Formation of composites in equilibrium plasmas

A generalized, multielectron version of the Planck-Larkin convergent hydrogenic partition function is presented. It is shown that compensation between bound and scattering states leads naturally to convergent expressions for multielectron bound-state partition functions. The nature of the compensation is studied by comparing a high-temperature expansion of the bound-state sum with a perturbation expansion in the coupling parameter $\beta e^2$ of the complete trace. The analytic form of high-order quantum perturbation terms is determined from a parametrized pseudopotential method. Rigorous evaluation of low-order quantum perturbation expressions is used to determine parameter values.