Background: An accurate description of nuclear pairing gaps is extremely important for understanding static and dynamic properties of the inner crusts of neutron stars and to explain their cooling process.
Purpose: We plan to study the behavior of the pairing gaps $Δ_F$ as a function of the Fermi momentum $k_F$ for neutron and nuclear matter in all relevant angular momentum channels where superfluidity is believed to naturally emerge. The calculations will employ realistic chiral nucleon-nucleon potentials with the inclusion of three-body forces and self-energy effects.
Methods: The superfluid states of neutron and nuclear matter are studied by solving the BCS gap equation for chiral nuclear potentials using the method suggested by Khodel et al., where the original gap equation is replaced by a coupled set of equations for the dimensionless gap function $χ(p)$ defined by $Δ(p) = Δ_F χ(p)$ and a non-linear algebraic equation for the gap magnitude $Δ_F = Δ(p_F)$ at the Fermi surface. This method is numerically stable even for small pairing gaps, such as that encountered in the coupled $^3PF_2$ partial wave.
Results: We have successfully applied Khodel's method to singlet ($S$) and coupled channel ($SD$ and $PF$) cases in neutron and nuclear matter. Our calculations agree with other ab-initio approaches, where available, and provide crucial inputs for future applications in superfluid systems.
Singlet pairing gaps of neutrons and protons in hyperonic neutron stars
在相对论平均场模型和Bardeen-Cooper-Schrieffer理论下研究了超声波中子星中的$^{1}S_{0}$核超流体。以Reid软核相互作用为核子-核子相互作用，计算了中子和质子的$^{1}S_{0}$配对能隙。我们详细研究了超子自由度对中子星物质中$^{1}S_{0}$核子对能隙的影响。结果表明，超子的出现对$^{1}S_{0}$中子配对能隙的重子密度范围和大小几乎没有影响，质子配对能隙在该区域$ρ_B=0.0-0.393$ fm $^{-3}$也略有减小.然而，如果重子密度变得大于0.393 fm ${^{-3}}$，则$^{1}S_{0}$质子配对间隙明显增大。此外，超子的存在还使质子超流的范围明显扩大。在我们的结果中，超子改变了$^{1}S_{0}$质子配对间隙，这必然改变了中子星的冷却性质。
本文从带有Argonne v 18力的从头算BCS能隙方程出发，在自洽能量密度泛函方法的基础上，用裸核子质量表征，提出了一个核子配对的半微观模型. BCS理论是在模型空间S0中用第一性原理计算的有效对相互作用在辅助空间S0中表示的。这种有效的相互作用补充了一个小的唯象附录，其中包含一个唯象参数普遍适用于所有中重原子核。我们认为后者是一种唯象的方式来考虑BCS理论的多体修正和有效质量效应。对于质子，库仑相互作用被直接引入。对几种半幻核的同位素链和等规链的计算证实了模型的正确性。强调了自洽基础的作用。
Microscopic mechanism of the Fayans pairing for the enhancement of charge radii
The University of Tokyo（东京大学）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所交叉理论与数学科学中心 (iTHEMS)）；Università degli Studi di Milano（米兰大学）；INFN, Sezione di Milano（意大利国家核物理研究所，米兰分部）；Universitat de Barcelona（巴塞罗那大学）；Institut de Ciències del Cosmos, Universitat de Barcelona（巴塞罗那大学宇宙科学研究所）；University of Aizu（会津大学）；RIKEN Nishina Center（理化学研究所仁科研究中心）
