Relativistic multipole operators for semileptonic weak and electromagnetic nuclear reactions.

Abstract

We discuss multipole operators that arise in a relativistic analysis of semileptonic weak and electromagnetic interactions with nuclei. These single-particle operators are evaluated between relativistic nucleon bound states that are solutions to the Dirac equation with potentials of the form produced by the \ensuremath{\sigma}-\ensuremath{\omega} model. The reduced matrix elements are given in terms of easily programmable radial integrals and can be applied to a number of reactions such as elastic and inelastic electron scattering, real photon processes, \ensuremath{\beta} decay, and charged lepton capture as well as more exotic interactions such as charged and neutral current neutrino reactions. As a specific example, we calculate the elastic and inelastic magnetic form factors of p-shell nuclei.