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

TL;DR

This study extracts nuclear Fermi momenta for deuteron, aluminum, and iron using CLAS electron scattering data, applying distribution fits to quasielastic peaks, and compares results with Fermi gas model predictions.

Contribution

It provides the first experimental determination of the Fermi momentum for the deuteron and extends measurements to other nuclei, using novel distribution fitting methods.

Findings

Fermi momenta: deuteron 116±7 MeV/c, aluminum 232±27 MeV/c, iron 244±28 MeV/c.

Distribution fits explain the quasielastic peak and the dip at x_B=1.

Results are consistent with Fermi gas model calculations.

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.