arXiv subjects

Bao-Jun Cai

Publications and source records attributed to Bao-Jun Cai.

42 records · Page 3Linked to original sources

arXiv2013

Extracting the nuclear symmetry potential and energy from neutron-nucleus scattering data

According to the Hugenholtz-Van Hove theorem, the symmetry energy and its density slope can be decomposed uniquely in terms of the single-nucleon potential in asymmetric nuclear matter which, at normal density, can be constrained by the nucleon optical model potential extracted from analyzing the nucleon-nucleus scattering data. To more accurately extract information on the symmetry energy and its density slope at normal density from neutron-nucleus scattering data, going beyond the well-known Lane potential, we include consistently the second order terms in isospin asymmetry in both the optical model potential and the symmetry energy decomposition. We find that the strength of the second-order symmetry potential $U_{sym,2}$ in asymmetric nuclear matter is significant compared to the first-order one U_{sym,1}$, especially at high nucleon momentum. While the $U_{sym,1}$ at normal density decreases with nucleon momentum, the $U_{sym,2}$ is found to have the opposite behavior. Moreover, we discuss effects of the $U_{sym,1}$ and $U_{sym,2}$ on determining the density dependence of the symmetry energy, and we find that the available neutron-nucleus scattering data favor a softer density dependence of the symmetry energy at normal density with a negligible contribution from the $U_{sym,2}$.

nucl-th↗

arXiv2012

Lorentz covariant nucleon self-energy decomposition of the nuclear symmetry energy

Using the Hugenholtz-Van Hove theorem, we derive analytical expressions for the nuclear symmetry energy $E_{sym}(ρ)$ and its density slope $L(ρ)$ in terms of the Lorentz covariant nucleon self-energies in isospin asymmetric nuclear matter. These general expressions are useful for determining the density dependence of the symmetry energy and understanding the Lorentz structure and the microscopic origin of the nuclear symmetry energy in relativistic covariant formulism. As an example, we analyze the Lorentz covariant nucleon self-energy decomposition of $E_{sym}(ρ)$ and $L(ρ)$ and derive the corresponding analytical expressions within the nonlinear $σ$-$ω$-$ρ$-$δ$ relativistic mean field model.

nucl-th↗

arXiv2012

Nuclear matter fourth-order symmetry energy in the relativistic mean field models

Within the nonlinear relativistic mean field model, we derive the analytical expression of the nuclear matter fourth-order symmetry energy $E_{sym,4}(ρ)$. Based on two accurately calibrated interactions FSUGold and IU-FSU, our results show that the value of $E_{sym,4}(ρ)$ at normal nuclear matter density $ρ_{0}$ is generally less than 1 MeV, confirming the empirical parabolic approximation to the equation of state for asymmetric nuclear matter at $ρ_{0}$. On the other hand, we find that the $E_{sym,4}(ρ)$ may become nonnegligible at high densities. Furthermore, the analytical form of the $E_{sym,4}(ρ)$ provides the possibility to study the higher-order effects on the isobaric incompressibility of asymmetric nuclear matter, i.e., $K_{sat}(δ)=K_{0}+K_{sat,2}δ^{2}+K_{sat,4}δ^{4}+\mathcal{O}(δ^{6})$ where $δ=(ρ_{n}-ρ_{p})/ρ$ is the isospin asymmetry, and we find that the value of $K_{sat,4}$ is generally small compared with that of the $K_{sat,2}$. In addition, we study the effects of the $E_{sym,4}(ρ)$ on the proton fraction $x_{p}$ and the core-crust transition density $ρ_{t}$ and pressure $P_{t}$ in neutron stars. Interestingly, we find that, compared with the results from the empirical parabolic approximation, including the $E_{sym,4}(ρ)$ contribution can significantly enhance the $x_{p}$ at high densities and strongly reduce the $ρ_{t}$ and $P_{t}$ in neutron stars, demonstrating that the widely used empirical parabolic approximation may cause large errors in determining the $x_{p}$ at high densities as well as the $ρ_{t}$ and $P_{t}$ in neutron stars within the nonlinear relativistic mean field model, consistent with previous nonrelativistic calculations.

nucl-th↗

arXiv2012

Single-nucleon potential decomposition of the nuclear symmetry energy

The nuclear symmetry energy $E_{sym}(ρ)$ and its density slope $L(ρ)$ can be decomposed analytically in terms of the single-nucleon potential in isospin asymmetric nuclear matter. Using three popular nuclear effective interaction models which have been extensively used in nuclear structure and reaction studies, namely, the isospin and momentum dependent MDI interaction model, the Skyrme Hartree-Fock approach and the Gogny Hartree-Fock approach, we analyze the contribution of different terms in the single-nucleon potential to the $E_{sym}(ρ)$ and $L(ρ)$. Our results show that the observed different density behaviors of $E_{sym}(ρ)$ for different interactions are essentially due to the variation of the symmetry potential $U_{sym,1}(ρ,k)$. Furthermore, we find that the contribution of the second-order symmetry potential $U_{sym,2}(ρ,k)$ to the $L(ρ)$ generally cannot be neglected. Moreover, our results demonstrate that the magnitude of the $U_{sym,2}(ρ,k)$ is generally comparable with that of $U_{sym,1}(ρ,k)$, indicating the second-order symmetry potential $U_{sym,2}(ρ,k)$ may have significant corrections to the widely used Lane approximation to the single-nucleon potential in extremely neutron(proton)-rich nuclear matter.

nucl-th↗

arXiv2009

Incompressibility of asymmetric nuclear matter

The incompressibility $K_sat(δ)$ of isospin asymmetric nuclear matter at its saturation density. Our results show that in the expansion of $K_sat(δ)$ in powers of isospin asymmetry $δ$, i.e., $K_sat(δ)$=K_{0}+K_{sat,2}δ^{2}+K_{sat,4}δ^{4}+O(δ^{6})$, the magnitude of the 4th-order K_{sat,4} parameter is generally small. The 2nd-order K_{sat,2} parameter thus essentially characterizes the isospin dependence of the incompressibility of asymmetric nuclear matter at saturation density. Furthermore, the K_{sat,2} can be expressed as K_{sat,2}=K_{sym}-6L-J_{0}/{K_{0}L in terms of the slope parameter $L$ and the curvature parameter $K_{\mathrm{sym}}$ of the symmetry energy and the third-order derivative parameter $J_0$ of the energy of symmetric nuclear matter at saturation density, and we find the higher order $J_0$ contribution to K_{sat,2} generally cannot be neglected. Also, we have found a linear correlation between K_{sym} and $L$ as well as between $J_{0}/K_{0}$ and $K_{0}$. Using these correlations together with the empirical constraints on $K_{0}$ and $L$, the nuclear symmetry energy $E_sym(ρ_{0})$ at normal nuclear density, and the nucleon effective mass, we have obtained an estimated value of K_{sat,2}=-370 +- 120 MeV for the 2nd-order parameter in the isospin asymmetry expansion of the incompressibility of asymmetric nuclear matter at its saturation density.

nucl-th↗

arXiv2009

Higher-order effects on the incompressibility of isospin asymmetric nuclear matter

Analytical expressions for the saturation density as well as the binding energy and incompressibility at the saturation density of asymmetric nuclear matter are given exactly up to 4th-order in the isospin asymmetry delta =(rho_n - rho_p)/rho using 11 characteristic parameters defined at the normal nuclear density rho_0. Using an isospin- and momentum-dependent modified Gogny (MDI) interaction and the SHF approach with 63 popular Skyrme interactions, we have systematically studied the isospin dependence of the saturation properties of asymmetric nuclear matter, particularly the incompressibility $K_{sat}(δ)=K_{0}+K_{sat,2}δ^{2}+K_{sat,4}δ^{4}+O(δ^{6})$ at the saturation density. Our results show that the magnitude of the high-order $K_{sat,4}$ parameter is generally small compared to that of the $K_{\sat,2}$ parameter. The latter essentially characterizes the isospin dependence of the incompressibility at the saturation density and can be expressed as $K_{sat,2}=K_{sym}-6L-\frac{J_{0}}{K_{0}}L$, Furthermore, we have constructed a phenomenological modified Skyrme-like (MSL) model which can reasonably describe the general properties of symmetric nuclear matter and the symmetry energy predicted by both the MDI model and the SHF approach. The results indicate that the high-order $J_{0}$ contribution to $K_{sat,2}$ generally cannot be neglected. In addition, it is found that there exists a nicely linear correlation between $K_{sym}$ and $L$ as well as between $J_{0}/K_{0}$ and $K_{0}$. These correlations together with the empirical constraints on $K_{0}$, $L$, $E_{sym}(ρ_{0})$ and the nucleon effective mass lead to an estimate of $K_{sat,2}=-370\pm 120$ MeV.

nucl-th↗