An examination of the cross-correlation effect in a three spin system composed of two nuclei and an electron
McGuire, Thomas Edward
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Present NMR theory treats the relaxation of one nucleus in a multispin system as the sum of two spin effects. This treatment neglects the fact that two or more spins may interact in such a way as to have an additional relaxation effect, the cross-correlation effect which is omitted in present theory. The error introduced by this neglect can be examined through the cross-terms which are arrived at through the Nuclear Overhauser Effect (NOE) and spin lattice relaxation. This paper derives or presents, using accepted theory, the equations of spin lattice relaxation and NOE for the cases of two and three loosely coupled nuclei in addition to two nuclei in the presence of an electron. Next data are presented, which are supported by this author's experiments, which show the cross-correlation effect in a system of two nuclei and an electron can lead to a substantial error if neglected. Finally, a modification of present theory is derived for two nuclei and an electron which takes into account the cross-correlation effect.