Solutions of the magnetic Eliashberg equations for heavy-fermion superconductors

Recently, a method was put forth to evaluate quantitatively gap functions and transition temperatures for heavy-fermion superconductors. This formalism involves a modification of the Eliashberg spin-fluctuation equations of Berk and Schrieffer, with the modification being the replacement of the Lindhard susceptibility by the experimentally derived susceptibility. In the case of ${\mathrm{UPt}}_3$, it was shown that both the mass renormalization and superconducting-transition temperature could be explained by this method. The purpose here is to discuss the results of the solutions to these equations in depth for the cases of ${\mathrm{UPt}}_3$ and ${\mathrm{UBe}}_{13}$, as well as some preliminary thoughts on other heavy-fermion metals.