Relativistic plane-wave impulse approximation for nuclear inelastic scattering of protons and electrons

We establish the general form of inelastic scattering amplitudes based on invariance principles and derive simple relations between these amplitudes and spin-transfer observables. We then examine a plane-wave relativistic impulse approximation for (p,p’) which is a simple extension of the relativistic impulse approximation for elastic scattering. We show under what approximations this amplitude reduces to the standard (nonrelativistic) impulse approximation and then examine the novel features of the free relativistic impulse approximation which results from less restrictive assumptions. We also derive free relativistic impulse approximation inelastic electron scattering form factors and then use our (p,p’) and (e,e’) formulations to extract nuclear structure information for the first two $1^{+}$ levels in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. We consider possible experimental signatures of the strong scalar and timelike vector potentials of modern relativistic theories.