Bloch Equations with Diffusion Terms

The phenomenological Bloch equations in nuclear magnetic resonance are generalized by the addition of terms due to the transfer of magnetization by diffusion. The revised equations describe phenomena under conditions of inhomogeneity in magnetic field, relaxation rates, or initial magnetization. As an example the equations are solved in the case of the free precession of magnetic moment in the presence of an inhomogeneous magnetic field following the application of a 90° pulse with subsequent applications of a succession of 180° pulses. The spin-echo amplitudes agree with the results of Carr and Purcell from a random walk theory.