Shape resonances photoionization

A possible role for shape resonances has been postulated in a number of the photoionization studies mentioned above [52, 53, 57, 60], although it has to be noted that except for camphor [57], the evidence for the existence of the shape resonance is not definitive. (It also then remains an open question how any such resonances, inferred from fixed geometry calculations, would manifest themselves in practice in large, and sometimes floppy, molecules, such as these chiral species.)... 

Photoionization of neutral atoms and molecules and electron-ion collisions, for example, are rich in infinite Rydberg series of Feshbach resonances. On the other hand, only a finite number of Feshbach (and possibly shape) resonances occur in electron-neutral collisions and photodetachment of an electron attached to a neutral species, with an exception of the following cases. 

In closing this section, we note that although the Koopmans picture is a simplification of the ionization dynamics, it provides a very useful zeroth order picture from which to consider the TRPES results. Any potential failure of this independent electron picture can always be experimentally tested directly through variation of the photoionization laser frequency resonance structures should lead to variations in the form of the spectra with electron kinetic energy, although the effect of resonances is more likely to be prominent in PAD measurements, and indeed an observation of a shape resonance in p-difluorobenzene has been reported [153, 154]. 

To insure the accuracy of a calculation using these singlecenter expansions, the convergence of the photoionization cross section with respect to each of these parameters must be checked. The rate of convergence of a calculation will depend on the nature of the system being studied. One useful empirical result which has been observed is that the peak position in the photoionization cross section due to a shape resonance in the a continuum approaches Its asymptotic value as This relationship has been verified for shape reso-... 

In sunutary, we have used prototype studies on N2 to convey the progress made in the study of shape resonances in molecular fields, particularly in molecular photoionization. This Included the identification of shape resonant features in photoionization spectra of molecules and the accrual of substantial physical insight into their properties, many of which are peculiar to molecular fields. 

Another recent advance in electron-molecule resonances is their role in molecular autoionization and photoionization. Here they show up as an exit-channel effect. The increasing availability of synchrotron sources and the proliferation of high-resolution laser spectroscopic techniques are leading to expanded interest in these processes because of the necessity to interpret the resonance features for a greater variety of molecules of chemical interest. Electron-molecule shape resonances are also responsible for structure in inner-shell electron energy-loss spectra in the region around the core ionization threshold acting as a final-state interaction, the same resonances... 

Shape resonances appear as broad maxima in the photoionization cross sections. Their width varies from about 4 eV (for O2) to 20 eV (for N2), but a shape resonance is often hidden beneath multiple, much narrower, and more intense autoionization resonances. 

An important characteristic of shape resonances is that they cause non-Franck-Condon effects in vibrationally resolved photoionization spectra. These effects are a consequence of the strong R-variation of the transition moment caused by the R-dependence of the form of the continuum molecular orbital. 

SHAPE RESONANCES IN THE PHOTOIONIZATION SPECTRA OF FREE AND CHEMISORBED MOLECULES... 

Fig. 6.20 Ionization width vs electric field for the Na (20,19,0,0) level near its crossing with the (21,17,3,0) level from experiment (data points) and from WKB-quantum defect theory (solid line). The levels are specified as (n./q.ni.M) Because the lineshapes are quite asymmetric (except for very narrow lines), the width in this figure is taken to be the FWHM of the dominant feature corresponding to the (20,19,0,0) level in the photoionization cross section. For the narrowest line, experimental widths are limited by the 0.7 GHz laser linewidth. Error limits are asymmetric because of the peculiar fine shapes and because of uncertainties due to the overlapping m = 1 resonance (from ref. 37).

The total width, T, is the sum of partial widths, which can be calculated but not observed separately. Only the total width can be observed experimentally. This width does not depend on whether the line is observed in an absorption, photoionization, photodissociation, or emission spectrum because the width (or the lifetime) is characteristic of a given state (or resonance). In contrast, the peak profile can have different line shapes in different channels the line profile, q, is dependent on the excitation and decay mode (see Sections 7.9 and 8.9). For predissociation into H+CT, the transition moment from the X1E+ state to the 3n (or 3E+) predissociating state is zero, consequently q = oo and the lineshape is Lorentzian. In contrast, the ratio of the two transition moments for transitions to the XE+ continuum of the X2n state and to the (A2E+)1E+ Rydberg states leads to q 0 for the autoionized peaks (see Fig. 8.26) (Lefebvre-Brion and... 

---