Many-body and model-potential calculations of low-energy photoionization parameters for Fr

The photoionization cross section $\sigma$, spin-polarization parameters $P$ and $Q$, and the angular-distribution asymmetry parameter $\beta$ are calculated for the $7s$ state of francium for photon energies below 10 eV. Two distinct calculations are presented, one based on many-body perturbation theory and another based on the model potential method. Although predictions of the two calculations are similar, the detailed energy dependence of the photoionization parameters from the two calculations differ. From the theoretical p-wave phase shifts, we infer quantum defects for $p_{1/2}$ and $p_{3/2}$ Rydberg series, permitting us to calculate positions of experimentally unknown $p$ states in francium.