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We investigate positron annihilation in electron liquid as a case study formany-body theory, in particular the optimized Fermi Hypernetted Chain (FHNC-EL)method. We examine several approximation schemes and show that one has to go upto the most sophisticated implementation of the theory available at the momentin order to get annihilation rates that agree reasonably well with experimentaldata. Even though there is basically just one number to look at, theelectron-positron pair distribution function at zero distance, it is exactlythis number that dictates how the full pair distribution behaves: In mostcases, it falls off monotonously towards unity as the distance increases. Caseswhere the electron-positron pair distribution exhibits a dip are precursors tothe formation of bound electron--positron pairs. The formation ofelectron-positron pairs is indicated by a divergence of the FHNC-EL equations,from this we can estimate the density regime where positrons must be localized.This occurs in our calculations in the range 9.4 <= r_s <=10, where r_s is thedimensionless density parameter of the electron liquid.Comment: To appear in Phys. Rev. B (2003

Many-body aspects of positron annihilation in the electron gas