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 $^3PF_2$ partial wave. Results: We have successfully applied Khodels 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.
