Proton scattering on an electron gas

TL;DR

This paper demonstrates that the Closed Time Path formalism effectively models proton scattering on an electron gas, revealing the importance of resummation and cancellations in high-density, quasi-particle regimes.

Contribution

It introduces the application of the Closed Time Path formalism to proton-electron gas scattering, highlighting how it simplifies handling final state interactions and the need for resummation in dense regimes.

Findings

Cross section proportional to photon density of states

Resummation needed for high-density electron gases

Strong cancellation between real and virtual electron-hole pairs

Abstract

It is shown in the case of proton scattering on an electron gas target that the Closed Time Path formalism can handle final state interactions of the target in equilibrium in a simple and natural manner. The leading order cross section is proportional to the photon density of states. The scattering needs a partial resummation of the perturbation series when the electron gas forms long living quasi-particles with high density of state during the collision. A strong cancellation between real and virtual electron-hole pairs is found in this case.