Resonance structure of the photoelectron $\beta_{nl}$ parameter versus autoionizing resonance minima in partial $\sigma_{nl\pm 1}$ cross sections: A model of ``complete'' experiments with \textit{fewer} measurements

The relationship between the structure of the autoionizing resonance minima in partial photoionization cross sections $\sigma_{nl \pm 1}$ and the resonance profile of the dipole photoelectron angular distribution parameter $\beta_{nl}$ in the vicinity of the resonance is established. From this, the information can be extracted (from known $\beta_{nl}$ alone) on the energy positions and ordering of autoionizing resonance minima in $\sigma_{l\pm1}$, the energies at which $\sigma_{l+1}$ and $\sigma_{l-1}$ are equal, signs and magnitudes of relative phase shifts of the photoionization amplitudes $D_{l\pm1}$ through the autoionizing resonance energy region, and the magnitudes of $D_ {l\pm1}$ at extreme points in $\beta_{nl}$; no tedious experimentation with electron spin polarization or light polarization is required. The established relationship expands our previously developed, so to speak ``point'' model of ``complete'' photoionization experiments with \textit{fewer} measurements [V.K. Dolmatov and S.T. Manson, PRA \textbf{58}, R2635 (1998)] onto a broader energy region [V.K. Dolmatov, E. Guler, S.T. Manson, PRA (submitted)].