Exchange interaction critical value

Exchange interaction,, in cV, for the transition metals, determined from experimental optical spectra (Moore, 1949, 1952), as indicated in the text. Also listed is the critical value of l/ = WJ5, above which the uniform-density-of-states model predicts ferromagnetism H /5 was obtained from the Solid State Table. 

There are two situations when / vanishes, and when intersystem crossing is thus most efficient. First, for r larger than a certain value, not more than a few molecular diameters, S) and [Tq) become degenerate. This condition holds for most of a diffusive excursion unless diffusion is restricted (as would be the case, e.g. in a micelle), so processes of t)q5e S) <-> Tq) provide the most efficient, and most common, pathway of intersystem crossing of radical pairs. Second, at some critical distance there exists a level crossing between S) and either T i) or, in the rare case of a positive exchange interaction, T+i). Because intersystem crossing is... 

This could be related to the exchange interaction J (Binder 1985, Kaneyoshi 1991a,b, Mills 1970). Binder and Landau (1984, 1985) pointed out that for JJJ, above some critical value, say 1.5, not only the surface Tq, but also surface critical exponents should vary with the JJJ > ratio. For JJJ], > 1, jS decreases, while for /jA/b < 1> the critical exponent is the same as for the Ising surface behavior (the critical exponent j8=0.78). The deviation of P from that of other surfaces like Ni and EuS is therefore the reflection of the strong coupling in the surface of lanthanide metals. However, it is predicted (Binder and Landau 1984, 1985) that the P of any extraordinary surface, where Js >Jsc. (the critical value for the surface J) and 7c(surface) > 7c(bulk), should be smaller than that of the 2-dimensional case, i.e. j8 = 0.125. The cause of this disagreement with experiment is unclear. 

Hereby 4o is the superconducting order parameter at T = 0 in the absence of any impurities. Furthermore an isotropic exchange interaction has been assumed. The dependence of Tc as function of n or a is shown in fig. 17.13. acrit denotes the critical value of the pair-breaking parameter a beyond which superconductivity can no longer exist. It is a it = i The functional dependence of (nO is described by... 

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