  We study the angular momentum mixing effects in the color superconductor with
non-spherical pairing. We first clarify the concept of the angular momentum
mixing with a toy model for non-relativistic and spinless fermions. Then we
derive the gap equation for the polar phase of dense QCD by minimizing the CJT
free energy. The solution of the gap equation consists of all angular momentum
partial waves of odd parity. The corresponding free energy is found to be lower
than that reported in the literature with p-wave only.
