Comparing proton momentum distributions in $A=3$ nuclei via $^3$He and $^3$H$(e,e'p)$ measurements.

We report the first measurement of the $(e,eu0027p)$ reaction cross-section ratio for Helium-3 ($^3$He) relative to Tritium ($^3$H). 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 $x_Bu003e1$, which minimized contributions from non quasi-elastic (QE) reaction mechanisms. The data is compared with calculations performed within the plane-wave impulse approximation (PWIA) using realistic spectral functions and momentum distributions. The measured and PWIA cross-section ratios agree within the measurement accuracy of about 3$%$ up to the nuclear Fermi-momentum ($approx 250$ MeV/$c$) and differ by $20% - 50%$ at higher momenta. 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$%$. This suggests that 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.