A recently developed moment theorem and an approximation scheme of Pryce and Stevens are used to compare 2nd-RPA and Tomita–Tanaka type decoupling procedures for Green function equations. The comparison is accomplished from the point of view of the moments of the paramagnetic resonance line shapes that the decouplings generate. An Ising system in an external magnetic field is taken as the model system. It is found that use of the more complicated 2nd RPA is justified only if accuracy to O(1/z2) is desired.
The application of the Green function method to the Mollow problem is reconsidered. This problem consists of an intense monochromatic electromagnetic field in resonance with a two-level atom. We obtain a solution to the infinite hierarchy of Green function equations of motion instead of decoupling the equations of motion. This solution gives an excitation spectrum in agreement with Mollow's results. We conclude that earlier discrepancies in the excitation spectrum were artifacts of the decoupling procedure. Finally, we comment upon the physical ideas associated with the present and previous Green function treatments of the Mollow problem.