Electromagnetic Single-nucleon Response involving Polarized Targets

Abstract

This work is an extension of our past study focused on a covariant representation of the electromagnetic (EM) current of spin-1/2 Dirac particles, specifically, nucleons. In the past study the EM responses that occur in unpolarized electron scattering from unpolarized nucleons were derived; however, scattering of polarized electrons from polarized nucleons was beyond the scope of that earlier work. Here such extensions are studied in detail. While in other work the EM response has already been developed for the double-polarization scattering problem, that effort was focused on high-energy collider physics. In the present study the formalism is recast into a set of EM response functions that have transparent dependencies on the relevant kinematic variables, especially on how these behave with respect to the momentum p of the (moving) struck, polarized nucleon. The motivation for such a reformulation of the problem is the desire to see a clear path to expansions in $p$ of the EM response for use in devising ``prescriptions for nuclear physics''. Results are provided where comparisons of the full (unexpanded) responses with various approximations that are frequently employed in studies of EM nuclear physics are made, demonstrating that under some circumstances such approximations are reasonable, whereas in other circumstances the expanded results are likely to be invalid. In addition, the EM current operators and approximations to them are discussed in detail.