Nondegenerate mixing

Orbital mixing. Simple spherical orbitals are shown to illustrate the concept. A. The first-order, degenerate mixing. B. The second-order, nondegenerate mixing. 

Figure 4.2 Detection by nondegenerate superposed absorber states, (a) Scheme of levels relevant to the mixing (by field of the states 1) and 2) and their photoionization by the LO (frequency v)and two mode SL (frequencies and ) fields, (b) Geometry of illumination and current directionality. As in Figure 4.1, the dark rim is a potential barrier dividing the sample into two separate regions.

A- and C-terms require that either or both the ground and excited states must be degenerate. A B-term signal can occur when both states are nondegenerate, but there is an additional nondegenerate state (TV) that can mix with either due to the applied magnetic field. Figure 1.8a illustrates the effect of TV on the excited state (Te). 

One doesn t need a real degeneracy to benefit from this effect. Consider a nondegenerate two-level system, 84, with the two levels of different symmetry (here labeled A, B) in one geometry. If a vibration lowers the symmetry so that these two levels transform as the same irreducible representation, call it C, then they will interact, mix, and repel each other. For two electrons, the system will be stabilized. The technical name of this effect is a second order Jahn-Teller deformation.67... 

The effect of suUur participation on the orbital g -shifts in the EPR spectra, illustrated in Pig. 20, accounts for the qualitatively different spectra observed for tyrosyl phenoxyl and Tyr-Cys phenoxyl radicals (Gerfen et al., 1996). The rhombicity of the simple tyrosyl radical EPR spectrum is a consequence of the splitting between gx and gy principal g -values. These g -shifts deviate from the free electron g--value ge = 2.00023) as a result of orbital angular momentum contributions. While a nondegenerate electronic state (such as the A" ground state for ere) contains no hrst-order unquenched orbital momentum, second-order spin-orbit mixing between close-lying a and a" functions results... 

Passive processes that are of spectroscopic interest of course require material resonances. For example, nondegenerate four-wave mixing pro-... 

At second order in optical fields (x = 2), only nonquadrature passive processes, harmonic generation and parametric three-wave mixing, are possible. In fully nondegenerate second order processes, three frequency components of the field at [Pg.71]

In the above case of a nondegenerate exciton band the dispersion for polaritons, resulting from mixing of photon states j = 1 with exciton states, is given by the first of equations (4.33), where we put f2(k) = = E(k)/h, = fuxi. Solving this equation with respect to 2(k), we obtain38... 

The mixing coefficient, a, is given by nondegenerate perturbation theory as... 

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