On the impossibility to perform a complete valence-shell photoionization experiment with closed-shell atoms

A detailed investigation of the relation between five dynamical parameters (partial photoionization cross section sigma, angular asymmetry parameter b eta and three spin polarization parameters A, alpha, xi) and five correspon ding theoretical values (three dipole matrix elements and two phase shift d ifferences) describing photoionization from p(3/2), d(3/2) and d(5/2) subsh ells of rare-gas atoms reveals a systematic ambiguity preventing the extrac tion of a unique set of five theoretical values from the experimental data which constitute a 'complete experiment'. Xe(5p(3/2))(-1) photoionization s erves as an example to illustrate the problem using a numerical procedure a s well as a mathematical analysis. A new equation is presented which connec ts four dynamical parameters. From these facts it follows that a complete e xperiment on closed-shell atoms with the extraction of five theoretical val ues is, in principle, impossible, if the photoelectron properties are measu red exclusively.