High-resolution photoabsorption measurement and multichannel quantum-defect-theory analysis of the 2${\mathit{p}}^5$3s${(}^1$${\mathit{P}}_1$) ns,nd autoionizing series of sodium

We measured the photoabsorption spectrum of sodium in the 2p subshell excitation region using synchrotron radiation and a 3-m spectrograph at a resolution of ±0.008 Å. In spite of the large number of overlapping structure due to the four ionization limits 2${\mathit{p}}^5$3s${(}^3$ ${\mathit{P}}_{210}$ and ${}_{}{}^1{}_{}{}^{}$ ${\mathit{P}}_1$), well separated autoionizing Rydberg series are detected converging to the 2${\mathit{p}}^5$3s${(}^1$ ${\mathit{P}}_1$) threshold. A three-channel quantum-defect-theory analysis is performed for the 2${\mathit{p}}^5$3s${(}^1$ ${\mathit{P}}_1$)ns and 2${\mathit{p}}^5$3s${(}^1$ ${\mathit{P}}_1$)nd autoionizing resonances. A simple n-channel multichannel quantum-defect-theory formula in terms of cofactors is presented for the calculation of the photoionization cross section for one open and (n-1) bound channels.