A field theory is presented for particles which interact via Coulomb and hard-core potentials, as relevant for classical plasmas, electrolytes, and charged colloidal solutions. We apply the method to the one-component plasma with hard cores (OCPHC), consisting of identical particles of fixed charge and diameter in a neutralizing background, and the symmetric two-component plasma with hard cores (TCPHC), consisting of equal numbers of positively and negatively charged particles of identical size. We obtain the first fea coefficients of a systematic low-density expansion of the free energy for both models exactly and in closed form. The OCPHC coefficients go over to the classical Abe result in the high-charge (or small hard-core diameter) limit. The TCPHC, on the other hand, exhibits diverging coefficients in the high-charge limit, which is due to the formation of strongly bound ion-pairs.
