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The resonance of spin X at frequency Vx is depicted in Fig. lOc as arising from two different transitions and the same is true for the A spin resonance. This is in agreement with our molecular point of view: every energy level corresponds to a The Energy Level and Transition Diagram 29 stationary state of the spin system and we may conceive of our sample as being composed of four classes of molecules such that all the molecules of one class exist in the same stationary state. A transition in which rnx changes may involve either a molecule in which rnA = + 1/2 or one in which rnA = -1/2 and, similarly, a transition of spin A may involve either a molecule with rnx = + 1/2 or one with rnx = -1/2.

C 1 b c II II' Fig. 18. Schematic diagram showing the splittings obtained in the b and c lines when the connected a transition is perturbed by an irradiation field H2 of frequency V2 48 Miscellaneous Aids for Spectral Assignment 3. The doublet splitting is proportional to the square root of the intensity of the irradiated line and to the amplitude H2 of the irradiation field. In addition to these three rules, which are valid for the symmetrical doublets observed when V2 is centered exactly on a connected transition, the following rules pertaining to the case of unsymmetric tickling may be found helpful: 4.

By means of the powerful tools of transformation theory and group theory, many invariants of spin systems and NMR spectra have been derived as aids in spectral analysis. Most of these invariants are, however, not as readily recognized in actual NMR spectra as is, for example, the center of gravity of a basic multiplet. For this latter reason, a comprehensive survey of all known invariants is not felt to be in the spirit of the present text and the interested reader is referred to the specialized literature (cf.

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