Interaction spin-lattice

Now the expectation (mean) value of any physical observable (A(t)) = Yv Ap(t) can be calculated using Eq. (22) for the auto-correlation case (/ = /). For instance, A can be one of the relaxation observables for a spin system. Thus, the relaxation rate can be written as a linear combination of irreducible spectral densities and the coefficients of expansion are obtained by evaluating the double commutators for a specific spin-lattice interaction X in the auto-correlation case. In working out Gm x) [e.g., Eq. (21)], one can use successive transformations from the PAS to the (X, Y, Z) frame, and the closure property of the rotation group to rewrite D2mG(Qp ) so as to include the effects of local segmental, molecular, and/or collective motions for molecules in LC. The calculated irreducible spectral densities contain, therefore, all the frequency and orientational information pertaining to the studied molecular system. 

The crystal field interacts directly only with the orbital motion of the unpaired electrons and it has an effect on the electronic spins only through the spin orbit coupling. The strongest spin-lattice interaction will therefore occur for ions with ground states having an appreciable orbital character. 

Analysis of Spectra. An understanding of the mechanism of polymer degradation must involve identification of the radical intermediates. However, anisotropy due to spin lattice interactions in the solid state invariably results in broad, poorly resolved ESR spectra and together with the low concentration of radicals which is usually present, can result in major problems with analysis. We have developed two approaches to this problem 1) increasing resolution and 2) sophisticated analysis routines. 

In practice nuclear spin-lattice relaxation is always within the Redfield limit, i.e. the interaction energy with the lattice is always much smaller than rc-1. This is true even with paramagnetic systems, where the nuclear spin-lattice interaction eneigy is often much larger than usual. On the other hand, it is not obvious that electrons are always in the Redfield limit. When electrons are outside the Redfield limit, although nuclear relaxation is in the Redfield limit, it is not easy... 

Electron spin-lattice interaction. The transition between a and p spin states takes place by the interaction between the A spins and the lattice vibration of surrounding molecules. The excess energy of the A spin system is transferred to the surrounding molecules to induce lattice vibration. This relaxation takes place even for an isolated electron spin having no interaction with other electron spins at all. 

In addition to this spin-spin interaction there exists an interaction between the spins and the surroundings, the so-called spin-lattice interaction. The characteristic constant is called the spin-lattice relaxation time T1. Tz is, below a certain temperature, nearly independent of temperature, whereas T1 is highly temperature-dependent (see Sect. 12.2.1.3). This provides means of studying the two rate processes separately. 

In addition to the spin-spin interaction, also in this case there exists interaction between the spins and their surroundings the so-called spin-lattice interaction. The characteristic constant of the order-disorder transition of this interaction process is the spin-lattice relaxation time (T1). T1 is highly dependent on temperature, whereas Tz is nearly temperature-independent. 

NMR Time Windows and Relevant Spin-Lattice Interactions... 

As noted in the papers by Schaefer and coworkers and by Lyerla and coworkers, Tip data may be complicated by the fact that mechanisms other than spin-lattice interactions (namely spin-spin relaxation) are possible which don t map motional characteristics. In the case of polystyrene, Schaefer and coworkers conclude that the spin-spin contributions are negligible, whereas Lyerla and coworkers find that the levels of spin-spin and spin-lattice contributions for isotatic polypropylene and atatic polymethyl methacrylate were temperature dependent. 

If we neglect spin-lattice interactions the equation for a density matrix p may be expressed as follows... 

Taking into account the Hamiltonian of the spin-lattice interactions Hsl at times Ti can be treated with the usual perturbation theory using the master equation. ... 

For revealing the main peculiarities of the effect of the multi-pulse sequence (71) a simplified theoretical treatment was suggested that does not include dipolar and spin-lattice interactions. Then the equation for a density matrix p of the spin-1... 

In contrast to the well-known Wigner-Witmer rule [24] that multiplicity is retained during a chemical reaction, the origin of the spin exclusion principle is both the retention and the distortion of symmetry. The fact is that from the viewpoint of rigorous invariance the initially singlet system cannot spontaneously pass into the triplet state. Spin-orbital and spin-lattice interactions probably play the main role in this transition. 

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