Constraining the density slope of nuclear symmetry energy at subsaturation densities using electric dipole polarizability in 208^{208}Pb

Nuclear structure observables usually most effectively probe the properties of nuclear matter at subsaturation densities rather than at saturation density. We demonstrate that the electric dipole polarizibility $\alpha _ {\text{D}}$ in $^{208}$Pb is sensitive to both the magnitude $E_{\text{sym}}(\rho_{\text{c}})$ and density slope $L(\rho_{\text{c}})$ of the symmetry energy at a subsaturation cross density $\rho_{\text{c}} = 0.11$ fm$^{-3}$. Using the experimental data of $\alpha _ {\text{D}}$ in $^{208}$Pb from RCNP and the recent accurate constraint of $E_{\text{sym}}(\rho_{\text{c}})$ from the binding energy difference of heavy isotope pairs, we extract a value of $L(\rho_{\text{c}}) = 47.3 \pm 7.8$ MeV. The implication of the present constraint of $L(\rho_{\text{c}})$ to the symmetry energy at saturation density, the neutron skin thickness of $^{208}$Pb and the core-crust transition density in neutron stars is discussed.Comment: 7 pages, 3 figures. Significantly expanded to include some details and discussions. Accepted version to appear in PR

Extended Skyrme interactions for nuclear matter, finite nuclei and neutron stars

Recent progress in theory, experiment and observation challenges the mean field models using the conventional Skyrme interaction, suggesting that the extension of the conventional Skyrme interaction is necessary. In this work, by fitting the experimental data of a number of finite nuclei together with a few additional constraints on nuclear matter using the simulated annealing method, we construct three Skyrme interaction parameter sets, namely, eMSL07, eMSL08 and eMSL09, based on an extended Skyrme interaction which includes additional momentum and density dependent two-body forces to effectively simulate the momentum dependence of the three-body force. The three new interactions can reasonably describe the ground-state properties and the isoscalar giant monopole resonance energies of various spherical nuclei used in the fit as well as the ground-state properties of many other spherical nuclei, nicely conform to the current knowledge on the equation of state of asymmetric nuclear matter, eliminate the notorious unphysical instabilities of symmetric nuclear matter and pure neutron matter up to a very high density of $1.2$ fm$^{-3}$, and simultaneously support heavier neutron stars with mass larger than two times solar mass. One important difference of the three new interactions is about the prediction of the symmetry energy at supra-saturation densities, and these new interactions are thus potentially useful for the determination of the largely uncertain high-density symmetry energy in future. In addition, a comparison is made for the predictions of nuclear matter, finite nuclei and neutron stars with the three new interactions versus those with three typical interactions BSk22, BSk24 and BSk26 from Brussels group.Comment: 18 pages, 6 figures, 5 tables. Results and discussions added. Accepted version to appear in PR

Isospin splitting of nucleon effective mass from giant resonances in 208^{208}Pb

Based on mean field calculations with Skyrme interactions, we extract a constraint on the isovector effective mass in nuclear matter at saturation density $\rho_0$, i.e., $m_{v}^{\ast}(\rho_0)=(0.77\pm0.03) m$ by combining the experimental data of the centroid energy of the isovector giant dipole resonance (IVGDR) and the electric dipole polarizability $\alpha_{\mathrm{D}}$ in $^{208}$Pb. Meanwhile, the isoscalar effective mass at $\rho_0$ is determined to be $m_{s}^{\ast}(\rho_0)=(0.91\pm0.05) m$ by analyzing the measured excitation energy of the isoscalar giant quadrupole resonance (ISGQR) in $^{208}$Pb. From the constrained $m_{s}^{\ast}(\rho_0)$ and $m_{v}^{\ast}(\rho_0)$, we obtain the isospin splitting of nucleon effective mass in asymmetric nuclear matter of isospin asymmetry $\delta$ at $\rho_0$ as $[m_n^{\ast}(\rho_0,\delta)-m_p^{\ast}(\rho_0,\delta)]/m = \Delta m^*_1(\rho_0) \delta + O(\delta^3)$ with the linear isospin splitting coefficient $\Delta m^*_1(\rho_0) = 0.33\pm0.16$. We notice that using the recently corrected data on the $\alpha_{\mathrm{D}}$ in $^{208}$Pb with the contribution of the quasideuteron effect subtracted slightly enhances the isovector effective mass to $m_{v}^{\ast}(\rho_0)=(0.80\pm0.03) m$ and reduces the linear isospin splitting coefficient to $\Delta m^*_1(\rho_0) = 0.27\pm0.15$. Furthermore, the constraints on $m_{v}^{\ast}(\rho)$, $m_{s}^{\ast}(\rho)$ and $\Delta m^*_1(\rho)$ at other densities are obtained from the similar analyses and we find that the $\Delta m^*_1(\rho)$ increases with the density.Comment: 7 pages, 3 figures. New results and discussions added. Accepted version to appear in PR

Electric Dipole Polarizability in 208^{208}Pb as a Probe of the Symmetry Energy and Neutron Matter around ρ0/3\rho_0/3

It is currently a big challenge to accurately determine the symmetry energy $E_{\text{sym}}(\rho)$ and the pure neutron matter equation of state $E_{\text{PNM}}(\rho)$, even their values around saturation density $\rho_0$. We find that the electric dipole polarizability $\alpha _ {\text{D}}$ in $^{208}$Pb can be determined uniquely by the magnitude of the $E_{\text{sym}}(\rho)$ or almost equivalently the $E_{\text{PNM}}(\rho)$ at subsaturation densities around $\rho_0/3$, shedding a light upon the genuine correlation between the $\alpha _ {\text{D}}$ and the $E_{\text{sym}}(\rho)$. By analyzing the experimental data of the $\alpha _ {\text{D}}$ in $^{208}$Pb from RCNP using a number of non-relativistic and relativistic mean-field models, we obtain very stringent constraints on $E_{\text{sym}}(\rho)$ and $E_{\text{PNM}}(\rho)$ around $\rho_0/3$. The obtained constraints are found to be in good agreement with the results extracted in other analyses. In particular, our results provide for the first time the experimental constraints on $E_{\text{PNM}}(\rho)$ around $\rho_0/3$, which are in harmony with the recent determination of $E_{\text{PNM}}(\rho)$ from microscopic theoretical studies and potentially useful in constraining the largely uncertain many-nucleon interactions in microscopic calculations of neutron matter.Comment: 5 pages, 3 figures. Accepted version to appear in PRC as a Rapid Communicatio

Two-Sample Smooth Tests for the Equality of Distributions

This paper considers the problem of testing the equality of two unspecified distributions. The classical omnibus tests such as the Kolmogorov-Smirnov and Cram\`er-von Mises are known to suffer from low power against essentially all but location-scale alternatives. We propose a new two-sample test that modifies the Neyman's smooth test and extend it to the multivariate case based on the idea of projection pursue. The asymptotic null property of the test and its power against local alternatives are studied. The multiplier bootstrap method is employed to compute the critical value of the multivariate test. We establish validity of the bootstrap approximation in the case where the dimension is allowed to grow with the sample size. Numerical studies show that the new testing procedures perform well even for small sample sizes and are powerful in detecting local features or high-frequency components.Comment: 40 pages, 3 figure

Form Factor Effects in the Direct Detection of Isospin-Violating Dark Matter

Isospin-violating dark matter (IVDM) provides a possible mechanism to ameliorate the tension among recent direct detection experiments. For IVDM, we demonstrate that the results of direct detection experiments based on neutron-rich target nuclei may depend strongly on the density dependence of the symmetry energy which is presently largely unknown and controls the neutron skin thickness that reflects the relative difference of neutron and proton form factors in the neutron-rich nuclei. In particular, using the neutron and proton form factors obtained from Skyrme-Hartree-Fock calculations by varying the symmetry energy within the uncertainty region set by the latest model-independent measurement of the neutron skin thickness of $^{208}$Pb from PREX experiment at JLab, we find that, for IVDM with neutron-to-proton coupling ratio fixed to $f_n/f_p=-0.7$, the form factor effect may enhance the sensitivity of Xe-based detectors (e.g., XENON100 and LUX) to the DM-proton cross section by a factor of $3$ in the DM mass region constrained by CMDS-II(Si) and even by more than an order of magnitude for heavy DM with mass larger than $80$ GeV, compared with the results using the empirical Helm form factor. Our results further indicate that the form factor effect can significantly modify the recoil spectrum of Xe-based detectors for heavy IVDM with $f_n/f_p=-0.7$.Comment: 17 pages, 8 figures, 1 table. Title changed slightly, more details and discussions added, especially a new Appendix added to present a generalized Helm-like empirical parametrization for proton and neutron form factors in terms of the neutron skin thickness of 208Pb. Accepted version to appear in JCA

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

Based on systematic analyses of several popular non-relativistic energy density functionals with mean-field approximation, we estimate the value of the fourth-order symmetry energy $E_{\text{sym,4}}(\rho)$ at nuclear normal density $\rho_0$ and its density dependence, and explore the correlation between $E_{\text{sym,4}}(\rho_0)$ and other macroscopic quantities of nuclear matter properties. We use the empirical values of some nuclear macroscopic quantities to construct model parameter sets by Monte Carlo method for the conventional Skyrme-Hartree-Fock (SHF) model, the extended Skyrme-Hartree-Fock (eSHF) model, the Gogny-Hartree-Fock (GHF) model, and the momentum-dependent interaction (MDI) model. The value of $E_{\text{sym,4}}(\rho_0)$ is estimated to be $1.02\pm0.49$ MeV for the SHF model, $1.02\pm0.50$ MeV for the eSHF model, $0.70\pm0.60$ MeV for the GHF model, and $0.74\pm0.63$ MeV for the MDI model. Moreover, our results indicate that the density dependence of $E_{\text{sym,4}}(\rho)$ is model dependent, especially at higher densities. Furthermore, we find that the $E_{\text{sym},4}(\rho_0)$ has strong positive (negative) correlation with isoscalar (isovector) nucleon effective mass $m_{s,0}^*$ ($m_{v,0}^*$) at $\rho_0$. In particular, for the SHF and eSHF models, the $E_{\text{sym,4}}(\rho)$ is completely determined by the isoscalar and isovector nucleon effective masses $m_{s}^*(\rho)$ and $m_{v}^*(\rho)$, and the analytical expression is given. In the mean-field models, the magnitude of $E_{\text{sym,4}}(\rho_0)$ is generally less than $2$ MeV, and its density dependence depends on models, especially at higher densities. $E_{\text{sym,4}}(\rho_0)$ is strongly correlated with $m_{s,0}^*$ and $m_{v,0}^*$.Comment: 10 pages, 2 figures, 4 tables. Presentation improved and discussions added. Accepted version to appear in PR

Nuclear collective dynamics in the lattice Hamiltonian Vlasov method

The lattice Hamiltonian method is developed for solving the Vlasov equation with nuclear mean-field based on the Skyrme pseudopotential up to next-to-next-to-next-to leading order. The ground states of nuclei are obtained through varying the total energy with respect to the density distribution of nucleons. Owing to the self-consistent treatment of initial nuclear ground state and the exact energy conservation in the lattice Hamiltonian method, the present framework of solving the Vlasov equation exhibits very stable nuclear ground state evolution. As a first application of the new lattice Hamiltonian Vlasov method, we explore the iso-scalar giant monopole and iso-vector giant dipole modes of finite nuclei. The obtained results are shown to be comparable to that from random-phase approximation and consistent with the experimental data, indicating the capability of the present method in dealing with the long-time near-equilibrium nuclear dynamics.Comment: 15 pages, 7 figures, 3 tables. Typos fixed to match the published version in PR

Numerical Predictions of Effective Thermal Conductivities for Three-dimensional Four-directional Braided Composites Using the Lattice Boltzmann Method

In this paper, a multiple-relaxation-time lattice Boltzmann model with an off-diagonal collision matrix was adopted to predict the effective thermal conductivities of the anisotropic heterogeneous materials whose components are also anisotropic. The half lattice division scheme was adopted to deal with the internal boundaries to guarantee the heat flux continuity at the interfaces. Accuracy of the model was confirmed by comparisons with benchmark results and existing simulation data. The present method was then adopted to numerically predict the transverse and longitudinal effective thermal conductivities of three-dimensional (3D) four-directional braided composites. Some corresponding experiments based on the Hot Disk method were conducted to measure their transverse and longitudinal effective thermal conductivities. The predicted data fit the experiment data well. Influences of fiber volume fractions and interior braiding angles on the effective thermal conductivities of 3D four-directional braided composites were then studied. The results show that a larger fiber volume fraction leads to a larger effective thermal conductivity along the transverse and longitudinal directions; a larger interior braiding angle brings a larger transverse thermal conductivity but a smaller one along the longitudinal direction. It is also shown that for anisotropic materials the periodic boundary condition is different from the adiabatic boundary condition and for periodic microstructure unit cell the periodic boundary condition should be used. Key words: effective thermal conductivities, anisotropic, multi-relaxation-time, lattice Boltzmann method, three-dimensional four-directional braided composite

Pairing effects on neutron matter equation of state and symmetry energy at subsaturation densities

Within the framework of BCS theory and Skyrme-Hartree-Fock model, we employ various microscopic pairing gaps and effective pairing interactions to study pairing effects on the equation of state (EOS) of neutron matter and the symmetry energy at subsaturation densities. We find pairing effects may have considerable contributions to the EOS of neutron matter at very low densities ($\lesssim 0.02~\rm{fm}^{-3}$), while only have a small impact on the symmetry energy at subsatruation densities. In addition, the reliability of the parabolic approximation for the isospin asymmetry dependence of nuclear matter EOS with pairing correlations included is also discussed.Comment: 6 pages, 3 figures. Some results updated and discussions added. Accepted version to appear in PR