Multipole NMR. IX. Polar graphical representation of nuclear spin polarizations

Abstract

A graphical representation of the nuclear spin states created in NMR experiments is described which is also applicable to quadrupolar spins ( I > 1 2 ). The multipole polarizations are formally shown to be components of a polarization tensor with respect to the set of basis vectors formed from spherical harmonics. Linear combinations of polarizations have, like atomic orbitals, characteristic “shapes” which can be visualized by diagrams of polar graphs. These diagrams are used to illustrate the rotations produced by rf pulses and the couplings resulting from quadrupolar interactions, and to trace the polarization pathways of a spin-1 system during the quadrupolar solid-echo and Jeener-Broekaert sequences. Also discussed is the relationship between the thermodynamic and multipole approaches to NMR.