Application of the collective approach to the thermodynamics of an electron gas

Abstract

The collective approach of Pines & Bohm has been applied to the problem of the thermodynamics of the N-particle electron gas including transverse radiation. Partitioning of the internal energy and certain of the other thermodynamic quantities is discussed generally. The system is seen to divide itself into three approximately independent subsystems: (1) an infinite set of free harmonic oscillators, corresponding to the transverse field, with an energy spectrum given by ωT(κ), where ωT(κ), is given by the dispersion relation for transverse electromagnetic waves in a plasma; (2) a set of 8 free harmonic oscillators corresponding to the longitudinal (plasma) oscillations, with an energy spectrum ωT(κ), given by the dispersion relation for plasma oscillations; and (3) a set of (N — 2s/3) quasi-particles of mass approximately equal to the electron mass, interacting via a short-range potential which is essentially screened Coulomb. Analytical expressions for the energy, pressure, and constant-volume specific heat of the transverse oscillators are given, together with approximate expressions applicable to the high-density—low-temperature and low-density—high-temperature limits. Detailed numerical calculations of the internal energy and pressure of the longitudinal modes are presented. In addition, the contributions to the energy and pressure from the particle portion are evaluated in the low-density—high-temperature limit as functions of the cut-off wave vector κc; κc is the maximum k-vector of the longitudinal oscillators.