On the Coulomb and higher-order sum rules in the relativistic Fermi gas

Abstract

Two different methods for establishing a space-like Coulomb sum rule for the relativistic Fermi gas are compared. Both of them divide the charge response by a normalizing factor such that the reduced response thus obtained fulfills the sum rule at large momentum transfer. To determine the factor, in the first approach one exploits the scaling property of the longitudinal response function, while in the second one enforces the completeness of the states in the space-like domain via the Foldy-Wouthuysen transformation. The energy-weighted and the squared-energy-weighted sum rules for the reduced responses are explored as well and the extension to momentum distributions that are more general than a step-function is also considered. The two methods yield reduced responses and Coulomb sum rules that saturate in the non-Pauli-blocked region, which can hardly be distinguished for Fermi momenta appropriate to atomic nuclei. Notably the sum rule obtained in the Foldy-Wouthuysen approach coincides with the well known non-relativistic one. Only at quite large momentum transfers (say 1 GeV/c) does a modest softening of the Foldy-Wouthuysen reduced response with respect to that obtained in the scaling framework show up. The two responses have the same half-width to second order in the Fermi momentum expansion. However, when distributions extending to momenta larger than that at the Fermi surface are employed, then in both methods the Coulomb sum rule saturates only if the normalizing factors are appropriately modified to account for the high momentum components of the nucleons.Comment: LaTex file with 8 .ps figure

Role of 2p–2h MEC excitations in superscaling

“…expresses (see Eqs. ( 4)) the impact of the medium on the single-nucleon electromagnetic cross section [35]. As far as the electric and magnetic form factors of the proton and the neutron G Ep ,G Mp , G En and G Mn are concerned, we adopt the Höhler parametrization of Ref.…”

Relativistic γ-scaling and the Coulomb sum rule in nuclei

“…represents the transverse component (with respect to q) of the momentum of the struck nucleon [2]. It follows that the required RFG dividing function is given by…”

“…Motivated by our recent work [1,2] on the Coulomb sum rule (CSR), in this paper we return to the related problem of y-scaling. In Refs [1] we devised a factor H L that, upon being divided into the longitudinal response function for quasielastic electron scattering, R L , produced a so-called reduced response,…”

Contrasting and parity-violating asymmetries in nuclei

“…We refer the reader to [10] for a more thorough discussion of the D's : here we simply recall that they vanish, as should be the case, when η F → 0 and that for ρ → 1 they evolve into the corresponding quantities for the QEP [11].…”