Nuclear reorientation in static and radio-frequency electro-magnetic fields

Abstract

Nuclear reorientation by external electromagnetic fields is treated using Fano's irreducible tensor formulation of the problem. Although the main purpose of this paper is the description of the effects of nuclear magnetic resonance (NMR) on an ensemble of oriented nuclei in the presence of a crystal electric field gradient (efg), the results are applicable to all types of nuclear or atomic orientation or angular correlation work. Relations are established that allow: (i) to calculate different perturbation coefficient-matricesG ^kk′ andG ^k1k1 from each other by multiplication with known matrices; (ii) to build up the solution for the mixed electric-magnetic interaction from the solution of the pure magnetic case; (iii) to deduce a high spin solution from a given low spin solution; (iv) to separate the perturbation matrix that connects only longitudinal degrees of orientation. Further we use a perturbation expansion of the solutionsG in powers of the perturbing part of the Liouville matrixL. The theory is applied to a number of exemplary cases: magnetic field dependence of nuclear orientation in the presence of quadrupole interactions; sign determination in electric quadrupole coupling; line shapes of nuclear acoustic resonance (NAR) signals; quadrupole splitting and multiquantum transitions in NMR with oriented nuclei.