Mean free path of a suddenly created fast electron moving in a degenerate electron gas

The many-body problem is a topic in its own right, with its own characteristic methods. Particularly, the model system of identical fermion particles, not localized in space and subject to Pauli’s exclusion principle, represents a genuinely important problem and the dynamical probing of correlated motions of constituents of such a many-body system is currently an active subfield in physics. In order to put the present study on inelastic scattering into a proper perspective, we follow below the wellknown 1 historical path of developments whose result is named in the literature as Landau’s Fermi liquid theory. By considering the liquid state of the rare fermionic isotope of neutral helium atoms, Landau concluded that the low-lying excited states of such a system can be described by quasiparticles. Implications for an electron gas were immediately (see Sec. II) recognized; the essential difference being the presence of charged free particles instead of neutral atoms. It is this difference that requires different modeling of an effective interaction in the mean free path calculation of an electron in the electron gas, and is the subject of our study. In his pioneering work on applying a field-theoretic 2 Green’s function method to a nonrelativistic many-body system of neutral atomic fermions, Galitskii derived 3 the following expression for the single-particle [E = (v 2 /2m) EF ] scattering rate