Effect of matrix elements on the pairing kernel in heavy-fermion superconductors

A method is derived for calculating the pairing kernel in heavy-fermion superconductors including matrix-element effects. Various models for the interaction vertex are considered, including pseudospin exchange, orbital exchange, and quadrupolar exchange. As an example, this formalism is applied to ${\mathrm{UPt}}_3$ with the use of relativistic wave functions from a local-density-band calculation.