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We calculate the Coulomb scattering amplitude for two electrons injected withopposite momenta in an interacting 2DEG. We include the effect of the Fermiliquid background by solving the 2D Bethe-Salpeter equation for thetwo-particle Green function vertex, in the ladder and random phaseapproximations. This result is used to discuss the feasibility of producingspin EPR pairs in a 2DEG by collecting electrons emerging from collisions at api/2 scattering angle, where only the entangled spin-singlets avoid thedestructive interference resulting from quantum indistinguishability.Furthermore, we study the effective 2D electron-electron interaction due to theexchange of virtual acoustic and optical phonons, and compare it to the Coulombinteraction. Finally, we show that the 2D Kohn-Luttinger pairing instabilityfor the scattering electrons is negligible in a GaAs 2DEG.Comment: 19 pages, 10 figure

Coulomb scattering cross section in a two-dimensional electron gas and production of entangled electrons