Non-crossing approximation

FWHM full width at half maximum NCA non-crossing approximation... 

Both the Anderson and the Kondo (or Coqblin-Schrieffer) model have been solved exactly for thermodynamic properties such as the 4f-electron valence, specific heat, static magnetic and charge susceptibilities, and the magnetization as a function of temperature and magnetic field B by means of the Bethe ansatz (see Schlottmann 1989, and references therein). This method also allows one to calculate the zero-temperature resistivity as a function of B. Non-equilibrium properties, such as the finite temperature resistivity, thermopower, heat conductivity or dynamic susceptibility, could be calculated in a self-consistent approximation (the non-crossing approximation), which works well and is based on an /N expansion where N is the degeneracy of the 4f level. 

With respect to one of these precursors, the term, tropoelastin, has been used as a designation for a non-cross linked elastin precursor of approximately 70,000 daltons (1). Since it is currently the best characterized of the non-crosslinked elastins and is used extensively by those familiar with elastin, this term will be retained. Elastin will be used to designate the protein in its crosslinked form. This term, however, is at best operational, since elastin is only isolated from tissues or cell culture by procedures that would be offensive to most protein chemists. As a component of extracellular matrices, elastin is extremely insoluble and in close association with many other extracellular components (2). In order to remove these components, harsh treatments such as autoclaving, extraction with alkali or... 

The exact form in which non-crosslinked elastin is secreted from smooth muscle cells is yet to be clearly defined. Foster et al. (36) have suggested that a non-cross linked elastin (pro-elastin) is secreted from smooth muscle cells in a form that is approximately 120,000 to 140,000 daltons. They have suggested that proelastin is cleaved to smaller molecular weight forms of non-crosslinked elastin. It should be noted, however, that this view is not entirely supported by data from other laboratories. There are two reports on the use of isolated mRNA from chick aorta suggesting only a 70,000 dalton non-cross linked elastin is the major product of translation (37,38). There is also a recent report suggesting that aortic mRMA translates a 200,000 dalton putative elastin product (39). We have recently isolated a non-crosslinked elastin from the aortas of copper deficient chicks that appears to be 100,000 daltons (27). Its amino acid composition is similar to that for tropoelastin (Table III). A major problem in resolving these points is that the trypsin-like proteinase associated with elastin is not easily denatured or separated from the non-crosslinked forms of elastin. The proteinase is also not readily inhibited by commonly used inhibitors for trypsin-like proteinases (26). 

During the computation, a number of non-cross-linked conformations were chosen at random, and the dimensions were evaluated approximately, using (65). 

Looking more carefully on the von Neumann-Wigner and the J-T theorems we can see significant differences Whereas the first one is connected with the dissociation processes in molecules and the question of crossing or non-crossing potential curves, the second one concerns the rigid molecules and the question of their equilibrium nuclear positions. The J-T effect was formulated prematurely without the exact knowledge what forms the molecular structure and what the break down of B-O approximation really means. Two important factors were never incorporated in the J-T effect the Frdhlich transformation and the centre-of-mass problem. These two factors are so profound that the J-T effect will never be satisfactorily explained without them. 

Apparent exceptions to the non-crossing rule usually result from the use of too approximate wave functipns. In other cases they may be due to the breakdown of the Bom-Oppenheimer approximation (which allows the electronic energy to be treated separately from vibrational and rotational eneigy). The situation is more complex for polyatomic molecules, but the rule is generally applicable although exceptions are known. 

Here the transition state is approximated by the lowest crossing pomt on the seam intersecting the diabatic (non-interacting) potential energy surfaces of the reactant and product. The method was originally developed... 

Equations (169) and (171), together with Eqs. (170), fomi the basic equations that enable the calculation of the non-adiabatic coupling matrix. As is noticed, this set of equations creates a hierarchy of approximations starting with the assumption that the cross-products on the right-hand side of Eq. (171) have small values because at any point in configuration space at least one of the multipliers in the product is small [115]. 

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