolate shape of |$^{38}$|Si to the oblate shape of |$^{42}$|Si is confirmed in the present model. We also emphasize the role of the tensor force in deformations of neutron-rich |$^{30,32}$|Si, and discuss its underlying physics.

Neon Isotope and Lambda Hypernuclei with the Nijmegen Hyperon Interaction

We optimize the nuclear parameterization for the description of Ne isotope in the deformed Skyrme–Hartree–Fock model, and succeed in providing an overall good description of the nuclear deformation in this model, which is consistent with the available experimental data and microscopic model results. The addition of a Λ hyperon, based on a realistic Nijmegen hyperon–nucleon potential, is found to have no large effect on the shape of the isotopic nuclei, indicating that the neon isotopic nuclei might not be good candidates for studying the deformation effect of hyperon in future experiments.

Stellar electron-capture rates on nuclei based on a microscopic Skyrme functional

We compute electron-capture rates for ${}^{54,56}$Fe and Ge isotopes using a self-consistent microscopic approach. The single-nucleon basis and the occupation factors in the target nucleus are calculated in the finite-temperature Skyrme Hartree-Fock model, and the ${J}^{\ensuremath{\pi}}={0}^{\ifmmode\pm\else\textpm\fi{}}$, ${1}^{\ifmmode\pm\else\textpm\fi{}}$, ${2}^{\ifmmode\pm\else\textpm\fi{}}$ charge-exchange transitions are determined in the finite-temperature random-phase approximation (RPA). The scheme is self-consistent; i.e., both the Hartree-Fock and the RPA equations are based on the same Skyrme functional. Several interactions are used in order to provide a theoretical uncertainty on the electron-capture rates for different astrophysical conditions. Comparing electron-capture rates obtained either with different Skyrme sets or with different available models indicates that differences up to one to two orders of magnitude can arise.

Generic constraints on the relativistic mean-field and Skyrme-Hartree-Fock models from the pure neutron matter equation of state

We study the nuclear symmetry energy S(rho) and related quantities of nuclear physics and nuclear astrophysics predicted generically by relativistic mean-field (RMF) and Skyrme-Hartree-Fock (SHF) models. We establish a simple prescription for preparing equivalent RMF and SHF parametrizations starting from a minimal set of empirical constraints on symmetric nuclear matter, nuclear binding energy and charge radii, enforcing equivalence of their Lorenz effective masses, and then using the pure neutron matter (PNM) equation of state (EoS) obtained from ab-initio calculations to optimize the pure isovector parameters in the RMF and SHF models. We find the resulting RMF and SHF parametrizations give broadly consistent predictions of the symmetry energy J and its slope parameter L at saturation density within a tight range of <~2 MeV and <~6 MeV respectively, but that clear model dependence shows up in the predictions of higher-order symmetry energy parameters, leading to important differences in (a) the slope of the correlation between J and L from the confidence ellipse, (b) the isospin-dependent part of the incompressibility of nuclear matter K_tau, (c) the symmetry energy at supra-saturation densities, and (d) the predicted neutron star radii. The model dependence can lead to about 1-2 km difference in predictions of the neutron star radius given identical predicted values of J, L and symmetric nuclear matter (SNM) saturation properties. Allowing the full freedom in the effective masses in both models leads to constraints of 30<~J<~31.5 MeV, 35<~L<~60 MeV, -330<~K_tau<~-216 MeV for the RMF model as a whole and 30<~J<~33 MeV, 28<~L<~65 MeV, -420<~K_tau<~-325 MeV for the SHF model as a whole. Notably, given PNM constraints, these results place RMF and SHF models as a whole at odds with some constraints on K_tau inferred from giant monopole resonance and neutron skin experimental results.

Two-Channel Skyrme–Hartree–Fock Model for Bose–Einstein Condensate Near Feshbach Resonance

We apply a two-channel Skyrme–Hartree–Fock model to describe an atomic Bose–Einstein condensate near a Feshbach resonance. In this model the single-atom wave-function has two components corresponding to the two intrinsic states of the atom related to the Feshbach resonance. From the variational principle we derive the corresponding system of two coupled equations for the single-atom wave-function—a generalization of the Gross–Pitaevskii equation. We carry out an exploratory gaussian variational calculation and show that the two-component model can successfully describe the collapse of the condensate near a Feshbach resonance.

Skyrme-Hartree-Fock plus Tensor Correction for Nuclear Matter

We study the equation of states of symmetric and pure neutron matter in the SkyrmeHartree-Fock (SHF) model with tensor corrections. We are aware now that the pion exchange interaction has a significant contribution to nuclear structure in light nuclei. The pion generates a strong tensor interaction between two nucleons, which cannot be treated within the Hartree-Fock framework for the spin-saturated system such as homogeneous nuclear matter. Therefore, we study the role of the tensor interaction based on the SHF model, in which we extend it by explicitly introducing two-particle-two-hole (2p-2h) excitations for the treatment of the tensor interaction in symmetric nuclear matter and pure neutron matter. We are able to describe infinite matter very well using the SHF model with tensor corrections. We also discuss the connection between the symmetry energy and the tensor interaction in this framework. Subject Index: 201