Autoionization resonance

From the available evidence Stener and co-workers [53, 60] conclude that the chiral parameter is more sensitive to small asymmetries in the molecular potential than to continuum collapse effects at resonance. At present, such conclusions must be provisional as there is little direct evidence. There is also no evidence regarding likely behavior at autoionization resonances, and this too deserves attention. 

Fig. 22.7 Schematic diagram of forced autoionization. Above the ionization limit the autoionizing state A, converging to a higher limit, is manifested as an autoionization resonance. Below the limit, in zero field the interaction of the perturber P with the Rydberg series results in the perturbation of the Rydberg series. Applying an electric field E depresses the ionization limit below P, and it appears as a forced autoionization resonance.

Fig. 22.8 The two different excitation schemes A and B used to observe the Ba 5d7d perturber as a forced autoionization resonance. Path A leads to a q parameter near zero, while B leads to a large q parameter (from ref. 21).

We can compare the forced autoionization resonance to the predictions of zero field QDT. The observed width, 15.5 cm-1, and the width from QDT, 15.3 cm-1, are in excellent agreement. However, the energy positions are different by 5 cm-1. Exactly why is not clear, but it is certainly the case that the Stark induced continuum is not in all respects like a zero field continuum. For example, with both lasers polarized parallel to the field, so as to excite m = 0 final states, the forced autoionization resonance analogous to the one shown in Fig. 22.9 exhibits structure due to the long lived, blue shifted, Stark states.20,21... 

N. Moiseyev, P.R. Certain, F. Weinhold, Complex-coordinate studies of helium autoionizing resonances, Int. J. Quant. Chem. 14 (1978) 727. 

Figure 26 RPAE calculated results for the 3p nd autoionizing resonances in the 4s photoionization cross section of free Ca,, and Ca from Ca Cgo. The results were obtained within the A-potential model both at the frozen-cage approximation level, a A [20] and dynamical-cage approximation level,...

Ca C60, ofs A, are displayed in the lower panel of Figure 26. The dynamical screening effect is seen to increase very much quantitatively, although does not alter qualitatively, the photoionization probability of Ca at the autoionizing resonance energies compared to the predictions of the frozen-cage approximation. 

All the cross section variations discussed above are the result of direct ionization. If autoionization (Section 1.2) occurs, it can have a substantial effect on PE band intensities at photon energies close to an autoionizing resonance frequency. 

Such studies provide very conplete information on the photolonlzatlon process, e.g., the cross sections, the photoelectron asymnetry parameters, and elgenphases. Our approach does not involve the integration of coupled Integro-dlfferentlal equations and its extension to nonlinear trlatomlc molecules has almost been completed. With these electronic continuum orbitals, autoionizing resonances can also be studied. Such applications within the framework of the random-phase approximation (A7) are underway. 

Recently, Bekov, Letokhov, Matveev and Mishin ) reported the observation of an autoionization state in gadolinium with the relatively long lifetime of 5 x 10 - s. The autoionization spectrum they observed by three-step laser spectroscopy is shown in Fig. 15. For isolated atoms, the width of the autoionization resonance is determined by its lifetime, so the 0.07 cm l half-width yields the estimated 0.5 ns lifetime. 

The use of autoionizing Rydberg levels converging to excited states of the ion to determine ionization potentials has been discussed above. If autoionization resonances as narrow as those found in gadolinium exist in the actinides, it should be possible to determine the isotope shifts and hfs of such features. (isotope shifts for actinides range up to 0.4 cm l per mass unit and odd atomic number actinides exhibit hfs with total widths of 4 to 6 cm l and hfs component spacing of 0.2 cm l or more for some transitions). 

The dependence of the gadolinium photoion yield at the absorption of the autoionization resonance of 6133.5 A on the pulsed-energy density, E3, of the ionizing laser. Laser band width 0.03 cm 1 (5). 

Deviations from predicted rotational intensity distributions are very common in ZEKE spectra. This is due to random near coincidence between extremely numerous rapidly- and slowly-autoionizing resonances (Rydberg series converging to excited rovibronic states of the ion). Since the waiting time between excitation and pulsed field ionization is long, and the very weak DC and stray electric fields present during the ZEKE waiting period can induce weak interactions... 

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. 

Both electronic and vibrational shape resonances arise from a direct process and can be explained by a single potential (McKoy, et al., 1984). Shape resonances (single Vi(r) or Vj(R)) differ from autoionization resonances and predissociation (with the exception of predissociation by rotation), which involve two potentials or two states with different quantum numbers. 

Measured values of the asymmetry parameter, / , for autoionization resonances exhibit considerable variation with the frequency of the photoionizing... 

Approximate values of (3 for autoionization resonances have been predicted, using the method of transferred angular momentum, for H2 (Dill, 1972) and O2 (Parr, et al, 1998). 

If the rotational structure is resolved between the two 2n3/2 and 2n1/2 ionization thresholds, it is possible to assign definite ion-core rotational J+ values to each autoionized resonance, and the resonances are then described by Hund s case (e). Their wavefunctions are explicitly known as linear combinations of the case (a) wave functions, due to the mixing by the rotational operator (the j-uncoupling operator, see Section 8.7, Eqs. (8.7.9) - (8.7.14)). Consequently, the resonances no longer have a well-defined A-value [for example (AB+2n)d<5 1nj can be mixed with (AB+2n)d7r xEj)] and the value of A cannot be predicted without calculations. Such a study has been performed for HBr (Irrgang, et al., 1998). 

Methods involving ri -correlated trial functions have also been developed for three-electron bound systems (117). One of them, the superposition of correlated configuration method of Woznicki (118), has been recently combined with the complex rotation method and succesfully applied to He autoionizing resonances (22,119-121). 

The doubly-negative hydrogen ion is an extremely interesting and challenging system. Existence of a bound state for such a system was excluded twenty years ago by Beck and Nicolaides (144). However it could exist in a triply excited autoionizing resonance state. Recently Sommerfeld, Riss, Meyer, and... 

M.P. Anscombe, R. de Nalda, 1. Kucukkara, J.P. Marangos, Role of atomic coherence effects in four-wave mixing using autoionizing resonances, Phys. Rev. A 68 (2003) 043810. 

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