Pair-creation collective modes in an electron gas

Abstract

High-energy modes of oscillation in a zero-temperature relativistic electron gas in a strong background magnetic field are reported. The modes propagate parallel to the magnetic field and appear both in a longitudinal and in two transverse polarizations. The underlying mechanism is the binding between electrons near the Fermi surface and virtual positrons, which is enhanced by the presence of the filled Fermi distribution, in a Cooper-pair-like phenomenon. The energy of the mode is of the order of the pair energy (over 1.02 MeV), and the mode exists only for wave numbers k above a critical value, such that the mode group velocity exceeds the velocity of an electron on the Fermi surface. Damping of the mode is insignificant at the critical wave number and increases with k to a relatively small maximum value.PACS number(s): 52.25. Mq, 52.60.+h, 12.20.Ds, 97.60.Jd

Electromagnetic responses of relativistic electrons

“…The appearance of non-zero imaginary parts indicates that the system is unstable to the decay into electron–hole (lower energies) or electron–positron (higher energies) pairs (Tsai & Erber 1974; Pulsifer & Kalman 1992). The former is well known to occur in the non-relativistic limit.…”

“…Analytic results for the response functions of the relativistic electron gas at have already appeared in the literature in the context of plasma physics (Jancovici 1962; Melrose & Hayes 1984; Barton 1990; Pulsifer & Kalman 1992; Barbaro & Quaglia 2005; McOrist & Weise 2007; Eliasson & Shukla 2011). Only expressions for the longitudinal and transverse parts of the electric permittivity, and , were derived.…”

Spin-dependent relativistic quantum magnetized electron gas

“…The spin-dependent contribution differs from the spin-independent contribution in (31) in three ways: the term 2n is absent, there is an additional multiplicative factor m/ε 0 n , and the sign a = ±1 multiplies the non-gyrotropic term rather than the gyrotropic term. These differences can be summarized by noting that they correspond to the term proportional to aeB + 1 2 (k 2 ) in the spin-independent case being modified according to Z (1,3) nn−a (ω, k z ) → Z (1,3) nn−a (ω,…”

“…to include the spin-dependent contribution. Using (31) allows one to generalize existing discussions of wave dispersion for parallel propagation in a quantum plasma [3,4] to include spin dependence, but we do not do so here.…”

“…Major simplification occurs to the tensorial form for parallel propagation. Parallel propagation combined with the completely degenerate limit is the only case that has been explored in any detail, even in the absence of spin-dependence [3,4].…”