  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 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.
