NMR double quantum transitions: An alternative derivation

Abstract

The general NMR absorption line shape function of Hoffman is used to derive the resonance condition for double quantum transitions. Strong absorption will occur at rf frequencies for which a pair of eigenvalues of the rotating frame Hamiltonian V lie close. It is shown how the eigenvalues of V may be found from a modified perturbation treatment, which is applicable also at near degeneracy of the eigenvalues. A small shift of the double quantum transition away from its first-order position may occur. The results obtained coincide with those of Anderson, Freeman, and Reilly with respect to the transition frequency and transition probability, but differ with respect to the eigenfunctions and eigenvalues obtained by these authors.