Discussion
The amplitude of the continuum wave function is clearly seen rising to a maximum in the vicinity of the nuclei at the shape resonant energy (~16 eV). The resonance is quite broad and the amplitude changes smoothly throughout this range, except for the "kick" seen at the central resonance energy (caused by resonant coupling with another nearby continuum channel).
The resonantly enhanced amplitude around the molecular interior provides greater overlap with the initial bound electron wave function in this region, and so an increased transition probability can be anticipated. This resonant peak can be seen here in the calculated 2σg+ → kσu+ partial channel cross-section (red curve). It can also be seen that the asymptotic phase, μa, varies very rapidly at the resonance and this can be expected to influence the photoelectron angular distribution at this point.
The contour plot shows the continuum wave function contracting inwards as the energy increases (decreasing de Broglie wavelength) and the angular nodes produce a pattern that closely resembles a drawing of an atomic f orbital, aligned along the internuclear axis. This f-wave angular momentum character of the resonant eigenchannel is a significant indicator, since the shape resonance is caused by trapping behind a l=3 centrifugal barrier in the electron-ion potential. The alternative p-wave-like continuum function does not possess a centrifugal barrier due to lower electron angular momentum, and so does not display a shape resonance.
The Animation
This animation shows the shape resonant σu+ symmetry photoelectron (continuum) function in the photoionization of N2, calculated using the CMS-Xα method, and its variation as the electron kinetic energy passes through the resonance (~16 eV).
The principal feature is a surface representing the real value of the function across the XZ plane that includes the two nitrogen nuclei, and its projection onto the top and bottom planes of the box, forming an alternative contour plot of the function. The positions of the nuclei along the Z axis are marked in blue, but on the lower plane only. Alongside is a little bar that show the rate of change in asymptotic phase of this continuum function.
