能隙的方向依赖性对非对称核物质中3SD1道及3D2道超流相的影响

The fermion pairing between different species with mismatched Fermi surfaces, which was discussed many years ago, promoted new interests in both theoretical and experimental studies in recent years. In the asymmetric nuclear matter contexts, the mismatched Fermi surfaces can be realized in the neutron-proton paring system where the asymmetry is small. In order to find the ground state of these systems, we intend to consider the angle (direction angle of k) dependence of the　pairing gap \delta(k) with the mechanism of the FFLO phase. The angle dependence has been neglected in the previous work on the studies of the superfluidity in the asymmetric nuclear matter by taking the angle-averaging procedure. However in the mismatched Fermi surfaces systems, the angle dependence can reduce the suppression from the splitting between the two Fermi surfaces. Following this, we will study the symmetries of the ground state and the effects of the angle dependence of the pairing gap on the 3SD1 and 3D2 superfluidity in asymmetric nuclear matter. Furthermore, we will study the FFLO state with the angle-dependent gap in order to provide more available data for the research of neutron star.

非对称核物质中的质子-中子配对实际上属于费米面不同的两成分费米子间的配对。对于这样的系统，两种费米面的差异会抑制平均费米面附近的对关联，而非S波能隙在动量空间的方向依赖性可以在一定程度上缓解这种抑制作用。但是在核物质超流性的计算中，往往采用角平均近似而忽略了能隙的方向依赖性(为简化计算)。本项目拟将考虑非对称核物质中非S波能隙的方向依赖性对3SD1道及3D2道超流相的影响，并将与FFLO态机制一起考虑以确定相应系统的超流基态，研究基态的对称性，并为研究中子星的热力学及动力学性质提供更可靠的能隙数据。

本项目中，我们们研究了能隙的方向依赖性对非对称核物质中3SD1道FFLO态的影响。当考虑能隙的方向依赖性时，FFLO态Cooper对动量在空间取向不再是简并的，我们发现了两种稳定的超流态（即FFLO–ADG-Orthogonal态和FFLO–ADG-Parallel态），分别对应Cooper对动量平行或者垂直于ADG(angle-dependent gap)的对称轴。FFLO–ADG-Orthogonal态存在于较低的非对称度下，而FFLO–ADG-Parallel态存在于较高非对称度下；并且当考虑FFLO态时，3SD1道超流态可以在较大非对称度范围内存在。此外，我们还一般地讨论了能隙的方向依赖性对两成分费米子D波超导系统的影响。对于化学势固定的D波配对系统，应该用Gap Susceptibility \kappa_{\Delta} 而非 \Delta<\delta\mu 来区分BCS态与Sarma态，并且发现当考虑能隙的方向依赖性时超流态可以在更大的 \delta\mu (费米面的差异)时存在。对于粒子数固定的D波配对系统，我们发现能隙的方向依赖性可以缓解 \delta\mu 对超流性的抑制。