Defect theory

When the chiral liquid crystal transforms from the unordered isotropic phase to the ordered helical phase, the liquid crystal molecules start to twist with respect to one another. The 

The surface elastic constant K2A is usually smaller than the bulk twist elastic constant K22- As an example, we assume K2A = O.5K22 [28]. The total elastic energy is plotted as a function of the 

As pointed out in the previous section, there are voids between the double-twist cylindas when they are packed in 3-D space. Liquid crystal must fill the void. Because of the boundary condition imposed by the cylinders, the hquid crystal director is not uniform in this space and forms a defect 

In the above equation, the second term is negative and tends to stabilize the blue phase. The other terms are positive and tend to destabilize the blue phase. Introducing q = q r and p = qoR, the above equation becomes 

The major cost of free energy is the elastic energy of the disclination, which tends to destabilize the blue phase. At a temperature slightly below the transition temperature to the isotropic phase, the free energy of the isotropic core is small and the liquid crystal in the disclination 

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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.

QUANTUM DEFECT THEORY OF THE DYNAMICS OF MOLECULAR RYDBERG STATES... 

A central feature of molecular quantum defect theory is the use of frame transformations. These provide an elegant way of treating the breakdown of the Bom-Oppenheimer approximation that occurs systematically once an electron is excited into a high Rydberg state. 

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... 

With regard to your second remark I would like to say this The calculations I showed for CaF and BaF Rydberg states are examples where the core field is a Coulomb field but where a very strong dipole field is superimposed. Here we have used the generalized version of quantum defect theory, which takes account of this modified long-range field. 

In Chapter 3 we considered briefly the photoexcitation of Rydberg atoms, paying particular attention to the continuity of cross sections at the ionization limit. In this chapter we consider optical excitation in more detail. While the general behavior is similar in H and the alkali atoms, there are striking differences in the optical absorption cross sections and in the radiative decay rates. These differences can be traced to the variation in the radial matrix elements produced by nonzero quantum defects. The radiative properties of H are well known, and the radiative properties of alkali atoms can be calculated using quantum defect theory. 

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).

In the first two chapters we have seen that the Na atom, for example, differs from the H atom because the valence electron orbits about a finite sized Na+ core, not the point charge of the proton. As a result of the finite size of the Na+ core the Rydberg electron can both penetrate and polarize it. The most obvious manifestation of these two phenomena occurs in the lowest states, which are substantially depressed in energy below the hydrogenic levels by core penetration. Core penetration is a short range phenomenon which is well described by quantum defect theory, as outlined in Chapter 2. 

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... 

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