Is the Wannier threshold law for angular distribution in double photoionization of atoms true at practically attainable energies of ejected electrons?

We calculated ab initio the three-fold differential cross section of a double single-photon Helium photoionization at equal energy sharing, and obtained from one the Gaussian width parameter, describing the angular interelectron correlations, for the total electrons energies range E from 0.1 eV to 100 eV. The results are in excellent agreement with experimental data but indicate that the Wannier threshold law for angular distribition is not correct at energies attainable in modern experiments. It is shown that the Gaussian width parameter dependence on energy is much better described by the modified threshold law, obtained by Kazansky and Ostrovsky [J. Phys. B 26, 2231 (1993)]. Also, we explored the Gaussian width parameter for a double photoionization of the targets with the strongly asymmetrical initial state configuration: the atomic Hydrogen negative ion and the Helium in the 2s1S and 3s1S excited states. We found that the Gaussian width parameter dependence on the total ejected electrons energy for this targets has a maximum at low energies. We show also that the correlation parameter dependence on the interelectron angle for these targets is essentially non-Gaussian and has a number of peaks equal to a number of initial state radial nodes, that reveals the new abilities for the qualitative analysis of electron structure.