标题： 扩展的南布-约纳-拉辛模型中的有限核 显示英文标题

标题： Finite nuclei in an extended Nambu-Jona-Lasinio model

摘要： 我们提出了一种新的理论框架，基于扩展的Nambu-Jona-Lasinio（eNJL）模型来研究有限核的性质，在这个模型中通过扩展SU(3) NJL模型并把重子当作夸克团簇，考虑了狄拉克海、自发的手征对称性破缺以及夸克自由度。然后可以采用该eNJL模型以统一的方式检查从重子物质到夸克物质的各种物质状态。在这项工作中，假设球对称的有限核，并忽略质心或旋转修正的情况下，我们基于具有附加配对关联的eNJL模型系统地研究了有限核的性质。发现我们的模型一般能够再现2016年原子质量评估（AME2016）中的2495个核（$A>2$）的结合能，均方根偏差为$5.38$MeV。这些偏差主要归因于幻数$N(Z) =28$、50和82处的壳隙过大以及假想的壳闭合出现在$N(Z)=34$、58和92处。同时，所得到的906个核的电荷半径比实验值系统性偏小，均方根偏差为$0.127$fm。在未来的研究中，我们希望通过仔细校准耦合常数的密度依赖性，并考虑费米海中核子和狄拉克海中夸克的微观集体修正来减少预测的不确定性。 显示英文摘要

摘要： We propose a new theoretical framework to investigate the properties of finite nuclei based on an extended Nambu-Jona-Lasinio (eNJL) model, where the Dirac sea, the spontaneous chiral symmetry breaking, and the quark degrees of freedom are considered by extending the SU(3) NJL model and treating baryons as clusters of quarks. The eNJL model can then be readily adopted to examine the matter states ranging from baryonic matter to quark matter in a unified manner. In this work, by assuming spherically symmetric finite nuclei and neglecting the center-of-mass or rotational corrections, we systematically investigate the properties of finite nuclei based on the eNJL model with additional pairing correlations. It is found that our model generally reproduces the binding energies of the 2495 nuclei ($A>2$) from the 2016 Atomic Mass Evaluation (AME2016) with the root-mean-square deviations $5.38$ MeV. The deviations are mainly attributed to the too large shell gaps at magic numbers $N(Z) =28$, 50, and 82 as well as the spurious shell closures at $N(Z)=34$, 58, and 92. Meanwhile, the obtained charge radii of 906 nuclei are systematically smaller than the experimental values with root-mean-square deviations $0.127$ fm. In our future study, we expect to reduce the uncertainties of our predictions by carefully calibrating the density dependence of coupling constants and considering deformations with microscopic collective corrections from the nucleons in the Fermi sea and quarks in the Dirac sea.