Operator technique for calculating superconfiguration-averaged quantities of atoms in plasmas

An operator technique for performing superconfiguration averages is presented. This technique is applicable in the calculation of local thermodynamic equilibrium (LTE) spectral moments as well as average rates for the various atomic processes in non-LTE collisional radiative models. It is shown that for any moment or rate the configuration average polynomials, in the shell occupation numbers, can be regarded as derivative operators that average over superconfigurations when acting on their corresponding partition functions. The superconfiguration-averaged quantities are obtained as generalized partition functions for which a set of recursion formulas is presented allowing a short calculation path. Using this technique, analytic expressions for thermodynamical quantities, such as internal energy and specific heat, are obtained, taking into account orbital relaxation and first-order energies in the Boltzmann factors. This allows for the supertransition array code to yield accurate and consistent data for the equation of state used in hydrodynamic simulations, in addition to radiative properties.