Probing elastic and inelastic breakup contributions to intermediate-energy two-proton removal reactions

The two-proton removal reaction from ${}^{28}$Mg projectiles has been studied at 93 MeV/u. First coincidence measurements of the heavy ${}^{26}$Ne projectile residues, the removed protons, and other light charged particles enabled the relative cross sections from each of the three possible elastic and inelastic proton removal mechanisms to be determined. These more final-state-exclusive measurements are key for further interrogation of these reaction mechanisms and use of the reaction channel for quantitative spectroscopy of very neutron-rich nuclei. The relative and absolute yields of the three contributing mechanisms are compared to reaction model expectations based on the use of eikonal dynamics and $sd$-shell-model structure amplitudes.

Figure 1

Event-by-event particle identification spectrum of the reaction residues from the ${}^{28}$Mg secondary beam. Plotted is the energy loss versus the corrected time of flight measured between scintillators before and after the target. The circle indicates the ${}^{26}$Ne two-proton removal reaction residues of interest.

Figure 2

Extrapolation of the measured cross section for the range of polar angles not covered by HiRA. (a) Solid angle covered by the HiRA array in the configuration used in the present study. (b) Geometric efficiency of the HiRA array. (c) Measured cross section for triple coincidences as a function of $\vartheta$, where “first hit” denotes the detected particle with the lower mass or the higher energy in the case of identical particles (see text).

Figure 3

(a) Missing-mass spectrum for events where two protons were detected. The cross section for observing two protons in coincidence with the ${}^{26}$Ne residue amounts to ${\sigma }_{\mathrm{obs}}^{pp}=0.25\left(2\right)$ mb. The spectrum was fitted with two Gaussian peaks. The lower peak, at the target mass, is due to the diffraction mechanism (green, solid line), and the larger peak is attributed to events where at least one proton was removed in an inelastic collision with the target. (b) Relative diffraction yield as a function of the smaller of the two proton energies, $E_{p_2}$. (c) Missing-mass difference spectrum for events where one of the detected particles is a proton and the other is a light ion, e.g., a deuteron or triton. The individual spectra have been shifted [$\Delta M_{\mathrm{miss}}=M_{\mathrm{miss}}-M{(}^8\mathrm{Be}),M{(}^7\mathrm{Be})$ etc.] and then added. From the fit the ratio of diffraction-stripping to stripping events was extracted.