Comparing proton momentum distributions in $A=2$ and 3 nuclei via ${}^2$H ${}^3$H and ${}^3$He $(e,e^{\prime }p)$ measurements

Abstract

We report the first measurement of the $(e,e^{\prime }p)$ reaction cross-section ratios for Helium-3 (${}^3$He), Tritium (${}^3$H), and Deuterium ($d$). The measurement covered a missing momentum range of $40\le p_{miss}\le 550$ MeV$/c$, at large momentum transfer ($⟨Q^2⟩\approx 1.9$ (GeV$/c$)${}^2$) and $x_B>1$, which minimized contributions from non quasi-elastic (QE) reaction mechanisms. The data is compared with plane-wave impulse approximation (PWIA) calculations using realistic spectral functions and momentum distributions. The measured and PWIA-calculated cross-section ratios for ${}^3$He$/d$ and ${}^3$H$/d$ extend to just above the typical nucleon Fermi-momentum ($k_F\approx 250$ MeV$/c$) and differ from each other by $\sim 20\%$, while for ${}^3$He/${}^3$H they agree within the measurement accuracy of about 3\%. At momenta above $k_F$, the measured ${}^3$He/${}^3$H ratios differ from the calculation by $20\%-50\%$. Final state interaction (FSI) calculations using the generalized Eikonal Approximation indicate that FSI should change the ${}^3$He/${}^3$H cross-section ratio for this measurement by less than 5\%. If these calculations are correct, then the differences at large missing momenta between the ${}^3$He/${}^3$H experimental and calculated ratios could be due to the underlying $NN$ interaction, and thus could provide new constraints on the previously loosely-constrained short-distance parts of the $NN$ interaction.

8 pages, 3 figures (4 panels)