An expansion for the free induction decay of spins one-half with dipole-dipole interaction

The author gives an expansion for the density matrix subsequent to a single 90 degrees resonant RF pulse for a system of spins with dipole-dipole interactions. The method is analogous to the usual multiple scattering expansion used to approximate the electron density of states in disordered metals but here is applied to certain super operators related to the quantum Liouville operator governing the equation of motion for the density matrix. A simple choice of unperturbed Hamiltonian is discussed giving rise to a systematic expansion. The expansion is not perturbative in the usual sense.