We report the first measurement of the $(e,ep)$ 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 ($langle Q^2 rangle approx 1.9$ (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.
تحميل البحث