Autoionization obtain

The Bell equation gives the correct behavior for the ionization cross section at both high- and low-impact energies. In cases where autoionization is important it is not always possible to reproduce the cross section from the single equation above, but if it is used in two separate fits, one from the ionization threshold to the autoionization threshold, and the second above the autoionization threshold, a good fit to the cross section may be obtained over the entire range. 

In this paper we examined quantum aspects of special classical configurations of two-electron atoms. In the doubly excited regime, we found quantum states of helium that are localized along ID periodic orbits of the classical system. A comparison of the decay rates of such states obtained in one, two and three dimensional ab initio calculations allows us to conclude that the dimension of the accessible configuration space does matter for the quantitative description of the autoionization process of doubly excited Rydberg states of helium. Whilst ID models can lead to dramatically false predictions for the decay rates, the planar model allows for a quantitatively reliable reproduction of the exact life times. 

As mentioned in Section II.A, the Pgl process is ideal for the application of the optical model. This is clear in the classical and semiclassical Pgl theory,24,25 for which opacity and cross-section formulas are completely equivalent to those given earlier in this chapter. The quantal optical model is also rigorously related to the elastic component of the quantal Pgl theory. Miller49 has shown that T(r), identified in Pgl as the autoionization width of the excited electronic state, may be accurately obtained by a standard Born-Oppenheimer electronic structure calculation as... 

The second form of ionization is similar to autoionization.31 In a nonhydrogenic atom is not a good quantum number and bound states of high nt are coupled to Stark continua of low n j. This form of ionization applies to those states other than the reddest Stark states. The extreme red Stark states have nx = 0 and ionize, as do the red H states, at the classical ionization limit given by Eq. (6.35), modified by Eq. (6.37) for m 0 states. This point has been demonstrated explicitly by Littman et al,32 who measured the time resolved ionization of Na m = 2 states subsequent to pulsed laser excitation. Their measured rates are in good agreement with the rates obtained by extrapolation of the rates of Bailey et al.20 shown in Fig. 6.8. 

Ba Rydberg energy levels (—) and continua (///) obtained by adding the second valence electron to these Ba+ levels. The horizontal arrows show the possible interactions between channels associated with different ion levels. Interactions with other bound states lead to series perturbations while interactions with continua lead to autoionization. 

A 6pn( state with an autoionization rate T is broadened, and its spectral density is described by a Lorentzian of width T centered at its energy Wq. A reasonable first approximation to the wavefunction is obtained by multiplying the zero order wavefunction of Eq. (19.6a) by the square root of a Lorentzian of width T ... 

We have thus far considered the probability of superelastic scattering on a single orbit. To obtain the scattering rate, or autoionization rate, we simply multiply this probability by the orbital frequency, 1/n3.4 Once again we find that T oc 1/n3 and that T decreases with increasing Z. The scattering description we have just given is a two channel description. This picture, when many channels are present, forms the basis of multichannel quantum defect theory.5... 

In Fig. 19.11 we show the time of flight spectra, obtained with 0 = 0, for electrons from a 6p3/2 ns1/2 state lying above the 6p1/2 ionization limit.25 With a 10 cm flight path for the electrons, the electrons ejected in autoionization to the Ba+ 6s 1/2 and 5dj states are barely resolved, while with the higher resolution afforded by a 45 cm flight path the electrons from autoionization to the 6s1/2 and 5dj states are well resolved, showing little autoionization to the Ba+ 5d5/2 state. To... 

An alternative to uniform complex scaling (used in the studies mentioned so far) is exterior complex scaling [45,46], where the scaling of the coordinates starts at some finite distance from the origin. This approach has been used extensively on electron scattering problems in the absence of resonances, for example, in Refs. [47-50], for a review see Ref. [51], as well as to obtain resonance parameters in connection with electronic autoionization [52,53]. 

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,...

It has, for example, been suggested that the threshold for formation of (C3H7)+ from propane represents ion-pair formation [172], Ion-pair contributions to ionization efficiency curves are eliminated in PIPECO. Autoionization may also provide alternative pathways to fragment ions however, these are difficult to identify and have not been widely discussed. All that is necessary to obtain a false critical energy for the second step in... 

Studies of electron-impact ionization of molecular nitrogen and oxygen near threshold [141, 142] have demonstrated that a Franck-Condon distribution of vibrational levels is not obtained because many ions are formed indirectly, via autoionizing states. The importance of autoionization can be seen in the case of where the Franck-Condon factors for transitions... 

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