Muffin-tin model in amorphous and liquid metals: General formalism and calculations for ans-phase-shift model

We present a general formalism for the calculation of the density of electronic states (DOS) of an amorphous or liquid metal in the muffin-tin model. The formalism embraces several theories which have been proposed to deal with strongly scattering systems such as transition and noble metals. We make use of the Lloyd formula for the DOS and find that while the effective-medium approximation can be used with this formula, most other theories violate the nonoverlapping condition of the muffin-tin model. We propose a method for avoiding this violation in the case of the quasicrystalline and the Ishida-Yonezawa approximations, improving and correcting some previous work. We have performed calculations using $s$-phase shifts to model the bound and resonance states in real metals and the results yield some insights into the range and validity of various liquid-metal theories.