PNNL

Abstract

The transverse electron spin magnetization of a paramagnetic center with effective spin S=? interacting with nonquadrupolar nuclei may be presented as a function of pairs of nuclei magnetization vectors which precess around the effective magnetic field directions. Each vector of the pair starts its precession perpendicular to both effective fields. The FID signal is proportional to the scalar product of the vectors for nuclear spin I=?. The ESE signal can be described using two pairs of magnetization vectors. The ESE shape is not equal to two back-to-back FID signals except in the absence of ESE envelope modulation. A recursion relation is obtained which allows calculation of ESE signals for larger nuclear spins in the absence of NQI. This relation can be used to calculate the time course of the ESE signal for arbitrary nuclear spin as a function of the nuclear magnetization vectors. Although this formalism allows quantitative calculation of modulation from nuclei, it also provides a qualitative means of visualizing the modulation based on simple magnetization vectors.