Multichannel quantum defect

D. Gauyacq I have a short comment on Prof. Schlag s remark on the multichannel quantum defect theory (MQDT) approach to ZEKE spectra The first ZEKE spectrum of NO was actually interpreted by using MQDT as early as 1987 [1]. In this work, a full calculation of the ZEKE peak intensities is carried out by the MQDT approach, which... 

Figure 11. Multichannel quantum defect theory simulations of the photoionization cross section of Ar versus excitation wavenumber, in the presence of a DC field of magnitude (a) 0.001 V/cm, (b) 0.1 V/cm, (c) 0.2 V/cm, (d) 0.3 V/cm and (e) 2.0 V/cm.

Figure 12. Multichannel quantum defect theory simulations of the photoionization cross section of N2, field = 0.3 V/cm (a) near n - 70 and (b) near n = 80, including N = 0, 2, Mj = I channels only, with excitation from J = 2, Mj = 1.

W. H. Miller I believe that the reason the multichannel quantum defect theory (MCQDT) works well is that it assumes the ordinary Bom-Oppenheimer approximation (i.e., that the electron follows the molecular vibrational and rotational motion adiabatically) in the region close to the molecule, but not so in the region far from the molecule (where the electron moves more slowly than molecular vibration and rotation). The frame transformation provides the transition between... 

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... 

Separation of the effects due to the long-range and short-range interactions greatly advances the understanding of the dynamics prevailing in continuum processes. Particularly useful general theoretical frameworks to this effect have been the R-matrix theory [44, 70] and the multichannel quantum defect theory (MQDT) [71, 72], They have been applied successfully to a wide variety of atomic and molecular systems, and the relevant material is too rich to be covered in this article. 

Multichannel quantum defect theory adapted to treat competing photoionization and photodissociation in NO Survey of NO photolysis... 

Recent work (66) using variable-wavelength photoelectron measurements and a multichannel quantum defect analysis of the principal autolonlzlng Rydberg series has sorted out this puzzle, with the result that the shape resonance was established to be approximately where expected, but was not at all clearly Identifiable without the extensive analysis used In this case. 

An alternative method to obtain the nonadiabatic wavefunctions [Eq. (4.1.1)], the coupled equation approach, will be discussed in Section 4.4.3. It has been used for an excited 1E+ state of H2 and the error is now smaller than 1 cm-1 for the lowest vibrational levels (Yu and Dressier, 1994). Multichannel Quantum Defect Theory (MQDT), discussed in Chapter 8, has also been used with success for the same problem by Ross and Jungen (1994). Finally, a variational numerical approach (Wolniewicz, 1996), gives very good results for H2. 

Vibrational autoionization corresponds to an exchange between the kinetic energy of the ejected electron and the vibrational energy of the core ion. This process occurs because the potential curves of the ion and Rydberg states are slightly different. Eq. (8.6.7) can be derived from a more sophisticated model using multichannel quantum defect theory (Raoult and Jungen, 1981). 

When a mechanism for each of the relevant decay channels is assumed and a set of specific interaction matrix elements is calculated by ab initio or semi-empirical methods, multichannel quantum defect theory (MQDT) (see Section 8.9) provides a basis for a unified and global treatment of the competing nonradiative decay processes and how these competing processes are sampled by specific experiments. Giusti-Suzor and Jungen (1984) were the first to apply MQDT to... 

G. Alber, P. Zoller, Structure of autoionizing Rydberg series in strong laser fields A multichannel-quantum-defect-theory approach, Phys. Rev. A 29 (1984) 2290. 

Mies, F.H., A multichannel quantum defect analysis of diatomic predissociation and inelastic atomic scattering, J. Chem. Phys., 80, 2514,1984. 

---