Direct and reverse transformations between electron density and electron momentum density

Abstract

Electron momentum distributions have been obtained from electron densities derived from the Thomas-Fermi, local-density-functional, and general-density-functional theories by the application of the procedure of Burkhardt, K\'onya, and Coulson and March (the BKCM procedure). The BKCM procedure has been modified so as to simulate the correct asymptotic behavior of the electron momentum distributions. It has been shown that, by means of reciprocal relationships to those in the direct BKCM procedure for estimating electron momentum density from a given electron density, a reverse transformation from electron momentum density to electron density can be effected. This reverse transformation enables one to obtain reasonable estimates of $〈{r}^{n}〉$ expectation values and form factors from a given electron momentum distribution. It is also noted that the shell structure, i.e., the maxima in the original radial electron density $4\ensuremath{\pi}{r}^{2}\ensuremath{\rho}(r)$, are reproduced upon reconstructing the radial electron density from an application of the reverse BKCM procedure. It is also shown that, with the use of extremely accurate experimental Compton profiles, the electron density along with its shell-structure characteristics can be estimated reasonably accurately.