Asymptotically Optimal Class of Translation Factors

This letter reports a comparison between two common translation factors (CTF) which have been claimed to be asymptotically optimal, and thus well suited for the calculation of partial cross-sections, alignment parameters, etc. As a quality criterion for the comparison, we employ the Euclidean and partial norms of the couplings between the states included and those discarded in the molecular expansion. Our main conclusion is that one can define a class of asymptotically optimal CTFs, whose properties are indicated. The actual form used in a calculation may then be chosen according to the numerical techniques available.