We obtain an improved approximation for the inverse vertex function ${\epsilon }_{\overrightarrow{\mathrm{k}}t}(\overrightarrow{\kappa },\omega )$ with exchange corrections. The imaginary part of the self-energy of hot electrons is calculated and compared with the random-phase-approximation (RPA) values. The RPA results differ significantly from Quinn's earlier RPA results owing to improved computational facilities. The mean free path of an electron 5 eV above the Fermi surface in aluminum is compared with Kanter's experimental value.

• Received 30 October 1970

DOI:https://doi.org/10.1103/PhysRevB.3.2982