Fast approximation to supershell partition functions: Explicit forms of the coefficients

Abstract

In a previous work, we derived a formula for supershell partition functions, which are the cornerstone of the Super-Transition-Array approach to radiative-opacity calculations. The new expression takes the form of a functional of the distribution of energies within the supershell and allows for fast and accurate computations, truncating the number of terms in the expansion. The latter involves coefficients (denoted Γk) for which we obtained a recursion relation. In the present short paper, as a complement of the previous one, we give an explicit formula for the coefficients Γk. Another recursion relation is also provided, as well as an alternative expression involving Bell polynomials. The connections with cycle indexes of permutation groups and with elementary symmetric polynomials are outlined.