Relativistic pionic effects in quasielastic electron scattering

Abstract

The impact of relativistic pionic correlations and meson-exchange currents on the response functions for electromagnetic quasielastic electron scattering from nuclei is studied in detail. Results in first-order perturbation theory are obtained for one-particle emission electronuclear reactions within the context of the relativistic Fermi gas model. Improving upon previous analyses where non-relativistic reductions of the currents were performed, here a fully relativistic analysis in which both forces and currents are treated consistently is presented. Lorentz covariance is shown to play a crucial role in enforcing the gauge invariance of the theory. Effects stemming uniquely from relativity in the pionic correlations are identified and, in particular, a comprehensive study of the self-energy contributions and of the currents associated with the pion is presented. First-and second-kind scaling for high momentum transfer is investigated.

Meson-exchange currents and final-state interactions in quasielastic electron scattering at high momentum transfers

“…Similar effects were also found at higher momentum transfers using a relativistic Fermi gas (RFG) model [5,6]. The same trend is confirmed by the results of the present study for q = 1 GeV/c, as shown in the upper panel of Fig.…”

“…An exhaustive analysis of (e, e ) world data demonstrated the scaling at energy transfers ω below the quasielastic (QE) peak [1,2], namely the independence of the reduced cross sections on the momentum transfer (first-kind scaling) and on the nuclear target (second-kind scaling) when plotted versus the appropriate scaling variable. It is well known that at energies above the QE peak scaling is violated in the transverse (T ) channel by effects beyond the impulse approximation: inelastic scattering [3,4], correlations, and meson-exchange currents (MEC) in both the one-particle one-hole (1p-1h) and two-particle two-hole (2p-2h) sectors [5][6][7][8].In contrast, the available data for the longitudinal (L) response are compatible with scaling throughout the QE region and permitted [9] the extraction of a phenomenological scaling function f L . In recent work [10][11][12] it was shown that only a few models [the relativistic mean field (RMF), the semirelativistic (SR) approach with Dirac-equation-based (DEB) and a "BCS-like" model] are capable of reproducing the detailed shape of f L , while other models fail to reproduce the long tail appearing at high ω. Theses models effectively account for the major ingredients needed to describe the (e, e ) responses for intermediate-to-high momentum transfers, namely relativistic effects and an appropriate description of the effective final-state interactions (FSI).…”

“…An exhaustive analysis of (e, e ) world data demonstrated the scaling at energy transfers ω below the quasielastic (QE) peak [1,2], namely the independence of the reduced cross sections on the momentum transfer (first-kind scaling) and on the nuclear target (second-kind scaling) when plotted versus the appropriate scaling variable. It is well known that at energies above the QE peak scaling is violated in the transverse (T ) channel by effects beyond the impulse approximation: inelastic scattering [3,4], correlations, and meson-exchange currents (MEC) in both the one-particle one-hole (1p-1h) and two-particle two-hole (2p-2h) sectors [5][6][7][8].…”

General study of superscaling in quasielastic(e,e')and(ν,μ

“…The symbol χ specifies neutrino-induced reactions (χ = +) or antineutrinoinduced reactions (χ = −), and the term σ 0 depends on the Fermi constant and the Cabibbo angle (see [13] for its explicit expression). The kinematic factors v K andv K come solely from the electromagnetic and weak leptonic tensors, respectively, and their explicit expressions can be found in [4,8,13]. The electromagnetic R K and weakR K response functions contain the whole dependence on the nuclear vertex coupling and are expressed by taking the appropriate components of the nuclear tensor [4,8,13].…”

“…The kinematic factors v K andv K come solely from the electromagnetic and weak leptonic tensors, respectively, and their explicit expressions can be found in [4,8,13]. The electromagnetic R K and weakR K response functions contain the whole dependence on the nuclear vertex coupling and are expressed by taking the appropriate components of the nuclear tensor [4,8,13]. This involves the matrix elements of the virtual photon or charged boson interaction with the nuclear electromagnetic or weak current.…”