Scaling Function and Nucleon Momentum Distribution

TL;DR

This paper revisits the connection between scaling functions from electron scattering data and the nucleon momentum distribution, extending analysis to positive scaling variables to gain new insights into nuclear spectral functions.

Contribution

It extends the analysis of scaling functions to positive y-values, offering a more comprehensive understanding of the nucleon momentum distribution in nuclei.

Findings

Different results obtained from positive y-region analysis.

New insights into energy and momentum distribution in spectral functions.

Extension of superscaling analysis to broader kinematic regions.

Abstract

Scaling studies of inclusive quasielastic electron scattering reactions have been used in the past as a basic tool to obtain information on the nucleon momentum distribution in nuclei. However, the connection between the scaling function, extracted from the analysis of cross section data, and the spectral function only exists assuming very restricted approximations. We revisit the basic expressions involved in scaling studies and how they can be linked to the nucleon momentum distribution. In particular, the analysis applied in the past to the so-called scaling region, {\it i.e.,} negative values of the scaling variable $y$, is extended here to positive $y$, since a "universal" superscaling function has been extracted from the analysis of the separated longitudinal data. This leads to results that clearly differ from the ones based solely on the negative-$y$ scaling region, providing new information on how the energy and momentum are distributed in the spectral function.