Microscopic analysis of homogeneous electron gas by considering dipole dipole interaction

TL;DR

This paper analyzes how dipole dipole interactions affect the thermodynamic properties of a zero-temperature homogeneous electron gas, revealing state-dependent behaviors and density-related energy growth.

Contribution

It provides analytic expressions for DDI energy in electron gas using perturbation theory and second quantization, highlighting its state-dependent and density-dependent characteristics.

Findings

DDI energy depends on density and angular momentum

Energy contributions are positive for even and negative for odd angular momenta

Energy magnitude decreases with increasing total angular momentum

Abstract

Implying perturbation theory, the impact of the dipole dipole interaction (DDI) on the thermodynamic properties of a homogeneous electron gas at zero temperature is investigated. Through the second quantization formalism, the analytic expressions for the ground state energy and the DDI energy are obtained. In this paper, the DDI energy has similarities with the previous works done by others. We show that its general behavior depends on density and the total angular momentum. Especially, it is found that the DDI energy has a highly state-dependent behavior. With the growth of density, the magnitude of DDI energy, which is found to be the summation of all energy contributions of the states with even and odd total angular momenta, grows linearly. It is also found that for the states with even and odd total angular momenta, the DDI energy contributions are corresponding to the positive and negative values, respectively. In particular, an increase of total angular momentum leads to decline in the magnitude of energy contribution. Therefore, the dipole dipole interaction reveals distinct characteristics in comparison with central like interactions.