Konwersatorium im. Leopolda Infelda

The derivation of exact results for quantum Coulomb gases has to face several difficulties originating from screening and recombination of charges into atoms, ions and molecules. The path integral representation at finite temperature is the most suitable tool for a proper account of those phenomena in partially ionized gases. It leads to the introductionof an equivalent classical system made of loops with arbitrary shapesdistributed according to Wiener measure. The equilibrium quantities of thegenuine quantum gas are then formally represented by Mayer-likediagrammatical series for that system of loops. The path integraldescription in terms of loops allows us to perform systematic resummations of Coulomb chains which remove long range divergences, as well as reexponentiations which incorporate recombination at short distances. Such operations can be carried out within well-prescribed topological and combinatorial rules, thanks to the classical nature of Gibbs factors in the loop world. Mayer-like series are then exactly transformed into the so-called screened cluster representation, where graphs are now built with particle clusters and screened interactions.

Within the screened cluster representation, we derive exact expressions for both thermodynamics and correlations of a partially ionized hydrogen gas in the Saha regime, defined by a double zero-temperature and zero-density limit. Such expressions properly account for contributions of molecular or ionic species, without any adjustable parameters like in phenomenological approaches. Moreover, they shed light on the partial screening of van der Waals forces by free charges, and its relation with the algebraic nature of screening in quantum plasmas.