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 beta and three spin polarization parameters A, alpha, xi) and five corresponding theoretical values (three dipole matrix elements and two phase shift differences) describing photoionization from p(3/2), d(3/2) and d(5/2) subshells of rare-gas atoms reveals a systematic ambiguity preventing the extraction of a unique set of five theoretical values from the experimental data which constitute a 'complete experiment'. Xe(5p(3/2))(-1) photoionization serves as an example to illustrate the problem using a numerical procedure as well as a mathematical analysis. A new equation is presented which connects four dynamical parameters. From these facts it follows that a complete experiment on closed-shell atoms with the extraction of five theoretical values is, in principle, impossible, if the photoelectron properties are measured exclusively.