Resonance behavior of atomic and molecular photoionization amplitudes

Abstract

The behavior of the partial photoionization amplitudes with a given orbital angular momentum $l$ in the complex plane in resonances is studied. In the autoionization resonances the trajectory of the amplitude in the complex plane corresponds to a circle. With increasing photoelectron energy the amplitude moves about a circle in the counterclockwise direction. The new expressions for the partial amplitudes in the resonance are proposed which are similar to the Fano form but contain the ``partial'' profile parameters which are connected with the Fano parameter $q$ by a simple relation. In the giant dipole resonances the amplitudes in the complex plane also move about a circle in the counterclockwise direction provided the Coulomb phase is excluded from the amplitude. In the correlational resonances created by channel interactions with the giant dipole resonance the trajectories of the amplitudes acquire a loop about which the amplitudes move in the counterclockwise direction. Very similar behavior of partial photoionization amplitudes in the complex plane is demonstrated also for the dipole transitions from the $K$ shells of the ${\mathrm{N}}_{2}$ molecule in the ${\ensuremath{\sigma}}^{*}$ shape resonance.