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We consider a quantum multi-component plasma made of point charged particlesinteracting via the two-body Coulomb potential. Within the Feynman-Kac pathintegral representation of the system in terms of a classical gas of loops, wederive screened activity series for the pressure in the grand-canonicalensemble. The method is based on the Abe-Meeron summations which remove alllong-range Coulomb divergences. Moreover, we show that the particle densitiescan be inferred from the diagrammatic series for the pressure, through partialdifferentiations with respect to suitable effective activities, consistentlywith the local charge neutrality. We briefly argue how these results can beused for including, in the equation of state at moderately low densities, thecontributions of recombined entities made with three or more particles.

Screened activity expansion for the pressure of a quantum multi-component plasma and consistency with the local charge neutrality