Dispersion Law of the Form $\epsilon(p)=\hbar^2p^2/2m +\widetilde V(p)-\widetilde V(0)$ for Elementary Excitations of Nonideal Fermi Gas in the Pair Interaction Approximation $(i\leftrightarrow j)$, $V(|x_i-x_j|)$

TL;DR

This paper derives the dispersion law for elementary excitations in a nonideal Fermi gas considering pair interactions, expressing it in terms of the Fourier transform of the interaction potential.

Contribution

It provides a derivation of the dispersion law for elementary excitations in a nonideal Fermi gas within the pair interaction approximation.

Findings

Derived the dispersion law formula involving Fourier transform of the potential

Clarified the role of pair interactions in excitation spectra

Established a theoretical basis for analyzing nonideal Fermi gases

Abstract

We give a derivation of the dispersion law $\epsilon(p)=\hbar^2p^2/2m +\widetilde V(p)-\widetilde V(0)$, where $\widetilde V(p)$ is the Fourier transform of the pair interaction potential $V(r)$. (The interaction between particles $x_i$ and $x_j$ is $V(|x_i-x_j|)$.)