Criterion for weak spin-orbit coupling in heavy-fermion superconductivity: A numerical renormalization-group study

A criterion for effective irrelevancy of the spin-orbit coupling in the heavy-fermion superconductivity is discussed on the basis of the impurity Anderson model with two sets of Kramers doublets. Using Wilson's numerical renormalization-group method, we demonstrate a formation of the quasiparticle as well as the renormalization of the rotational symmetry-breaking interaction in the lower Kramers doublet (quasispin) space. A comparison with the quasispin conserving interaction exhibits the effective irrelevancy of the symmetry-breaking interaction for the splitting of two doublets Delta larger than the characteristic energy of the local spin fluctuation T_K. The formula for the ratio of two interactions is also determined.