Gauge and Lorentz invariant one-pion exchange currents in electron scattering from a relativistic Fermi gas

A consistent analysis of relativistic pionic correlations and meson-exchange currents for electroweak quasielastic electron scattering from nuclei is carried out. Fully relativistic one-pion-exchange electromagnetic operators are developed for use in one-particle emission electronuclear reactions within the context of the relativistic Fermi gas model. Then the exchange and pionic correlation currents are set up fully respecting the gauge invariance of the theory. Emphasis is placed on the self-energy current which, being infinite, needs to be renormalized. This is achieved starting in the Hartree–Fock framework and then expanding the Hartree–Fock current to first order in the square of the pion coupling constant to obtain a truly gauge invariant, one-pion-exchange current. The model is applied to the calculation of the parity-conserving and parity-violating inclusive responses of nuclei. Interestingly, in the pionic correlations terms exist which arise uniquely from relativity, although their impact on the responses is found to be modest.