Effective masses and perturbation theory in the theory of simple metals

The model (or pseudo) Schrödinger equation describing free-electron-like metals is solved by a modified perturbation method in which the diagonal matrix element of the potential is accounted for exactly by defining two κ-dependent effective masses which incorporate it from the outset. The new perturbation approach is used to derive mass-renormalized expressions for the energy of electronic states, the screened form factor, and the energy-wave-number characteristic. Numerical results for the effective masses are obtained using the optimized model potential, and a constant-mass approximation is used to estimate corrections to the form factors and energy-wave-number characteristics calculated from ordinary perturbation theory. The magnitude of these corrections suggests that mass-renormalized results may be required to predict metallic properties.