Systematic analysis of proton- and deuteron-induced one-proton knockout reactions

TL;DR

The study addresses why the one-proton knockout cross section induced by deuterons is about 1.5 times that induced by protons, instead of the naively expected ~4. It introduces DWIA for protons and an extended DWIA-BU framework that includes deuteron breakup to describe deuteron-induced knockout, comparing with data for neutron-rich nuclei. The key finding is that deuteron breakup and absorption differences fundamentally shape the ratio, with DWIA-BU reproducing the observed ~1.4–1.5 range while DWIA alone underestimates the data; the ratio also depends on the bound-state angular momentum via radial wavefunctions. These results clarify the mechanism behind the observed enhancement and offer a path to extending the approach to inclusive reactions and other projectiles in neutron-rich systems.

Abstract

The ratios of the one-proton knockout cross sections by a deuteron to those by a proton are about 1.5, indicating that using deuteron is more efficient than proton in yielding large knockout cross sections. However, this ratio differs from the intuitive expectation, and its underlying mechanism remains unclear. The purpose of this study is to clarify the mechanism behind the observed ratio by theoretically describing and analyzing the deuteron- and proton-induced one-proton knockout reactions. Proton-induced one-proton knockout reactions are described within the standard distorted-wave impulse approximation (DWIA) framework, while deuteron-induced one-proton knockout reactions are treated with a new approach, DWIA-BU, that incorporates deuteron breakup into the DWIA. The ratios calculated with the DWIA-BU reproduce the experimental data reasonably, whereas those with the DWIA significantly underestimate them. The ratio of the corresponding elementary cross sections remains about 3.5 regardless of the energy, and the difference in absorption between the deuteron and the proton influences the ratios of knockout cross sections, resulting in agreement between the calculated ratios and the experimental data. It is found that the deuteron breakup is essential to reproduce the experimental ratio. The ratios of the knockout cross sections are primarily determined by the difference in the elementary cross sections and that in the absorption between the deuteron and the proton.

Figures (10)

• Figure 1: Definition of coordinates of the A($p,2p$)B and A($d,dp$)B reactions.
• Figure 2: The ratios of the cross sections induced by a deuteron to those by a proton for the 12 neutron-rich nuclei at around 240 MeV per nucleon. The filled circles, the filled triangles, and the filled square represent the results obtained with the DWIA-BU, DWIA, and PWIA-BU. Experimental data are taken from Ref. miwa2019.
• Figure 3: Energy distributions of the weights $W^{p}_{j}$ (red) and $W^{d}_{j}$ (blue) for $^{58}\mathrm{Ti}$, calculated with the PWIA and PWIA-BU, respectively. The weights $W^{p}_{j}$ and $W^{d}_{j}$ are defined in Eq. \ref{['eq_weight']}. The horizontal axis shows the energy per nucleon of the elementary process in the proton-rest frame
• Figure 4: $dp$ total cross section $\sigma_{dp}^{\rm tot}$ (black solid line) and $pN$ total cross section $\sigma_{pp}^{\rm tot}$ (red dashed line) as a function of the incident energy per nucleon in the proton-rest frame. As for $\sigma_{pp}^{\rm tot}$, the parametrization in Ref. bertulani2010 is adopted.
• Figure 5: Same as Fig. \ref{['Fig_hist_58Ti_PW']} but calculated with the DWIA and DWIA-BU.