Electron-Nucleon Interaction in Quasi-Free Scattering. II Non-Relativistic Hamiltonian thorugh Fourth Order

The interaction of non-relativistic nucleons with relativistic electrons can be expressed by a Hamiltonian expanded in a power series of the recoil nucleon velocity. In this paper third- and fourth-order terms are calculated. Free electron-nucleon-scattering and quasi-free electron scattering on 12C are studied and results through various orders are compared with the relativistic formulae. A different off-shell behaviour of the relativistic approach is found, which is independent of the higher-order terms and seems responsible for the different results of knock-out reactions.