Nuclear pairing from microscopic forces: singlet channels and higher-partial waves

Abstract

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 ${\Delta }_F$ 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 $\chi (p)$ defined by $\Delta (p)={\Delta }_F\chi (p)$ and a non-linear algebraic equation for the gap magnitude ${\Delta }_F=\Delta (p_F)$ at the Fermi surface. This method is numerically stable even for small pairing gaps, such as that encountered in the coupled ${}^{3}P{F}_2$ 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.

18 pages and 9 figures

References in corpus (12)

• Chiral effective field theory and nuclear forces
• Rapid Cooling of the Neutron Star in Cassiopeia A Triggered by Neutron Superfluidity in Dense Matter
• Strongly paired fermions: Cold atoms and neutron matter
• Quantum Monte Carlo calculation of the equation of state of neutron matter
• Low-momentum interactions with smooth cutoffs
• Chiral three-nucleon interaction and the carbon-14 dating beta decay
• Equation of state of low--density neutron matter and the ${}^1{S}_0$ pairing gap
• ${}^1{S}_0$ superfluid phase--transition in neutron matter with realistic nuclear potentials and modern many--body theories
• Density-dependent nucleon-nucleon interaction from three-nucleon forces
• Low Momentum Nucleon-Nucleon Interactions and Shell-Model Calculations
• Dependence of the BCS 1S0 superfluid pairing gap on nuclear interactions
• Microscopic evaluation of the pairing gap

Cited by in corpus (1)

• Pairing in neutron matter: New uncertainty estimates and three-body forces