Neutron radii in nuclei and the neutron equation of state

The root-mean-square radius for neutrons in nuclei is investigated in the Skyrme Hartree-Fock model. The main source of theoretical variation comes from the exchange part of the density-dependent interaction which can be related to a basic property of the neutron equation of state. A precise measurement of the neutron radius in 208Pb would place an important new constraint on the equation of state for neutron matter. The Friedman-Pandharipande neutron equation of state would lead to a very precise value of 0.16+/-0.02 fm for the difference between the neutron and the proton root-mean-square radius in 208Pb.     

Peninsula of neutron stability of nuclei in the neighborhood of neutron magic number N = 126

The properties of the ground state of even-even nuclei with extreme neutron excess that are remote from the known neutron drip line (NDL) are calculated. The calculations are based on the Hartree-Fock method with Skyrme forces SkM*, SkI2, Sly4, Ska) with allowance for axial deformation and the BCS pairing approximation. It is shown that the isotone chain at the neutron number N = 126 beyond the NDL forms a peninsula of nuclei that are stable with respect to the emission of one neutron (PNS). The neutron and proton density distributions of the PNS nuclei have spherical symmetry. A mechanism for restoring the stability of nuclei beyond the NDL is discussed. The obtained results are compared with those from Hartree-Fock-Bogoliubov calculations for long isotope chains of Zr and Pd up to the NDL.     

Neutron skin thickness and nuclear matter properties

Linear correlations are found among the isovector nuclear matter properties in both the Skyrme-Hartree-Fock (SHF) and the relativistic mean-field (RMF) models. In addition, we found a kind of correlation between the isovector nuclear matter properties and the incompressibility in the SHF model. The Skyrme parameters are related analytically to nuclear matter properties with the Thomas—Fermi approximation. By using a linear correlation between the neutron skin thickness and the pressure of the neutron matter in the SHF model, we show that the neutron skin thickness of ²⁰⁸Pb gives crucial information about not only the neutron equation of state but also the isovector nuclear matter properties and the parametrization of Skyrme interaction. The text was submitted by the authors in English.     

一种同位旋相关的核物质状态方程

在Hartree–Fock近似下,从扩展的Skyrme有效相互作用出发,给出了一种同位旋相关的核物质状态方程.分析了在不同相对中子过剩时的核物质状态方程.发现在核物质的饱和点处,许多物理量的同位旋相关性能够近似地与相对中子过剩满足抛物线规律.     

Equation of state and symmetry energy within the stability valley

We apply the direct variational method to derive the equation of state for finite nuclei within the stability valley. The extended Thomas-Fermi approximation for the energy functional with Skyrme forces is used. Applying the leptodermous expansion for the profile nucleon densities, we have studied the neutron coat and the isospin symmetry energy for neutron-rich nuclei. Using the equation of state for the pressure, we derive the region of spinodal instability of finite nuclei and its dependence on the mass number, the asymmetry parameter and the Skyrme force parameters. We suggest the procedure of derivation of the isospin symmetry energy from the analysis of the isospin shift of the chemical potential = - beyond the beta-stability line. We show that both the structure of the neutron coat and the position of the drip line depend significantly on the Skyrme force parameters.     

Neutron Skin Thickness of Nuclei and Effective Nucleon-Nucleon Interactions

The Skyrme energy density functional is applied to study the ground state properties of a series of finite nuclei. The charge rms radii, neutron rms radii, and the neutron skin thickness for some nuclei are calculated and compared with the experimental data. The constraint on the effective interactions, especially, the density dependence of the isospin-dependent. part of Skyrme interactions is extracted by the data of neutron skin thicknesses of ^208Pb and isotopes of Sn.     

Anisotropic pressure in dense neutron matter under the presence of a strong magnetic field

Dense neutron matter with recently developed BSk19 and BSk21 Skyrme effective forces is considered in magnetic fields up to ¹⁰²⁰ G at zero temperature. The breaking of the rotational symmetry by the magnetic field leads to the differentiation between the pressures along and perpendicular to the field direction which becomes significant in the fields H>Hth∼¹⁰¹⁸ G. The longitudinal pressure vanishes in the critical field ¹⁰¹⁸<Hc?¹⁰¹⁹ G, resulting in the longitudinal instability of neutron matter. For the Skyrme force fitted to the stiffer underlying equation of state (BSk21 vs. BSk19) the threshold Hth and critical Hc magnetic fields become larger. The longitudinal and transverse pressures as well as the anisotropic equation of state of neutron matter are determined under the conditions relevant for the cores of magnetars.     

Peninsulas of the neutron stability of nuclei in the vicinity of neutron magic numbers

On the basis of the Hartree-Fock method as implemented with Skyrme forces (Ska, SkM*, Sly4, and SkI2) and with allowance for an axial deformation and nucleon pairing in the Bardeen-Cooper-Schrieffer approximation, the properties of extremely neutron-rich even-even nuclei were calculated beyond the neutron drip line known earlier from theoretical calculations. It was shown that the chains of isotopes beyond the neutron drip line that contain N = 32, 58, 82, 126, and 184 neutrons form peninsulas of nuclei stable against the emission of one neutron and, in some cases, peninsulas of nuclei stable against the emission of two neutrons. The neutron- and proton-density distributions in nuclei forming stability peninsulas were found to be spherically symmetric. A mechanism via which the stability of nuclei might be restored beyond the neutron drip line was discussed. A comparison with the results of calculations by the Hartree-Fock-Bogolyubov method was performed for long chains of sulfur and gadolinium isotopes up to the neutron drip line.     

Phase transition to the state with nonzero average helicity in dense neutron matter

The possibility of the appearance of the states with a nonzero average helicity in neutron matter is studied in the model with the Skyrme effective interaction. By providing the analysis of the self-consistent equations at zero temperature, it is shown that neutron matter with the Skyrme BSk18 effective force undergoes at high densities a phase transition to the state in which the degeneracy with respect to helicity of neutrons is spontaneously removed.     

Investigation of the properties of nuclei with extreme neutron excess in the vicinity of neutron magic numbers

Properties of even-even nuclei with extreme neutron excess in the vicinity of neutron magic numbers up to and beyond the neutron drip line (NDL) are calculated by the Hartree-Fock (HF) method using Skyrme forces (Ska, SkM*, Sly4, SkI2, SkP) with allowance for axial deformation and BCS-approximation pairing. It is shown that chains of isotones with the neutron numbers N = 32, 58, 82, 126, 184, and 258 beyond the NDL form peninsulas of nuclei stable with respect to emission of one neutron, and occasionally peninsulas of nuclei stable with respect to the emission of two neutrons. The length of these peninsulas in (N, Z) space depends on the choice of the Skyrme forces, while their locations are at the same N = 32, 58, 82, 126, 184, and 258 and do not depend on the choice of forces. The investigated isotones restore stability beyond the NDL due to the complete filling of subshells with high angular momentum and to the intrusion of corresponding neutron levels in the region of discrete bound states. The stability of the numerical solution to the HF equations for nuclei belonging to the peninsulas of stability is analyzed.     

Investigating the neutron and proton density distributions in extremely neutron-rich nuclei

Manifestations of the neutron halo in extremely neutron-rich nuclei are investigated by the Hartree-Fock method using the Skyrme forces (SkM*, Ska, Sly4, SkI2) with allowance for axial deformation. The investigated nuclei, which lie beyond the theoretical neutron drip line (NDL), form peninsulas of nuclei stable with respect to one-neutron emission and belong to chains of isotones with the neutron number N = 32, 58, 82, 126, 184, and 258.     

Comparison between microscopic and phenomenological nuclear pairing calculations

The isospin and density dependent effective pairing interaction is revisited by fitting the neutron gaps from the microscopic calculations for the neutron matter and the symmetric nuclear matter.The neutron pairing gaps for 1S0 channel for asymmetric nuclear matter are obtained from the BCS gap equation with a realistic bare nucleon-nucleon interaction in the Skyrme mean field.It is shown that the neutron gaps obtained from the new effective pairing interaction for the asymmetric nuclear matter are much imp...     

Equation of State of Spin-Polarized Neutron Metier

Within the spin-dependent Brueckner-Hatree-Fock framework, the equation of state of the spin-polarized neutron matter has been investigated by adopting the realistic nucleon-nucleon interaction AV₁₈ supplemented with a microscopic three-body force. The related physical quantities such as spin-symmetry energy, magnetic susceptibility and the Landau parameter G₀ in spin channel, have been extracted. The three-body force effects have been studied and discussed with a special attention. It is shown that in the whole range of spin-polarization, the energy per particle of spin-polarized neutron matter fulfills a quadratic relation versus the spin-polarization parameter δ= (p-p )/p . The predicted spin-symmetry energy is positive in the density region up to ρ = 0.8fm^-3 and increase monotonically as increasing density so that no any evidence is found for a spontaneous transition to a ferromagnetic state in neutron matter. The three-body force effect is to strongly increase the spin-symmetry energy and reduce the magnetic susceptibility at high densities, as a consequence , to make neutron matter become more stable against spin fluctuation. The obtained Landau parameter G₀ and its density dependence may serve as a constraint on the spin-spin parts of the phenomenological Skyrme and Skyrme-like interactions .     

热核静态性质的一个简单模型

以扩展Skyrme力为基础,计入唯象的表面效应和Coulomb相互作用,推导了核系统的能量密度。对于有限温度情形,通过索末菲展开,得到了能量密度、自由能密度以及熵密度的解析公式。由此计算了热核物质和有限核的状态方程,每核子熵及每核子自由能。对计算结果作了比较和分析,预言了在同一框架下研究热核动力学演化的可能性。 关键词：     

Effect of tensor nucleon-nucleon forces on the nucleon-nucleus optical potential

In the approximation of unpolarized nuclear matter, the optical potential for nucleon-nucleus scattering is calculated on the basis of the effective Skyrme interaction with allowance for tensor nucleon-nucleon forces. It is shown that the tensor Skyrme forces make a significant contribution to the imaginary part of the optical potential. The effect of tensor nucleon-nucleon forces on the radial distribution of the imaginary part of the optical potential is investigated by considering the example of elastic neutron scattering by ⁴⁰Ca nuclei at scattering energies of about a few tens of MeV.     

Symmetry energy: nuclear masses and neutron stars

We describe the main features of our most recent Hartree-Fock-Bogoliubov nuclear mass models, based on 16-parameter generalized Skyrme forces. They have been fitted to the data of the 2012 Atomic Mass Evaluation, and favour a value of 30MeV for the symmetry coefficient J , the corresponding root-mean square deviation being 0.549MeV. We find that this conclusion is compatible with measurements of neutron-skin thickness. By constraining the underlying interactions to fit various equations of state of neutron matter calculated ab initio our models are well adapted to a realistic and unified treatment of all regions of neutron stars. We use our models to calculate the composition, the equation of state, the mass-radius relation and the maximum mass. Comparison with observations of neutron stars again favours a value of J = 30 MeV.     

Isoscalar and isovector nuclear matter properties and neutron skin thickness

Isoscalar and isovector nuclear matter properties are investigated in the Skyrme Hartree-Fock (SHF) and the relativistic mean field (RMF) models. The Skyrme parameters are related analytically to the isoscalar and the isovector nuclear matter properties of the Hamiltonian density. Linear correlations are found among the isovector nuclear matter properties of the Hamiltonian density in both the SHF and the RMF models. We also discovered that the correlations between the isovector properties and the incompressibility K show a singularity at the critical incompressibility K_c=306 MeV. It is shown that the neutron skin thickness gives crucial information about not only for the neutron EOS but also about the isovector nuclear matter properties and about the parameterization of Skyrme interaction. Charge exchange spin-dipole (SD) excitations are proposed to determine the neutron skin thickness model independently.     

Effective nucleon-nucleon interactions and nuclear matter equation of state

Nuclear matter equations of state based on Skyrme, Myers-Swiatecki and Tondeur interactions are written as polynomials of the cubic root of density, with coefficients that are functions of the relative neutron excess δ. In the extrapolation toward states far away from the standard one, it is shown that the asymmetry dependence of the critical point ( ,) depends on the model used. However, when the equations of state are fitted to the same standard state, the value of is almost the same in Skyrme and in Myers-Swiatecki interactions, while is much lower in Tondeur interaction. Furthermore, does not depend sensitively on the choice of the parameter γ in Skyrme interaction. Received: 5 May 2000 / Accepted: 16 January 2001