Spin Echo Measurements of Nuclear Spin Coupling in Molecules

Abstract

A new type of nuclear spin-spin coupling in molecules in liquids is investigated by means of the spin echo technique. A coupling interaction of the rotationally invariant from $\ensuremath{\hbar}J{\mathbf{I}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{I}}_{2}$ in the nuclear induction Hamiltonian predicts the detailed shape of the spin echo envelope. Echo modulation frequencies corresponding to the coupling $J$ and the chemical shift between nonequivalent protons are measured in a variety of compounds. A generalized method for calculating the spin echo is presented for large chemical shift and weak coupling among an arbitrary number of spins. The damping of the echo modulation, due to spin relaxation and molecular effects which interrupt the $J$ coupling, is accounted for by a phenomenological treatment of the quantum-mechanical expectation value of nuclear magnetization.