Probing Few-Body Nuclear Dynamics via ${}^3\mathrm{H}$ and ${}^3\mathrm{He}$ $(e,e^{\prime }p)\mathrm{pn}$ Cross-Section Measurements

We report the first measurement of the $(e,e^{\prime }p)$ three-body breakup reaction cross sections in helium-3 (${}^3\mathrm{He}$) and tritium (${}^3\mathrm{H}$) at large momentum transfer [$⟨Q^2⟩\approx 1.9(\mathrm{GeV}/c{)}^2$] and $x_B>1$ kinematics, where the cross section should be sensitive to quasielastic (QE) scattering from single nucleons. The data cover missing momenta $40\le p_{\text{miss}}\le 500\mathrm{MeV}/c$ that, in the QE limit with no rescattering, equals the initial momentum of the probed nucleon. The measured cross sections are compared with state-of-the-art ab initio calculations. Overall good agreement, within $\pm 20\%$, is observed between data and calculations for the full $p_{\text{miss}}$ range for ${}^3\mathrm{H}$ and for $100\le p_{\text{miss}}\le 350\mathrm{MeV}/c$ for ${}^3\mathrm{He}$. Including the effects of rescattering of the outgoing nucleon improves agreement with the data at $p_{\text{miss}}>250\mathrm{MeV}/c$ and suggests contributions from charge-exchange (SCX) rescattering. The isoscalar sum of ${}^3\mathrm{He}$ plus ${}^3\mathrm{H}$, which is largely insensitive to SCX, is described by calculations to within the accuracy of the data over the entire $p_{\text{miss}}$ range. This validates current models of the ground state of the three-nucleon system up to very high initial nucleon momenta of $500\mathrm{MeV}/c$.

Figure 1

Absolute cross section as a function of $p_{\text{miss}}$ for ${}^3\mathrm{He}$ (left) and ${}^3\mathrm{H}$ (right). The different sets of data points, depicted by black circles and squares, correspond to the cross sections measured in the low-$p_{\text{miss}}$ and high-$p_{\text{miss}}$ kinematical settings respectively. The lines correspond to cross sections calculated from different theoretical models, Cracow (solid red), $\mathrm{CK}+CC1$ (dashed blue) and Sargsian-FSI (dotted green, $p_{\text{miss}}>250\mathrm{MeV}/\mathrm{c}$ only). The different kinematical settings have different average elementary electron-nucleon cross sections and therefore have a different overall scale for both data and calculations.

Figure 2

The ratio of the experimental cross section to different PWIA calculations plotted versus $p_{\text{miss}}$ for ${}^3\mathrm{He}(e,e^{\prime }p)$ (top) and ${}^3\mathrm{H}(e,e^{\prime }p)$ (bottom). Red squares show the ratio to the Cracow calculation while blue circles show the ratio to the Ciofi-Kaptari spectral-function-based calculations (CK+$CC1$) (see text for details). Open symbols show the ${}^3\mathrm{He}(e,e^{\prime }p)$ data of Ref. [5], taken at lower $Q^2$ and $x\sim 1$ kinematics, compared with the PWIA calculations of Ref. [32, 46, 47, 48]. The inner and outer bars show the statistical and statistical plus systematic uncertainties, respectively. The shaded regions show 10% and 20% agreement intervals.

Figure 3

Top: The ratio of the experimental cross sections to the calculation of Sargsian that includes FSI of the leading nucleon for ${}^3\mathrm{He}$ (filled upright triangles) and ${}^3\mathrm{H}$ (open inverted triangles). Bottom: the ratio of the measured total ${}^3\mathrm{He}+{}^3\mathrm{H}$ cross section to the Cracow PWIA calculation (red squares) and the Sargsian calculation that includes FSI (black triangles). The inner and outer bars show the statistical and statistical plus systematic uncertainties respectively. On both panels the shaded regions show 10% and 20% agreement intervals.