Nucleon momentum distribution extracted from the experimental scaling function

TL;DR

This paper investigates how the scaling function from electron scattering data relates to the nuclear spectral function and momentum density, incorporating effects of transfer momentum, the scaling variable, and short-range correlations.

Contribution

It provides analytical connections between the scaling function and the spectral function, extending analysis to both positive and negative y-values, and models short-range correlations in the nuclear momentum distribution.

Findings

Analytical expressions for derivatives of the scaling function are derived.

The scaling function is modeled using the Gumbel density distribution.

Different nucleon momentum distribution parametrizations are considered.

Abstract

The connection between the scaling function, directly extracted from the analysis of electron scattering data, and the nuclear spectral function or nuclear momentum density is investigated at depth. The dependence of the scaling function on the two independent variables in the scattering process, the transfer momentum ($q$) and the scaling variable ($y$), is taken into account, and the analysis is extended to both, positive and negative $y$-values, i.e., below and above the center of the quasielastic peak, respectively. Analytical expressions for the derivatives of the scaling function, evaluated at the finite limits of integration dealing with the kinematically allowed region, are connected with the spectral function. Here, contributions corresponding to zero and finite excitation energies are included. The scaling function is described by the Gumbel density distribution, whereas short-range correlations are incorporated in the spectral function by using some simple models. Also different parametrizations for the nucleon momentum distribution, that are compatible with the general properties of the scaling function, have been considered.