Non-spherical-electron-cloud equivalent volume V in the refractive index formula

Abstract

The formula of refractive index n, which is derived recently from the electromagnetic induction refraction mechanism, contains a parameter V, i.e., the equivalent volume of electron cloud. Dozens of calculated n results by using this formula in previous researches are in good agreement with the measured ones. V determines some properties of materials, such as refractive index and band gap. It is not yet known how to calculate V values of non-spherical electron clouds. In this paper, a calculation method for V values of non-spherical electron clouds is presented as follows: The electron cloud is divided into many little volume elements, and the equivalent volume of each little volume element is calculated with the wave function; V value of the electron cloud is the sum of the equivalent volumes of all its little volume elements. V value of the electron cloud in H2 molecule is obtained in this way. Refractive index of H2 gas is calculated with the V value of H2 molecule, and the calculated refractive index is consistent with the measured datum. In addition to calculating V value, the method can also calculate V shape. Distribution contour of the equivalent volume of electron cloud in the H2 molecule is like an apple. This work determines the general method of using wave functions to calculate V values and refractive indices, is helpful to promote the applications of the formula of refractive index, and provides a means for better understanding the relationship between material properties and its V values.