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 σ, angular asymmetry parameter β and three spin polarization parameters A ,α,ξ) 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.