  In this paper, a generalization of standard spin fluctuation theory is
considered by replacing the simple Hubbard interaction by the screened
Hartree-Fock interaction for f electrons. This model is then used in both an LS
and a JJ coupling scheme to construct the particle-particle scattering vertex
in an on-site approximation. This vertex is shown to lead to an instability for
a superconducting pair state which obeys Hunds rules, with L=5, S=1, and J=4.
The degeneracy of this state is broken by anisotropy of the quasiparticle
wavefunctions. Detailed calculations are presented for the case of $UPt_3$.
