Sequential Nature of $(p,3p)$ Two-Proton Knockout from Neutron-Rich Nuclei

Twenty-one two-proton knockout $(p,3p)$ cross sections were measured from neutron-rich nuclei at $\sim 250\mathrm{MeV}$/nucleon in inverse kinematics. The angular distribution of the three emitted protons was determined for the first time, demonstrating that the $(p,3p)$ kinematics are consistent with two sequential proton-proton collisions within the projectile nucleus. Ratios of $(p,3p)$ over $(p,2p)$ inclusive cross sections follow the trend of other many-nucleon removal reactions, further reinforcing the sequential nature of $(p,3p)$ in neutron-rich nuclei.

Figure 1

Overview of the secondary target area. The liquid hydrogen target (blue) is surrounded by the MINOS time projection chamber (yellow), which tracked the scattered protons. The angle between each proton and the beam axis $\theta$, the angle between each pair of protons $\lambda$ and the angles between the protons in the plane perpendicular to the beam axis ${\phi }_s\le {\phi }_m\le {\phi }_l$ are drawn.

Figure 2

(Left) Experimental $(p,2p)$ and $(p,3p)$ cross sections [27]. Error bars contain systematic and statistic uncertainties added in quadrature. (Right) Ratio (${\sigma }_{k+1}/{\sigma }_k$) of ($k+1$)-nucleon and $k$-nucleon removal cross sections with removed nucleons from same species (open markers) as a function of the evaporation cost asymmetry $\mathrm{\Delta }C$, with $k=1–9$. The data are taken from [44, 50, 51, 52, 53, 54, 55, 56]. See [44] for details. Ratios of $(p,3p)$ over $(p,2p)$ cross sections for the same incident nucleus from this Letter are shown (red diamonds).

Figure 3

Two-dimensional plot for a $(p,3p)$ reaction of the two smaller angles ${\phi }_s$ and ${\phi }_m$ in the plane perpendicular to the beam axis. (a) Experimental data for ${}^{81}\mathrm{Ga}(p,3p)$ (b) pair breakup model (c) pair knockout model (d) sequential model. Theoretical distributions have been normalized to the data.

Figure 4

Distribution for the projected angle ${\phi }_s$ (top), the beam angle $\theta$ (middle) and the angle between the scattered protons $\lambda$ (bottom) for ${}^{81}\mathrm{Ga}(p,3p)$ and ${}^{81}\mathrm{Ga}(p,2p)$ (in insets). Predictions from pair breakup, pair knockout, and sequential model are superposed. Translucent bands show the dependence on the model parameters (see text for details).