Consequences of resonant impurity scattering in anisotropic superconductors: Thermal and spin relaxation properties

We present a systematic discussion of the effect of resonant impurity scattering on anisotropic model states of heavy-fermion superconductors. The impurity scattering is treated in the self-consistent T-matrix approximation including a renormalization of the frequency ω and the quasiparticle energy ${\xi }_k$. Model states considered include the axial and polar states familiar from superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ as well as two states, termed hexial and hybrid, occurring in the group-theoretical classification of singlet states in hexagonal symmetry. We calculate the density of states, the critical temperature and the order parameter, the specific heat, the thermal conductivity, and the spin-lattice relaxation rate. Vertex corrections are included in the calculations of two-particle quantities. The observed properties of the prototype Fermi-liquid material ${\mathrm{UPt}}_3$ show many qualitative features in common with our model. However, it turns out to be difficult to identify any given state with certainty. An experimental test of our predictions on the behavior as a function of impurity concentration, particularly in the gapless regime at low temperatures, would allow for a more definitive characterization of the superconducting state.