标题： 从铅和钙同位素的两核子分离能中得到的对称能 显示英文标题

标题： Symmetry Energy from Two-Nucleon Separation Energies of Pb and Ca Isotopes

摘要： 我们利用不同的核质量数据，研究了对称能与两质子和两中子分离能之间的关系。 为此，我们采用了连续介质中的变形相对论哈特里-博戈留波夫理论（DRHBc）、FRDM2012 和 AME2020 数据。 首先，我们通过减去库仑能的贡献，研究了铅和钙同位素中的两质子和两中子分离能。 它们与中子数以及中子皮厚度有很强的相关性。 通过两分离能的相对差值，我们从钙和铅同位素中推导出对称能。 由于核表面对对称能有贡献，我们使用多种质量模型减去表面贡献，从而推导出体积对称能。 从 DRHBc 质量表数据中得到的对称能系数$a_{sym}$为铅同位素 20.0$\sim $22.7 MeV，钙同位素为 18.7$\sim$19.3 MeV，而其他质量表的数据结果为：从 AME2020（FRDM2012）数据中得到铅同位素为 19.6$\sim$22.1（20.7$\sim$22.3）MeV，钙同位素为 18.9$\sim$19.0（19.6$\sim$19.7）MeV。 对不对称系数的体积贡献，$a_{sym}^v$，也针对每种质量模型提供了，该贡献取决于表面能系数与体积能系数的比值，$a_s / a_v$。 由于比值$a_s / a_v$既不由核理论确定，也不由实验数据确定，我们通过使用比值$a_s / a_v$作为自由参数来研究$a_{sym}^v$，并得到了$a_{sym}^v = $为 27.0 MeV，几乎与核模型和同位素链无关，比值$a_s / a_v$被约束为$a_s / a_v = 1.10 \sim 1.13$。 显示英文摘要

摘要： We investigate the symmetry energy in relation with the two-proton and two-neutron separation energies using different nuclear mass data. For this aim, we exploit the deformed relativistic Hartree-Bogoliubov theory in the continuum (DRHBc), FRDM2012 and AME2020 data. First, we study the two-proton and two-neutron separation energies in Pb and Ca isotopes by subtracting the contribution of Coulomb energy. They show a strong correlation with neutron number as well as with the neutron skin thickness. By taking the relative difference of both separation energies, we derive the symmetry energy from Ca and Pb isotopes. Since the nuclear surface contributes to the symmetry energy, we deduce the volume symmetry energy by subtracting the surface contribution using several mass models. The obtained symmetry energy coefficient, $a_{sym}$, is 20.0 $\sim $ 22.7 MeV for Pb isotopes and 18.7 $\sim$ 19.3 MeV for Ca isotopes from the DRHBc mass table data, while the results from other mass tables are 19.6 $\sim$ 22.1 (20.7 $\sim$ 22.3) MeV for Pb isotopes and 18.9 $\sim$ 19.0 (19.6 $\sim$ 19.7) MeV for Ca isotopes from AME2020 (FRDM2012) data. The volume contribution to the asymmetry coefficient, $a_{sym}^v$, which depends on the ratio of the surface to the volume energy coefficients, $a_s / a_v$, is also provided for each mass model. Since the ratio $a_s / a_v$ is neither determined by nuclear theory, nor by experimental data, we have investigated $a_{sym}^v$ by using the ratio $a_s / a_v$ as a free parameter, and have obtained $a_{sym}^v = $ 27.0 MeV, almost irrespective of nuclear model and isotopic chain, with the ratio $a_s / a_v$ constrained as $a_s / a_v = 1.10 \sim 1.13$.