LOW-DENSITY LIMIT OF THE CORRELATION-ENERGY IN THE RANDOM-PHASE APPROXIMATION FOR CHARGED-PARTICLES OF ARBITRARY STATISTICS

Within the random-phase approximation (RPA) or ring sum, the ground-state correlation energy for a uniform gas of charged particles with density parameter r(s) tends as r(s) --> infinity to (-0.803 Ry) r(s)-3/4. This limit holds for fermions, as for bosons and distinguishable particles. For electrons, the next term in the low-density expansion (of order r(s)-1) cancels the exchange energy. Corrections to RPA must cancel the r(s)-3/4 term, and can modify the r(s)-1 term.