Effect of Matrix Elements on the Pairing Kernel in Exchange Mediated   Superconductors
  A method is derived for calculating the pairing kernel in exchange mediated superconductors including matrix element effects. Various models for the interaction vertex are considered, including spin exchange, orbital exchange, and quadrupolar exchange. As an example, this formalism is applied to $UPt_3$ using relativistic wavefunctions from a local density band calculation. 
M. R. Norman