Problems of quantum-statistical thermodynamics of plasmas: High- and low-temperature limits and analyticity

The OCP plasma model which has been the favourite plasma model of Gabor Kalman is simple but on the other side connected with some principal difficulties, and gave rise to some controversies. We discuss here the three main problems of Coulomb systems, the limit cases of the parameter xi similar to (e(2)/(h) over bar root T) : xi -> +/-infinity and xi -> 0. We show first that Taylor expansions in (1/xi) similar to (h) over bar are in general divergent and have asymptotic character and expansions in xi similar to e(2) are convergent. We study the analytic properties of the partition functions and the thermodynamic functions. Assuming analytizity with respect to the relevant physical parameter for pair interactions xi similar to (e(i)e(j)/(h) over barT) we can show that the analyticity with respect to this parameter allows to extend several OCP-properties, except the exchange functions, to many component systems by analytic continuation of the case delta < 0 to xi > 0. In particular follows that the Taylor coefficients of analytic OCP functions may be extended to any multi-component Coulomb system. Further, we discuss also the most difficult case xi -> 0 and the problem with contributions linear in the interaction, the so-called Hartree terms.