Sum rules for the polarization correlations in photoionization and bremsstrahlung

The polarization correlations in doubly differential cross sections are investigated for photoionization and ordinary bremsstrahlung. These correlations describe the polarization transfer between incident light and ejected photoelectrons as well as between an incoming electron beam and bremsstrahlung light, respectively. They are characterized by a set of seven real parameters C_{i j}. We show that the squares of these parameters are connected by simple "sum rules." These sum rules can be applied for both one-electron systems and also for atoms, if the latter are described within the independent particle approximation. In particular, they are exact in their simplest form (i) for the photoionization of K -, L_{I ,I I}-, and M_{I ,I I}-atomic shells, as well as (ii) for bremsstrahlung in which the electron is scattered into s_{1 /2} or p_{1 /2} states, as in the tip (bremsstrahlung) region. Detailed calculations are performed to verify the derived identities and to discuss their possible applications for the analysis of modern photoionization and bremsstrahlung experiments. In particular, we argue that the sum rules may help to determine the entire set of (significant) polarization correlations in the case when not all C_{i j} are available for experimental observation.