Quantum partition functions of composite particles in a hydrogen-helium plasma via path integral Monte Carlo.
We compute two- and three-body cluster functions that describe contributions of composite entities, like hydrogen atoms, ions H(-), H2(+), and helium atoms, and also charge-charge and atom-charge interactions, to the equation of state of a hydrogen-helium mixture at low density. A cluster function has the structure of a truncated virial coefficient and behaves, at low temperatures, like a usual partition function for the composite entity. Our path integral Monte Carlo calculations use importance sampling to sample efficiently the cluster partition functions even at low temperatures where bound state contributions dominate. We also employ a new and efficient adaptive discretization scheme that allows one not only to eliminate Coulomb divergencies in discretized path integrals, but also to direct the computational effort where particles are close and thus strongly interacting. The numerical results for the two-body function agree with the analytically known quantum second virial coefficient. The three-body cluster functions are compared at low temperatures with familiar partition functions for composite entities.
Laboratoire de Physique, Ecole Normale Supérieure de Lyon, UMR CNRS 5672, 46 allée d'Italie, 69364 Lyon Cedex 07, France.
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Wendland
Institut UTINAM, Université de Franche-Comté, UMR CNRS 6213, 16, route de Gray, 25030 Besançon Cedex, France.
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Ballenegger
Laboratoire de Physique, Ecole Normale Supérieure de Lyon, UMR CNRS 5672, 46 allée d'Italie, 69364 Lyon Cedex 07, France.
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Alastuey