Nuclear spin echo model based on Floquet–Lyapunov theory

Abstract

The method of nuclear spin-echo amplitude calculation based on the density matrix technique is improved. The Floquet-Lyapunov theorem for a system of the ordinary differential equations with coefficients periodically dependent on time is used to find the solution of the Schrodinger equation for the time-evolution operator which describes behavior of a nuclear spin in the presence of a radiofrequency pulsed magnetic field. NOR spin echo for the case of nuclear spin I=1 and NMR spin echo for I=1/2 are considered as the simplest illustrations of the approach. The appearance of multiple spin echoes is predicted in the case of strong radiofrequency field.