Hunds Rule Theory for Heavy Fermion Superconductors

In this paper, a generalization of standard spin fluctuation theory is considered which takes into account orbital degeneracy effects which are critical for describing f electrons. This theory leads to an instability for a superconducting pair state which obeys Hunds rules. Such a state has L=5, S=1, and J=4. The degeneracy of this state is broken by crystalline effects, and realistic calculations for $UPt_3$ find a resultant pair state with $\Gamma_6^-$ symmetry, consistent with current experimental constraints.