Impurity Scattering and Gap Structure in the Anisotropic Superconductor UPt$_3$

The thermal conductivity, $\kappa$, of the heavy fermion superconductor UPt$_3$ was measured down to T$_c$/10. The absence of a linear term in the temperature dependence as T$\rightarrow$0 strongly suggests there are no zero energy quasiparticle excitations, in contradiction with the gapless behaviour often inferred from specific heat. A non-vanishing anisotropy ratio $\kappa_c$/$\kappa_b$ as T$\rightarrow$0 establishes a new property of the gap structure: the presence of nodes along the c-axis. Furthermore, recent calculations by Fledderjohann and Hirschfeld show these cannot be point nodes with a linear k-dependence.