Superscaling in nuclei: A search for a scaling function beyond the relativistic Fermi gas model

Abstract

We construct a scaling function f͑Ј͒ for inclusive electron scattering from nuclei within the coherent density fluctuation model (CDFM). The latter is a natural extension to finite nuclei of the relativistic Fermi gas model within which the scaling variable Ј was introduced by Donnelly and collaborators. The calculations show that the high-momentum components of the nucleon momentum distribution in the CDFM and their similarity for different nuclei lead to quantitative description of the superscaling in nuclei. The results are in good agreement with the experimental data for different transfer momenta showing superscaling for negative values of Ј, including those smaller than −1.

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

“…As already mentioned in previous work [16], this asymmetry of the RMF description constitutes a basic difference from other models presented in the literature [55][56][57] where the long tail in f (ψ ) is largely absent.…”

“…Ingredients beyond the impulse approximation, i.e., multinucleon knockout, either induced by exchange currents, correlations, or rescattering effects, are surely needed to get more strength in the scaling function which will be then closer to the experiment. This is in fact the case of the coherent density fluctuation model (CDFM) for correlations presented in [55][56][57]. This model is an extension of the RFG applied to finite nuclei, and its prediction is also shown for comparison in Fig.…”

Scaling function, spectral function, and nucleon momentum distribution in nuclei

“…The CDFM has been applied to studies of the superscaling phenomenon [20][21][22][23] in inclusive electron-nucleus scattering, as well as to analyses of neutrino and antineutrino scattering by nuclei of both charge-changing [23,35] and neutral-current [36] types. Before entering into a discussion of the RMF results, it is interesting to point out the significant differences introduced by the other models.…”

“…Since it is impossible within the MFA to describe simultaneously the density and momentum distributions in nuclei [4,[7][8][9][10][11][12], a consistent analysis of the role of the NN correlations is required using theoretical methods that go beyond the MFA to obtain a successful description of the relevant experiments. The present study uses the results found from studies of y scaling [1][2][3][13][14][15] and superscaling (based on ψ-scaling variable) [15][16][17][18][19][20][21][22][23] obtained from analyses of inclusive electron scattering data. The latter consists in constructing a "superscaling function" f (ψ) obtained by removing the single-nucleon content from the double-differential cross section and plotting it versus a scaling variable ψ(q, ω).…”

“…When scaling of both the first and second type occurs, one says that superscaling has taken place. It was pointed out [18,[20][21][22][23] that the physical reason for the superscaling is the specific high-momentum tail of n(p), which arises due to NN correlations and is similar for all nuclei. As was pointed out in Ref.…”