Pseudoatom version of the rigid-muffin-tin approximation

The electron-phonon coupling parameter ($\lambda$) is calculated for the metals K, Al, Cu, and Nb using the rigid-muffin-tin approximation but with the Fermi energy as an adjustable parameter and phase shifts obtained by fitting the Fermi-surface dimensions. A pseudoatom muffin-tin potential is obtained by making a suitable choice of the Fermi-energy parameter. In simple metals the choice is defined in terms of the screening constraint. In transition metals an arbitrary choice (half the "band-structure" value) is suggested. For the simple metals $\lambda$ changes by a factor of 3 or more over the range of Fermi energies considered but agrees well with experimental estimates at the pseudoatom value. In niobium the shift leaves the average value of $\lambda$ essentially unaltered but changes the anisotropy so as to better match the experimental anisotropy. Provided the same criteria are used for determining the Fermi-energy parameter, very similar results are obtained using a scaling procedure suggested by Butler and based on the atomic-sphere approximation.