Degenerate spin system

For the case of an undistorted octahedral field, as in MgO and CaO, the spin-orbit interaction produces a threefold degenerate ground state that behaves as an S= 1 spin system in a magnetic field with + (2.0023) for a... 

In this article we consider problems concerning the interpretation of unsaturated, steady-state NMR spectra of spin systems which are in a state of dynamic equilibrium. Spin exchange processes may occur with frequencies between a few sec-1 and several thousand sec-1 and thus modify the spectral lineshapes. In this case we use the terms dynamic NMR and dynamic spectra. The analysis of dynamic NMR lineshapes constitutes an important, and often unique, source of information about intra- and inter-molecular reaction rates. This is especially true for degenerate reactions where the products are chemically identical with the substrates. For this and similar reasons, dynamic NMR analysis has attracted considerable attention for about twenty years. 

Next we deal with the nature of the correction Awc. The resonance signals in a spectrum may be composed of overlapping, closely spaced components. Usually this is caused by either weak spin-spin couplings (we consider here only those which are included explicitly in the assumed model of an exchanging spin system) or by almost degenerate transitions in the spin multiplets. (81) Such effects should be compensated for by the correction Awc which can be determined from measurement of an apparent line-width, wa, in a theoretical spectrum calculated for a reasonably assumed value of the natural line-width, wtheor The correction (wa — wtheor) is virtually independent of the value... 

The H- ll9Sn HDMR experiments may often be applied to the analysis of type A X spin systems with degenerate transitions and only two groups of magnetically equivalent nuclei. For example, the energy level diagram for an A3X system is shown in Fig. 3. 

Kramers theorem requires that all half-integer spin systems be at least doubly degenerate in the absence of a magnetic held. Next, note that the splitting of these levels by a magnetic held depends on its orientation relative to the axes of the ZFS tensor of the metal ion. The VTVH MCD saturation magnetization curve behavior reflects the difference in the population of these levels and their spin expectation values in a specific molecular direchon. This direction must be perpendicular to the polarizations of the transition (Mih where i / j are the two perpendicular polarizations... 

Replication degenerates to a random production of sequences in the limit q- j and corresponds to the limit r->oo, the case of maximum disorder. Direct and complementary replication (see also part C) are the analogs of ferro- and antiferromagnetic cases of the spin system. In the range q < 1 we have K<0, which corresponds to the condition pj<0 for ferromagnetic interaction. For complementary or plus-minus replication, we have... 

Ising model this case corresponds to the limit Jx O, where the two-dimensional Ising lattice degenerates to the one-dimensional spin system. We are dealing with a degenerate phase transition ... 

The OOA was not designed for and does not apply to temperature dependencies of any kind in JT crystals. In particular, one cannot expect a reasonable estimate of the temperature of phase transitions in crystal lattice (structural), electron orbital, and/or spin system. This follows from the partitioning procedure that includes averaging over vibrational degrees of freedom. One can see the same reason from another perspective. The pseudo spin of a JT site, as the basic concept used in the OOA, operates in the basis of degenerate ground state wave functions. Excited vibronic states are beyond the pseudo spin setup. Therefore, in the OOA, by its very definition, temperature population of excited states does not make sense. 

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