Nuclear Fermi Momenta of $^{2}$H, $^{27}$Al and $^{56}$Fe from an Analysis of CLAS data

Abstract

Nuclear Fermi momentum is a basic property of a nucleus where many nucleons dwell. However, in experiments only the nuclear Fermi momenta of just a few nuclei are measured using quasielastic electron scattering on the nuclear targets so far. Particularly, we still do not know experimentally the Fermi momentum of the lightest nucleon composite -- the deuteron. In this paper, we apply both gaussian distribution and Cauchy distribution to describe the quasielastic peak in the cross section of electron-nucleus scattering. The dip of the cross-section ratio at about $x_{\rm B}=1$ is explained with the nuclear Fermi momentum. By performing the least-square fits to the published CLAS data in the narrow kinematic region of quasielastic scattering, we obtain the nuclear Fermi momenta of $^{2}$H, $^{27}$Al and $^{56}$Fe, which are $116\pm 7$ MeV/c, $232\pm 27$ MeV/c, and $244\pm 28$ MeV/c respectively. The extracted nuclear Fermi momenta are compared to the simple calculations based on Fermi gas model, and the consistencies are found.