An Application of the W.K.B. Method to the Cohesive Energy of Monovalent Metals

Abstract

A new method is developed which, within the limits of the spherical cell approximation first presented by Wigner and Seitz, will permit the evaluation of the cohesive energy, lattice constant, and compressibility of a monovalent metallic solid without the explicit computation of a central field for the atom. Analytic formulas for approximate solid state wave functions are produced in the region outside the atomic core by utilizing Imai's form of the W.K.B. method with the phase constant determined explicitly in terms of the known quantum defect of the free atom. These wave functions are applied to the determination of the minimum ground state energy in the alkali metals and of the sphere radius at which this occurs as functions of the quantum defects of the free atoms. These functions, when applied to Fröhlich's semi-empirical formula, yield a rapid and accurate method for the computation of the ground-state energy as a function of sphere radius.