Superscaling in a dilute Fermi gas and the nucleon momentum distribution in nuclei

Abstract

The superscaling observed in inclusive electron scattering is described within the dilute Fermi gas model with interaction between the particles. The comparison with the relativistic Fermi gas (RFG) model without interaction shows an improvement in the explanation of the scaling function $f({\ensuremath{\psi}}^{\ensuremath{'}})$ in the region ${\ensuremath{\psi}}^{\ensuremath{'}}l\ensuremath{-}1$, where the RFG result is $f({\ensuremath{\psi}}^{\ensuremath{'}})=0$. It is found that the behavior of $f({\ensuremath{\psi}}^{\ensuremath{'}})$ for ${\ensuremath{\psi}}^{\ensuremath{'}}l\ensuremath{-}1$ depends on the particular form of the general power-law asymptotics of the momentum distribution $n(k)\ensuremath{\sim}1/{k}^{4+m}$ at large $k$. The best agreement with the empirical scaling function is found for $m\ensuremath{\simeq}4.5$ in agreement with the asymptotics of $n(k)$ in the coherent density fluctuation model where $m=4$. Thus, superscaling gives information about the asymptotics of $n(k)$ and the $\mathit{NN}$ forces.