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Multi-particle photoionization by a single photon

The shape amplitude representation for photo-fragmentation by a single photon, given in a recent publication (Walter et al 2003 Phys. Rev. Lett. 90 233001), is applied in detail to double ionization of helium and molecular hydrogen. In particular, in the case of molecular hydrogen the symmetries of the matrix element are examined in different coordinate systems, leading to a simplification of existing selection rules and allowing new ones to be derived. The implications of this representation for multi-differential cross sections and circular dichroism are given.