Multiple Mechanisms in Proton-Induced Nucleon Removal at $\sim 100\mathrm{MeV}/\text{Nucleon}$

We report on the first proton-induced single proton- and neutron-removal reactions from the neutron-deficient ${}^{14}\mathrm{O}$ nucleus with large Fermi-surface asymmetry $S_n-S_p=18.6\mathrm{MeV}$ at $\sim 100\mathrm{MeV}/\text{nucleon}$, a widely used energy regime for rare-isotope studies. The measured inclusive cross sections and parallel momentum distributions of the ${}^{13}\mathrm{N}$ and ${}^{13}\mathrm{O}$ residues are compared to the state-of-the-art reaction models, with nuclear structure inputs from many-body shell-model calculations. Our results provide the first quantitative contributions of multiple reaction mechanisms including the quasifree knockout, inelastic scattering, and nucleon transfer processes. It is shown that the inelastic scattering and nucleon transfer, usually neglected at such energy regime, contribute about 50% and 30% to the loosely bound proton and deeply bound neutron removal, respectively. These multiple reaction mechanisms should be considered in analyses of inclusive one-nucleon removal cross sections measured at intermediate energies for quantitative investigation of single-particle strengths and correlations in atomic nuclei.

Figure 1

Particle identification of projectilelike residues. Particle’s velocity ($\nu$) is deduced from TOF. Combining $B\rho$ and velocity allows to determine particle’s mass-to-charge ratio $A/Q$. $Z_{\mathrm{eff}}$ is the deduced effective atomic number with $\mathrm{\Delta }E$ and velocity using the Bethe-Bloch formula. The energy deposit of a charged particle in a material is related to its velocity, charge, and mass, as shown in the $\mathrm{\Delta }E\text{−}\nu$ spectra with (w/) the $A/Q$ selections from 1.59 to 1.66 (b) and from 1.81 to 1.93 (c). Black contours in (b) and (c) select ${}^{13}\mathrm{O}$ and ${}^{13}\mathrm{N}$, respectively.

Figure 2

Parallel momentum distributions of ${}^{13}\mathrm{N}$ and ${}^{13}\mathrm{O}$. The black-filled markers show the experimental data. The orange bands represent the uncertainties from the background subtractions. The gray empty bins indicate the other systematic uncertainties. Panels (a)–(c) compare the data to DWIA and QTC calculations (blue dotted lines), with additional contributions from inelastic excitation for ${}^{13}\mathrm{N}$ and $(p,d)$ transfer for ${}^{13}\mathrm{O}$ (red dashed lines). Panel (d) displays the QTC calculation as a black solid line, while the calculation without ($\mathrm{w}/\mathrm{o}$) $(p,d)$ transfer is represented by a blue dotted line. The blue solid line in (a) shows the distribution of the unreacted ${}^{14}\mathrm{O}$ beam (shifted by $-200\mathrm{MeV}/c$) to demonstrate the experimental response, which introduces a shift and broadening of the momentum due to energy losses and detector resolutions. Theoretical distributions have been convoluted with the experimental response and their integrals have been normalized to the experimental cross sections, without any momentum shift to match the data. Note that the sharp $(p,d)$ transfer peak is smoothed out by the experimental response. See SM [58] for theoretical distributions before experimental response convolution.

Figure 3

$R_s$ as a function of $\mathrm{\Delta }S$ from the present work (blue dots and black squares) compared to the trend extracted from Be or C induced nucleon-removal cross sections analyzed with the eikonal model [19, 20, 21] (gray shaded region). The square brackets indicate the total systematic uncertainties. Red solid and black dashed lines are shown to guide the eyes.