Variational calculations of asymmetric nuclear matter

We report on variational calculations of the energy E(ρ, β) of asymmetric nuclear matter having ? = ?_n + ?_p = 0.05 to 0.35 fm^?3, and β = (?_n ? ?_p/g9 = 0 to 1. The nuclear h used in this work consists of a realistic two-nucleon interaction, called v₁₄, that fits the available nucleon-nucleon scattering data up to 425 MeV, and a phenomenological three nucleon interaction adjusted to reproduce the empirical properties of symmetric nuclear matter. The variational many-body theory of symmetric nuclear matter is extended to treat matter with neutron excess. Numerical and analytic studies of the β-dependence of various contributions to the nuclear matter energy show that at ? < 0.35 fm^?3 the β⁴ terms are very small, and that the interaction energy EI(ρ, β) defined as E(ρ, β) ? T_F(ρ, β), where T_F is the Fermi-gas energy, is well approximated by EI₀(?) + β²EI₂(ρ). The calculated symmetry energy at equilibrium density is 30 MeV and it increases from 15 to 38 MeV as ? increases from 0.05 to 0.35 fm^?3.     

Branches of zero sound excitations in asymmetric nuclear matter: The dependence on density

Results from calculating zero sound excitations in isospin asymmetric nuclear matter are presented. A polarization operator constructed in the random phase approximations is used in the calculations. Three branches of the complex solutions ω_sτ(k), τ = p,n,np are presented. The type of branch depends on that of the considered branch damping. An imaginary part of the solution corresponds to the damping of collective excitations due to mixing with the background of noninteracting (1) proton particle–hole pairs (ω _sp (k)), (2) neutron particle–hole pairs (ω _sn (k)), and (3) both proton and neutron particle–hole pairs (ω _snp (k)). The behavior of the solutions upon variations in density depends on the value of the asymmetry parameter.     

On the properties of asymmetric nuclear matter

The properties of asymmetric nuclear matter withα=(ρ _n-ρ _p)/ρ≦ 0.4 are studied within the framework of the lowest order Brueckner theory, atk _F =1.35fm^?1 (ρ=0.166 fm^?3). TheK-matrix is calculated self-consistently from the Reid soft core nucleon-nucleon interaction. In the case ofρ _n ≠ρ _p theK-matrix contains a term which does not conserve the total isospin of the interacting unlike-nucleon pair. At α=0.4 the relative magnitude of this term is of the order of 1 %. The symmetry energy is found equal to 23.1 MeV.     

Resummation of in-medium ladder diagrams: s-wave effective range and p-wave interaction

An exploratory study of chiral four-nucleon interactions in nuclear and neutron matter is performed. The leading-order terms arising from pion-exchange in combination with the chiral 4??-vertex and the chiral NN3??-vertex are found to be very small. Their attractive contribution to the energy per particle stays below 0.6 MeV in magnitude for densities up to ?? = 0.4 fm^?3. We consider also the four-nucleon interaction induced by pion-exchange and twofold ??-isobar excitation of nucleons. For most of the closed four-loop diagrams the occurring integrals over four Fermi spheres can either be solved analytically or reduced to easily manageable one- or two-parameter integrals. After summing the individually large contributions from 3-ring, 2-ring and 1-ring diagrams of alternating signs, one obtains at nuclear matter saturation density ?? ₀ = 0.16 fm^?3 a moderate contribution of 2.35 MeV to the energy per particle. The curve $\bar E(\rho )$ rises rapidly with density, approximately with the third power of ??. In pure neutron matter the analogous chiral four-body interactions lead, at the same density ?? _n , to a repulsive contribution that is about half as strong. The present calculation indicates that long-range multi-nucleon forces, in particular those provided by the strongly coupled ??N??-system with its small mass-gap of 293 MeV, can still play an appreciable role for the equation of state of nuclear and neutron matter.     

非对称核物质中质子和中子的1S0态超流性

利用Brueckner-Hartree-Fock和BCS理论方法，计算了非对称核物质中处于¹S₀态的质子和中子的对关联能隙，着重研究和讨论了能隙的同位旋依赖性和三体核力的影响.结果表明：随核物质的同位旋非对称度增大，中子¹S₀态超流相存在的密度范围逐渐缩小而且对关联能隙峰值稍有升高；质子¹S₀态超流相存在的密度范围迅速扩大而且对关联能隙峰值显著降低.三体核力对非对称核物质中¹S₀态中子超流性及其同位旋依赖性的影响相对较小，但对¹S₀态质子超流性具有重要影响，而且其效应随核子数密度增大而迅速增强.三体核力的主要作用是强烈地抑制了具有高非对称度的核物质中高密度区域的¹S₀态质子超流性，导致质子超流相存在的密度范围显著缩小. 关键词： 同位旋非对称核物质 质子和中子超流性 三体核力 BCS理论     

Isospin splitting of nucleon effective mass and symmetry energy in isotopic nuclear reactions

Within an isospin and momentum dependent transport model, the dynamics of isospin particles(nucleons and light clusters) in Fermi-energy heavy-ion collisions are investigated for constraining the isospin splitting of nucleon effective mass and the symmetry energy at subsaturation densities. The impacts of the isoscalar and isovector parts of the momentum dependent interaction on the emissions of isospin particles are explored, i.e., the mass splittings of m_n~*=m_p~* and m_n~* m_p~*(m_n~* m_p~*). The single and double neutron to proton ratios of free nucleons and light particles are thoroughly investigated in the isotopic nuclear reactions of ~(112)Sn+~(112)Sn and ~(124)Sn+~(124)Sn at incident energies of 50 and 120 MeV/nucleon, respectively. It is found that both the effective mass splitting and symmetry energy impact the kinetic energy spectra of the single ratios, in particular at the high energy tail(larger than 20 Me V). The isospin splitting of nucleon effective mass slightly impacts the double ratio spectra at the energy of 50 MeV/nucleon. A soft symmetry energy with stiffness coefficient of γ_s =0.5 is constrained from the experimental data with the Fermi-energy heavy-ion collisions.     

Isospin and symmetry energy study in nuclear EOS

This paper summarizes the isoscaling and isospin related studies in asymmetry nuclear reactions by different dynamic and statistical models. Isospin dependent quantum molecular dynamics model (IQMD) and lattice gas model (LGM) are used to study the isoscaling properties and isoscaling parameters dependence on incident energies, impact parameters, temperature and other parameters. In the LGM model, the signal of phase transition has been found in free neutron (proton) chemical potential difference Δµ_n or Δµ_p as a function of temperature, or in free neutron and proton chemical potential difference Δµ_n−Δµ_p. Density dependence of symmetry energy coefficient C _sym(ρ/ρ ₀) is also studied in the frame of LGM, with the potential parameters which can reproduce the nuclear ground state property, soft density dependence of symmetry energy is deduced from the simulation results. Giant dipole resonance (GDR) induced by isospin asymmetry in entrance channel is also studied via IQMD model, and the dynamic dipole resonance shows isospin sensitivity on the isospin asymmetry of entrance channel and symmetry energy of the nuclear equation of state (EOS). GDR can also be regarded as a possible isospin sensitive signature.

     

Some characteristics of nuclear densities

We propose a simple expression for nuclear densities, which brings out the following important nuclear properties: (i) shell effects in proton and neutron central densities, (ii) approximate global constancy of neutron central densities, (iii) approximate constancy ofRN ^?1/3 and R_pZ^?1/3 whereR is the nuclear half-density radius andR _p is the rms radius of the proton density, (iv) larger surface thickness and rms radius for neutron density as compared to those for proton density.     

The spin-isospin decomposition of the nuclear symmetry energy from low to high density

The energy per particle BA in nuclear matter is calculated up to high baryon density in the whole isospin asymmetry range from symmetric matter to pure neutron matter.The results,obtained in the framework of the Brueckner-Hartree-Fock approximation with two-and three-body forces,confirm the well-known parabolic dependence on the asymmetry parameterβ=(N?Z)/A(β^2 law)that is valid in a wide density range.To investigate the extent to which this behavior can be traced back to the properties of the underlying interaction,aside from the mean field approximation,the spin-isospin decomposition of BA is performed.Theoretical indications suggest that theβ^2 law could be violated at higher densities as a consequence of the three-body forces.This raises the problem that the symmetry energy,calculated according to theβ^2 law as a difference between BA in pure neutron matter and symmetric nuclear matter,cannot be applied to neutron stars.One should return to the proper definition of the nuclear symmetry energy as a response of the nuclear system to small isospin imbalance from the Z=N nuclei and pure neutron matter.     

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...     

Zero-sound branches in asymmetric nuclear matter

A polarization operator constructed in the random phase approximation is used to obtain zero-sound excitations in isospin asymmetric nuclear matter (ANM). Two families of the complex solutions ω_sτ(k),τ= p,n are presented. The imaginary part of the solutions corresponds to the damping of the collective mode due to its overlapping with the particle-hole modes and the subsequent emission of a proton (ω_sp(k)) or a neutron (ω_sn(k)). The dependence of the solutions on the asymmetry parameter is studied.     

The reaction12C(α,p 0)15N around 18 mev excitation energy of16O

Proton angular distributions of the reaction¹²C(α, p ₀)¹⁵N have been measured at excitation energies from 17.5 to 18.7 MeV. The shape of the angular distributions changes strongly betweenθ _cm = 26°–162°. The integrated cross section shows a smooth behaviour in contrast to the (α, n) mirror reaction. The results can be explained by an interference of the known 18.18 MeV, 2⁺ state with a strong isospin mixed 18.1, 3^? state in the¹⁶O compound nucleus.     

Fermi sea effects on pion and kaon properties in the Nambu-Jona-Lasinio model

We study modifications of hadronic properties in dense nuclear and neutron matter, in the context of a generalized three-flavor Nambu-Jona-Lasinio model, focussing mainly on Fermi sea effects. In symmetric nuclear matter, we observe the splitting between K^± and the occurrence of a low-lying K⁻ branch at baryonic densities around 0.4 times normal nuclear matter density ϱ₀. This branch is not significantly affected by the inclusion of strange matter in the medium while the flavor asymmetry is preserved. A similar π⁺ branch is found in neutron matter at neutron densities around 0.3ϱ₀. These low-lying modes are particle-hole excitations of the Fermi sea and decrease smoothly with density. In any case, the vacuum does not exhibit signs of instability associated with boson condensation.     

Phase transitions (π-condensation) in nuclei and neutron stars

It is shown that in nuclear matter at Z = N for density n < n₀ (n₀ nuclear density) an electrically neutral condensate of π⁺, π^-, π⁰ mesons arises. The results of the calculations for the case of the neutron star (Z ? N) are given.In this case there are two phase transitions: one corresponds to π⁰ condensation and second to the electrically neutral π⁺, π^- condensation. The π^- condensate apparently does not appear even at very high densities.     

Nuclear symmetry energy in terms of single-nucleon potential and its effect on the proton fraction of <Emphasis Type="Italic">β</Emphasis>-stable <Emphasis Type="Italic">npeμ</Emphasis> matter

Momentum and density dependence of single-nucleon potential u_τ (k, ρ, β) is analyzed using a density dependent finite range effective interaction of the Yukawa form. Depending on the choice of the strength parameters of exchange interaction, two different trends of the momentum dependence of nuclear symmetry potential are noticed which lead to two opposite types of neutron and proton effective mass splitting. The 2nd-order and 4th-order symmetry energy of isospin asymmetric nuclear matter are expressed analytically in terms of the single-nucleon potential. Two distinct behavior of the density dependence of 2nd-order and 4th-order symmetry energy are observed depending on neutron and proton effective mass splitting. It is also found that the 4th-order symmetry energy has a significant contribution towards the proton fraction of β-stable npeμ matter at high densities.     

Isospin dependence of the nuclear level width in the compound nucleus 30P

The excitation functions of ²⁹Si(p, α₀)²⁶Al, ²⁹Si(p, α₁)²⁶Al and ²⁹Si(p, α₂)²⁶Al were measured with high beam energy resolution in order to determine the isospin dependence of the nuclear level width of the composite nucleus, ³⁰P, at an average excitation energy of 19.6 MeV. From an auto-correlation analysis of these excitation functions, the level widths of the T_< = 0 and T_> = 1 isospin states are determined as 81 ± 17 keV and 104 ± 35 keV, respectively. An analysis including isospin mixing is also performed. With the aid of the statistical theory of nuclear reactions, the coherence energies are used to deduce the relative densities of two isospin states. The predictions of the Fermi gas model of level densities including isospin are in good agreement with the obtained results.     

Variational calculations of ν8 models of nuclear matter

We report variational calculations of ν8 models of nuclear matter which contain central, spin, isospin, tensor and spin-orbit potentials. These semi-realistic models can explain the nucleon-nucleon scattering in 1S0, 3S1?3D1, 1P1 and 3P2?3F2 states up to ～ 300 MeV. The variational wave function has two-body central, spin, isospin, tensor and spin-orbit correlations. The terms in the cluster expansion of the energy expectation value, that do not contain the spin-orbit correlations are summed by chain summation techniques developed for the ν6 models. Of the terms containing spin-orbit correlations, the two-body and three-body-separable ones are calculated, and the magnitude of the rest is estimated. Results for three phase-equivalent ν8 models, which differ significantly in the strength of tensor and spin-orbit potentials, are reported. They suggest that simple ν8 models may not be able to simultaneously explain the binding energy and density of nuclear matter.     

Vector mesons in asymmetric nuclear matter

The propagation of a vector meson (ϱ and ω) in dense asymmetric nuclear matter (with the number density of protons and neutrons different) is studied. Of particular interest is the density dependence of the vector meson masses, as also their variation with the asymmetry parameter, mass splitting among the ϱ isospin multiplets and the change of the form of the ϱ meson self-energy or the polarization tensor (II_μν) when the p ↔ n symmetry is broken. Contributions of both the Fermi sea and Dirac vacuum have been considered. It is shown that while the density dependent dressing of the vector meson propagator lifts the dispersion characteristics into the region of instability, the Dirac vacuum on the other hand contributes with opposite sign, thereby enhancing the possibility of stable collective modes even for higher values of vector meson momenta. The role of tensor coupling on the dispersion characteristics is also presented.     

Low-lying intrinsic energy levels in the nucleus170Ho

The band-head energies of the two-quasiparticle states expected in the doubly odd deformed nucleus¹⁷⁰Ho are calculated for a zero range residual interaction. The results are compared with the available experimental information. It is concluded that the ground state has the Nilsson configuration 6⁺{7/2^?[523↑] _p }+5/2[512↑] _n being the 2.76m isomer whereas the 43s isomer is the 1⁺ ∑=0 state arising from the same configuration and lies at about 100 keV excitation energy in agreement with the experiment. The first excited state in this nucleus is predicted to be the 4^?{3/2⁺[411↑] _p +5/2^?[521↑] _n } state close to the ground state with the corresponding 1^? ∑=0 member expected to appear well above the 1⁺ isomer.