Free localized spin system

Block equations can be constructed that describe the macroscopic magnetization of the spin system including the relaxation mechanism involving spin exchange caused by molecular collisions. These equations were solved as a function of the exchange frequency, wex, for the nitroxide free radical case. Spectra were computed by assuming the degrees of motional freedom observed with the labeled androstane or cholestane molecules localized at the air-water interface. 

Extension of this methodology to porous packing elements (e.g., catalyst support pellets) is not straightforward. The challenge arises because the signal we wish to measure is associated with the liquid (water) in the bed. However, the signal intensity acquired from a specific region of water depends on its local environment, because the nuclear spin relaxation times of water in different physical environments will vary. In this system, the different environments will be (i) free water in the bulk of the inter-pellet space, (ii) water within the intra-pellet pore space, and... 

A spin-free eigenket for the total AB system will have exact quantum numbers AT[A] at all intermolecular separations R. In the limit of infinite intermolecular separation there are additional exact quantum numbers, jRTa[Aa] for molecule A and ATB[AB] for molecule B. These quantum numbers are not exact at finite R, but may still be approximate quantum numbers. We call jKTa[Aa], ATb[Ab] local quantum numbers for the total AB system, and [Aa], [Ab], the local permutational symmetry. 

Such localized states as under discussion here may arise in a system with local permutational symmetries [Aa] and [AB], If [Aa] + [S] and [Ab] = [5], the outer direct product [Aa] 0 [AB] gives rise to a number of different Pauli-allowed [A], If the A and B subsystems interact only weakly, these different spin-free [A] levels will be closely spaced in energy. The extent of mixing of these closely spaced spin-free states under the full Hamiltonian, H = HSF + f2, may then be large. Thus, systems which admit a description in terms of local permutational symmetries may in some cases readily undergo spin-forbidden processes, such as intersystem crossing. 

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