Effect of tensor force on density dependence of symmetry energy within the BHF Framework

The effect of tensor force on the density dependence of nuclear symmetry energy has been investigated within the framework of the Brueckner-Hartree-Fock approach. It is shown that the tensor force manifests its effect via the tensor $^3SD_1$ channel. The density dependence of symmetry energy $E_{sym}$ turns out to be determined essentially by the tensor force from the $\pi$ meson and $\rho$ meson exchanges via the $^3SD_1$ coupled channel. Increasing the strength of the tensor component due to the $\rho$-meson exchange tends to enhance the repulsion of the equation of state of symmetric nuclear matter and leads to reduction of symmetry energy. The present results confirm the dominant role played by the tensor force in determining nuclear symmetry energy and its density dependence within the microscopic BHF framework.Comment: 5 pages, 3 figure

Three-body force effect on neutrino emissivities of neutron stars within the framework of the Brueckner-Hartree-Fock approach

The three-body force (TBF) effect on the neutrino emissivity in neutron star matter and the total neutrino emissivity of neutron stars have been investigated within the framework of the Brueckner-Hartree-Fock approach by adopting the AV18 two-body interaction plus a microscopic TBF. The neutrino emissivity from the direct Urca process turns out to be much larger than that from the modified Urca process. Inclusion of the TBF reduces strongly the density thresholds of the direct Urca processes involving electrons and muons. The TBF effect on the total neutrino emissivity of neutron stars is shown to be negligibly weak for neutron stars with small masses. For neutron stars with large masses, the TBF effect becomes visible and inclusion of the TBF may enhance the total neutrino emissivity by about 50% for neutron stars with a given mass of $M=1.6M_{\odot}$.Comment: 7 pages, 3 figure

Three-body force effect on the properties of nuclear matter under the gap and continuous choices within the BHF approach

We have calculated and compared the three-body force effects on the properties of nuclear matter under the gap and continuous choices for the self-consistent auxiliary potential within the Brueckner-Hartree-Fock approach by adopting the Argonne $V18$ and the Bonn B two-body potentials plus a microscopic three-body force (TBF). The TBF provides a strong repulsive effect on the equation of state of nuclear matter at high densities for both the gap and continuous choices. The saturation point turns out to be much closer to the empirical value when the continuous choice is adopted. In addition, the dependence of the calculated symmetry energy upon the choice of the self-consistent auxiliary potential is discussed.Comment: 6 pages, 5 figure

Angle-dependent Gap state in Asymmetric Nuclear Matter

We propose an axisymmetric angle-dependent gap (ADG) state with the broken rotational symmetry in isospin-asymmetric nuclear matter. In this state, the deformed Fermi spheres of neutrons and protons increase the pairing probabilities along the axis of symmetry breaking near the average Fermi surface. We find that the state possesses lower free energy and larger gap value than the angle-averaged gap state at large isospin asymmetries. These properties are mainly caused by the coupling of different m_{j} components of the pairing gap. Furthermore, we find the transition from the ADG state to the normal state is of second order and the ADG state vanishes at the critical isospin asymmetry m_{j} where the angle-averaged gap vanishes.Comment: 23 pages, 7 figure

Origin of symmetry energy in finite nuclei and density dependence of nuclear matter symmetry energy from measured alpha-decay energies

Based on the Skyrme energy density functional, the spatial distribution of the symmetry energy of a finite nucleus is derived in order to examine whether the symmetry energy of a finite nucleus originates from its interior or from its surface. It is found that the surface part of a heavy nucleus contributes dominantly to its symmetry energy compared to its inner part. The symmetry energy coefficient $a_{\text{sym}}({A})$ is then directly extracted and the ratio of the surface symmetry coefficient to the volume symmetry coefficient $\kappa$ is estimated. Meanwhile, with the help of experimental alpha decay energies, a macroscopic method is developed to determine the symmetry energy coefficient of heavy nuclei. The resultant $a_{\text{sym}}({A})$ is used to analyze the density dependence of the symmetry energy coefficient of nuclear matter around the saturation density, and furthermore, the neutron skin thickness of $^{208}\text{Pb}$ is deduced which is consistent with the pygmy dipole resonance analysis. In addition, it is shown that the ratio $\kappa$ obtained from the macroscopic method is in agreement with that from the Skyrme energy density functional. Thus the two completely different approaches may validate each other to achieve more compelling results.Comment: 6 pages, 3 figures, to appear in Phys. Rev.

Symbolic Dynamics of the Diamagnetic Kepler Problem Without Involving Bounces

Without involving bounce events, a Poincar\'e section associated with the axes is found to give a map on the annulus for the diamagnetic Kepler problem. Symbolic dynamics is then established based on the lift of the annulus map. The correspondence between the coding derived from this axis Poincar\'e section is compared with the coding based on bounces. Symmetry is used to reduce the symbolic dynamics. By means of symbolic dynamics the admissibility of periodic orbits is analyzed, and the symmetry of orbits discussed

Constraints on neutron skin thickness in 208Pb and density-dependent symmetry energy

Accurate knowledge about the neutron skin thickness $\Delta R_{np}$ in $^{208}$Pb has far-reaching implications for different communities of nuclear physics and astrophysics. Yet, the novel Lead Radius Experiment (PREX) did not yield stringent constraint on the $\Delta R_{np}$ recently. We employ a more practicable strategy currently to probe the neutron skin thickness of $^{208}$Pb based on a high linear correlation between the $\Delta R_{np}$ and $J-a_{\text{sym}}$, where $J$ and $a_{\text{sym}}$ are the symmetry energy (coefficient) of nuclear matter at saturation density and of $^{208}$Pb. An accurate $J-a_{\text{sym}}$ thus places a strong constraint on the $\Delta R_{np}$. Compared with the parity-violating asymmetry $A_{\text{PV}}$ in the PREX, the reliably experimental information on the $J-a_{\text{sym}}$ is much more easily available attributed to a wealth of measured data on nuclear masses and on decay energies. The density dependence of the symmetry energy is also well constrained with the $J-a_{\text{sym}}$. Finally, with a `tomoscan' method, we find that one just needs to measure the nucleon densities in $^{208}$Pb starting from $R_{m} = 7.61\pm0.04$ fm to obtain the $\Delta R_{np}$ in hadron scattering experiments, regardless of its interior profile that is hampered by the strong absorption.Comment: 13 pages, 4 figure

Magnetization of neutron star matter

The magnetization of neutron star matter in magnetic fields is studied by employing the FSUGold interaction. It is found that the magnetic susceptibilities of the charged particles (proton, electron and muon) can be larger than that of neutron. The effects of the anomalous magnetic moments (AMM) of each component on the magnetic susceptibility are examined in detail. It is found that the proton and electron AMM affect their respective magnetic susceptibility evidently in strong magnetic fields. In addition, they are the protons instead of the electrons that contribute most significantly to the magnetization of the neutron star matter in a relative weak magnetic field, and the induced magnetic field due to the magnetization can be appear to be very large. Finally, the effect of the density-dependent symmetry energy on the magnetization is discussed.Comment: 6 pages, 3 figure

Density-dependent symmetry energy at subsaturation densities from nuclear mass differences

We extract the mass-dependent symmetry energy coefficients $a_{\text{sym}}({A})$ with the nuclear mass differences reducing the uncertainties as far as possible. The estimated $a_{\text{sym}}({A})$ of $^{208}\text{Pb}$ is $22.4\pm 0.3$ MeV, which is further used to analyze the density-dependent nuclear matter symmetry energy at subsaturation densities. The slope parameter of the symmetry energy at the saturation density $\rho_{0}$ is $L=50.0\pm15.5$ MeV. Furthermore, it is found that, at the density of $\rho=0.69\rho_{0}=0.11$fm$^{-3}$, the symmetry energy $S(\rho=0.11\text{fm}^{-3})=25.98\pm0.01$ MeV and the correspondingly slope parameter is $L=49.6\pm6.2$ MeV, which are consistent with other independent analysis.Comment: 4 pages, 1 figur

Symmetry energy at subsaturation densities and the neutron skin thickness of 208Pb

The mass-dependent symmetry energy coefficients $a_{sym}(A)$ has been extracted by analysing the heavy nuclear mass differences reducing the uncertainties as far as possible in our previous work. Taking advantage of the obtained symmetry energy coefficient $a_{sym}(A)$ and the density profiles obtained by switching off the Coulomb interaction in $^{208}\text{Pb}$, we calculated the slope parameter $L_{0.11}$ of the symmetry energy at the density of $0.11\text{fm}^{-3}$. The calculated $L_{0.11}$ ranges from 40.5 MeV to 60.3 MeV. The slope parameter $L_{0.11}$ of the symmetry energy at the density of $0.11\text{fm}^{-3}$ is also calculated directly with Skyrme interactions for nuclear matter and is found to have a fine linear relation with the neutron skin thickness of $^{208}\text{Pb}$, which is the difference of the neutron and proton rms radii of the nucleus. With the linear relation the neutron skin thickness $\Delta R_{np}$ of $^{208}\text{Pb}$ is predicted to be 0.15 - 0.21 fm.Comment: 5 pages, 2 figure