Double photoionization .1. A new parametrization of the triple differential cross section from first principles

We have combined a laboratory frame independent particle approach with a body-fixed frame collective coordinates approach to derive new exact parametrizations of the triple differential cross section for double photoionization. The latter disentangle the kinematical from the dynamical effects to the largest possible extent. In addition, they provide an expansion of the so-called correlation factor with respect to the configurations of the electronic pair. The present approach is particularly suitable for the physical analysis of experimental data, as illustrated by the applications reported in the companion paper.