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 ${\Gamma }_k$) 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 ${\Gamma }_k$. 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.