  The cross section of elastic electron-proton scattering taking place in an
electron gas is calculated within the Closed Time Path method. It is found to
be the sum of two terms, one being the expression in the vacuum except that it
involves dressing due to the electron gas. The other term is due to the
scattering particles-electron gas entanglement. This term dominates the usual
one when the exchange energy is in the vicinity of the Fermi energy.
Furthermore it makes the trajectories of the colliding particles more
consistent and the collision more irreversible, rendering the scattering more
classical in this regime.
