Spectroscopic Evidence for the5fCoulomb Interaction in UAl2and UPt3

The $5f$ spectral weight in the heavy-fermion materials U${\mathrm{Al}}_2$ and U${\mathrm{Pt}}_3$ has been measured by electron spectroscopy, and compared to that in density-functional calculations. The one-electron $5f$ widths are both too large to account for the enhanced values of the specific-heat coefficient $\gamma$, and too small to account for the measured widths. In the Anderson Hamiltonian, both discrepancies arise from the $5f$ Coulomb interaction. It is pointed out that an enhanced $\gamma$ value does not imply enhanced magnitude of the $5f$ spectral weight at $E_{\mathrm{F}}$.