Nuclear spin configuration

The nuclear spin product functions will be represented by where n represents a given nuclear spin configuration characterized by nuclear spin quantum number Wj and for nuclei j and k, respectively. 

Equation 29.20 applies only to a one-line spectrum, and the sensitivity decreases when the radical sample exhibits HFS. As a simple case, reconsider the H3C spectrum, with its four lines one of the outside lines represents only one-eighth of the total number of radicals in the sample because the 1 3 3 1 intensity ratios reflect the statistical weights of the various nuclear spin configurations. Thus the detection sensitivity falls off rapidly with progressive HFS. 

Fig. 4 shows another approach to the same problem. Here the energies of the four electronic pair states are plotted versus the radical pair distance for a certain hypothetical nuclear spin configuration and for high magnetic field. The... 

Fig. 4. Schematic representation of the electric energies of a radical pair with a hypothetical nuclear spin configuration vs. inter-radical distance...

Phas matrix elements beween S and states of the same nuclear spin configurations k only, and these are given by... 

Not only is the electron-spin state conserved in all these reactions but also the nuclear spin state. Hence, the nuclear spin polarizations present in the pairs are transferred into the diamagnetic products, where they can be detected. Those nuclear spin configurations that slowed down intersystem crossing are over-populated in the product(s) of the exit channel on the same side as the entry channel of the scheme those that accelerated it are overpopulated in the product(s) of the exit channel on the other side. 

Fig. 6 compares the lineshapes of the ( T>- Z transition for a single molecule and an ensemble of about 10 molecules. The ensemble spectrum was obtained with the laser in resonance with the fluorescence excitation line of the Oi ensemble. The transition shows an asymmetric hneshape with a steep decrease towards higher microwave frequencies for both the single molecule and the ensemble case. The line-shape results from the hyperfine interaction of the triplet electron spin with the pen-tacene proton spins (/ = 1/2). Each proton can exist in one of its two nuclear spin states which yields 2 nuclear spin configurations. The h3fperfine interaction of each of these nuclear configurations causes a slight shift of the resonance. As pointed out in Section 4.1. In zero-field the hyperfine interaction is a second-order effect which leads to the observed opposite asynunetric lineshapes for the ((T>- Z and the ( T>- Z transitions (see Fig. 5). 

For a single molecule one would expect that it sees only one nuclear spin configuration and that a very narrow magnetic resonance line would be observable. Apparently, it experiences all of these configurations during the many optical... 

Radical pair theory states that the rate of 5 - To mixing is directly related to the nuclear spin configuration through the hyperflne interaction, which in turn determines the recombination yield. The nuclear spin polarisation generated in both the recombined and escaped products is known as chemically induced dynamic nuclear polarisation [6, 31-33]. 

As previously mentioned, all simulations were done using the Slice package and wherever possible repeated with the Hybrid program as a way of verilying the results. Unless otherwise mentioned, the spin parameters used in the simulation are those detailed in Table 5.3 and the kinetic parameters are those detailed in Table 5.4 (diffusion controlled conditions) or Table 5.5 (partially diflusion controlled conditions). The initial nuclear spin configuration was selected randomly at the start of every... 

The first step in the algorithm is to calculate the relaxation probability for each nuclear spin configuration k as... 

If the probability of > C7(0,1], then the coefficient for the state j with a nuclear spin configuration k collapses as with the exponential term mod-... 

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