Relativistic Coulomb sum rules for (e,e’)

Abstract

A Coulomb sum rule is derived for the response of nuclei to (e, e ′ ) scattering with large three-momentum transfers. Unlike the nonrelativistic formulation, the relativistic Coulomb sum is restricted to spacelike four-momenta for the most direct connection with experiments; an immediate consequence is that excitations involving antinucleons, e.g., NN pair production, are approximately eliminated from the sum rule. Relativistic recoil and Fermi motion of target nucleons are correctly incorporated. The sum rule decomposes into one-and two-body parts, with correlation information in the second. The one-body part requires information on the nucleon momentum distribution function, which is incorporated by a moment expansion method. The sum rule given through the second moment (RCSR-II) is tested in the Fermi gas model, and is shown to be sufficiently accurate for applications to data.

Recent Progress in Quantum Hadrodynamics

“…The correct form of the relativistic sum rule, the effects of nuclear binding, and the use of the off-shell current are analyzed in [Fe94,Ko95]. An important recent contribution [Jo95] indicates that the solution to this problem may now be in hand.…”

Inelastic nucleon contributions in(e,e′)nuclear response functions

“…Since real photons are purely transverse, W A L = 0 at Q 2 = 0, i.e., at ω = |q|. In order to analyze nuclear (e, e ′ ) data for the purpose of extracting two-body correlation functions [15,16] the function W A L must be evaluated over the entire range 0 ≤ ω ≤ |q|. Its behavior near Q 2 = 0 is therefore an important qualitative feature which must be maintained.…”

Nuclear binding effects in relativistic Coulomb sum rules

“…Both modifications introduce a degree of model-dependence in the RCSR which is not present in the nonrelativistic formulation, nor in the relativistic formulation of Ref. [3]. We show how these features can be incorporated into the theory to allow the evaluation of the one-body contribution Σ (1) (q), and the subsequent extraction of the two-body correlation function C(q) from the measured Coulomb response.…”

“…1 The purpose of this work is to provide practical methods for the analysis of the longitudinal (e, e ′ ) response of nuclear targets, at the higher energies now available at the Continuous Electron Beam Accelerator Facility (CEBAF) and other electron accelerators. In a previous paper [3], we derived a relativistic Coulomb sum rule (RCSR) which incorporates the relativistic effects of nucleon recoil at large q, as well as of Fermi motion. In the present work we extend this theoretical approach to include the effects of nuclear interactions on the RCSR.…”

“…Under the assumptions of Ref. [3] mentioned above, we obtain a RCSR which can be expressed in terms of one-and two-body contributions: Σ(q) ≡ Σ (1) (q) + C(q) + Σ (2) un (q), (1.2) where the one-body contribution is of the form Σ (1) (q) ≡ 2 pσ n σ (p) r σ (p, q), (1.3) C(q) includes two-body correlation information in momentum space, and Σ (2) un (q) is the uncorrelated two-body part which is related to the square of the nuclear elastic form factor, as discussed in Ref. [3].…”