The Longitudinal and Transverse Responses in the Inclusive Electron Scattering

The splitting between the charge-longitudinal and spin-transverse responses is explained in a model whose inputs are the effective interactions in the particle-hole channels in the first order boson loop expansion. The interplay between ω-meson exchange and box diagrams mainly governs the longitudinal response, while in the transverse one the direct ∆ excitations almost cancel the one-loop correction and the response is ruled by the ρ-meson rescattering. 1 The experimental and theoretical situations The experimental outcomes in the quasi-elastic peak (QEP) region are at present still controversial both on the experimental and theoretical point of view. Starting from d σ dΩdǫ = σM {vLRL(q, ω) + vTRT (q, ω)} the Saclay experimentalists [1, 2] where able to perform the Rosenbluth separation thus getting both RL and RT . The longitudinal response was drastically quenched with respect to the Free Fermi Gas (FFG) model, while the transverse one was remarkably increased. The first difficulties came from the non-fulfillment of the Coulomb sum rule, that, being expected to provide the nuclear charge, was quenched to a, say, 90% in case of C but to a 60% in the case of Ca. Few years ago the Rosenbluth separation has also been performed at Bates [3]. The quenching of the sum rule for the Ca turned out to be of about a 10%, in sharp contrast with the Saclay data. Very recently Jourdan [4] outlined that the Rosenbluth separation is not free from theoretical ambiguities, and others are introduced in deriving the sum rule: the distortion of the outgoing electron must be correctly accounted for, before separating the channels; further, relativity prevents us to define the Coulomb sum rule in a natural way [5]. Jourdan showed that the corrected sum rule derived from world set of data is compatible with Z within a 1% incertitude. This outcome is, in principle, not strongly contradictory with the Saclay results: the Coulomb sum rule in fact properly reads ∞