Recoil frame photoelectron angular distributions for valence photoionization of CF$_4$

Results of recent momentum imaging experiments on photoionization of CF$_4$ have shown that upon valence ionization producing several states the CF$_4^+$ cation dissociates to produce CF$_3^+$ + F, thereby allowing the measurement of the photoelectron angular distribution relative to the axis of recoil. For ionization from the 4t$_2$ orbital, the experiment shows a dramatic reversal in the angular distribution of the photoejected electron over a narrow range energies of less than 2 eV. We present the results of photoionization calculations using both the complex Kohn variational and Schwinger variational methods that reveal two overlapping shape resonances of a$_1$ and t$_2$ symmetry whose interference is responsible for this behavior and which require coupling between the ionization channels producing the degenerate components of the A$^2$T$_2$ state of the CF$_4^+$ ion. It is shown that ionization from the 3t$_2$ orbital shows similar resonances but not the dramatic changes in angular dependence with photon energy. Comparison of theory and experiment is also presented for ionization from the 1t$_1$ and 1e orbitals.