Exchange Interaction in a Degenerate Electron Gas: Contribution of Electrons with Opposite Spins, Found in One Quantum State

Abstract

The contribution of the Coulomb exchange interaction between pairs of electrons found in one quantum state is calculated. For this case it is shown that in an unpolarized, degenerate, weakly nonideal electron gas the frequency of a Langmuir wave with zero wave vector is \( \sqrt{3/2} \) times greater than the Langmuir frequency. With increase of the spin polarization (with decrease of the number of pairs of electrons in one quantum state) the frequency shift decreases monotonically to zero.