Effect of plasmon excitations in relativistic quantum electron gas

Abstract

In this research, we use the generalized quantum multistream model to describe collective qusiparticle excitations in electron gas with arbitrary degree of degeneracy and relativity. The effective Schrödinger–Poisson and square-root Klein–Gordon–Poisson models are applied to study the energy band structure and statistical parameters of finite temperature quantum and relativistic quantum electron gas in neutralizing background charge. Based on the plasmon energy bandgap appearing above the Fermi level, a new equation of state for quasiparticle (collective) excitations with new plasma parameter definition is suggested for dense plasmas applicable to a wide range of electron temperature and density. The new criterion for quasiparticle excitations reveals some interesting aspects of relativistic quantum matter at extreme condition, such as the plasmon blackout and collective quantum pressure collapse, which are studied in the frameworks of both non-relativistic and relativistic quantum phenomena. Current quasiparticle model predicts density-temperature regimes in warm-dense matter for which collective excitations become ineffective. On the other hand, the energy band structure model predicts the quasiparticle pressure collapse in temperature–density regime close to that of white dwarf stars. The energy band structure is a powerful concept in condensed matter physics and is shown to have applications for collective quantum excitations in electron gas. It can also have direct applications in quasiparticle dielectric response and thermodynamic properties of electron gas in inertial confinement fusion, stellar core, compact stars, and charged relativistic quantum environments. It is interesting that the basic thermodynamic behavior of non-relativistic and relativistic quantum electron gases closely match up to temperature and number density of typical white dwarfs where the gravitational collapse is prone to occur. This evidently confirms the relevance of non-relativistic quantum plasmon model to study the collective excitations in warm dense matter and white dwarfs.