Retarded Green’s Function Calculation of Magnetic Resonance Dipolar Lineshapes for Rotating Molecules or Atomic Groups in Solids

Abstract

The powerful Two-times Green's function formalism is applied to the calculation of the NMR dipolar lineshape corresponding to hindered rotating spin-carrying molecules or atomic groups in solids. The rotation of the molecules is quantum-mechanically considered as one-phonon induced transitions between the hindered rotaror levels. The nuclear spin system is assumed to be coupleed to the bath of thermal phonons through the phonon-rotation interaction. The retarded Green's functions, pertinent to the lineshape problem, are determined by a second order decoupling of their equations of motion. The lineshape expression is shown to be a weighted superposition of Lorentzians