Multichannel theory

First let us introduce the T operator. In the multichannel theory we have the two possibilities ... 

Bricogne, G. (1988) A Bayesian statistical theory ofthe phase problem. I. A multichannel maximum-entropy formalism for constructing generalized joint probability distributions of structure factors, Acta Cryst., A44, 517-545. 

A YI can be designed to have more than two channels. As the two-channel YI sensor is a special case of the more general /V-channel or multichannel YI, the theory of the YI is treated for the general /V-channel YI. As shown in this section, in the multichannel YI all pairs of parallel output channels act as a two-channel YI, each with a unique distance between its two arms. In Fig. 10.5 the layout of the 4-channel YI sensor described in this chapter is shown. 

Theory An Autoanalyzer serves as the most versatile and important instrument in a well-equipped clinical laboratory that caters for the rapid screening of serum levels for upto forty (40) important chemical substances in the field of diagnostic medicine. These autoanalyzers may be either Single Channel i.e., performing only one determination on each sample or Multichannel i.e., carrying out several different determinations on each sample. 

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... 

To arrive at a more unique way of characterizing autoionizing states in the absence of information about the continuum phase we can recast the QDT equations into an R matrix form which is at the same time similar to the original development of QDT from multichannel scattering theory.2 The relation between the different forms of scattering matrix is discussed by Mott and Massey,11 Seaton,2 and Fano and Rau.12... 

The two-particle Boltzmann collision term if and the three-particle contribution for k = 0 were considered in Section II. It was possible to express those collision integrals in terms of the two- and three-particle scattering matrices. It is also possible to introduce the T matrix in if for the channels k = 1, 2,3, that is, in those cases where three are asymptotically bound states. Here we use the multichannel scattering theory, as outlined in Refs. 9 and 26. 

All the work just mentioned is rather empirical and there is no general theory of chemical reactions under plasma conditions. The reason for this is, quite obviously, that the ordinary theoretical tools of the chemist, — chemical thermodynamics and Arrhenius-type kinetics - are only applicable to systems near thermodynamic and thermal equilibrium respectively. However, the plasma is far away from thermodynamic equilibrium, and the energy distribution is quite different from the Boltzmann distribution. As a consequence, the chemical reactions can be theoretically considered only as a multichannel transport process between various energy levels of educts and products with a nonequilibrium population20,21. Such a treatment is extremely complicated and - because of the lack of data on the rate constants of elementary processes — is only very rarely feasible at all. Recent calculations of discharge parameters of molecular gas lasers may be recalled as an illustration of the theoretical and the experimental labor required in such a treatment22,23. ... 

E. Brandas, M. Rittby, N. Elander, Multichannel Complex Scaled Titchmarsh Weyl Theory a Model for Diatomic Fragmentation, Lect. Notes Phys. 325 (1989) 345. 

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. 

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