Superscaling, scaling functions, and nucleon momentum distributions in nuclei

Abstract

The scaling functions $f({\ensuremath{\psi}}^{'})$ and $F(y)$ from the ${\ensuremath{\psi}}^{'}$- and $y$-scaling analyses of inclusive electron scattering from nuclei are explored within the coherent density fluctuation model (CDFM). In addition to the CDFM formulation in which the local density distribution is used, we introduce a new equivalent formulation of the CDFM based on the one-body nucleon momentum distribution (NMD). Special attention is paid to the different ways in which the excitation energy of the residual system is taken into account in $y$ and ${\ensuremath{\psi}}^{'}$ scaling. Both functions, $f({\ensuremath{\psi}}^{'})$ and $F(y)$, are calculated using different NMDs and compared with the experimental data for a wide range of nuclei. The good description of the data for $y<0$ and ${\ensuremath{\psi}}^{'}<0$ (including ${\ensuremath{\psi}}^{'}<\ensuremath{-}1$) makes it possible to show the sensitivity of the calculated scaling functions to the peculiarities of the NMDs in different regions of momenta. It is concluded that the existing data on ${\ensuremath{\psi}}^{'}$ and $y$ scaling are informative for NMDs at momenta not larger than $2.0--2.5\phantom{\rule{0.3em}{0ex}}{\text{fm}}^{\ensuremath{-}1}$. The CDFM allows us to study simultaneously and on the same footing the role of both basic quantities---the momentum and density distributions---for the description of scaling and superscaling phenomena in nuclei.