The resonant model potential form factor: General theory and application to copper, silver and calcium

Abstract

The model potential method is reformulated for d band metals. The (non-local and energy-dependent) ionic model potential v₀(E) is written as w₀(E)+U(E-E). w₀(E) is a standard Heine-Abarenkov-like model potential which behaves as -Ze²/r outside the model region (w₀ is approximated in this work by a local potential). The resonance part U/(E-E) takes care of the d resonance; U is a finite range Hermitian operator which acts only on d states and is separable in each m channel. The metal pseudopotential is Sigma _ionsv₀(E)+V_e( rho _sc) where V_c( rho _sc) is the potential due to the screening density rho _sc(r) which is equal to the true (d+sp) electronic density outside the region where the true and model potential are not equal. A first-order calculation of the screened form factor is carried out. The resonant-part energy parameter E is first renormalized to E, which turns out to be similar to the mean d band energy E_d of Harrison (1969) and Moriarty (1970), and a consistent procedure to expand a physical quantity in terms of the renormalized potential is proposed. The screening density is calculated to first order using a recent formula for the integrated density of states appropriate for a singular resonant potential. The depletion charge density problem is considered.