Establishing the \textrm{\(^{\bold{40}}\)Ca(p,p$\boldsymbolα$)} reaction at 392 MeV under quasi-free scattering conditions

TL;DR

This work establishes a high-energy, high-resolution framework for probing α-clustering in nuclei via the quasi-free reaction Ca-40(p,pα) at 392 MeV. Using the double-arm GR and LAS spectrometers at RCNP, the team achieves state-by-state resolution of the Ar-36 residual spectrum and extracts the α-separation-energy distribution. Distorted-wave impulse approximation analyses with Woods-Saxon α-cluster inputs yield an α-spectroscopic factor of about 0.51, consistent with prior 101.5 MeV measurements, demonstrating energy-independent reaction mechanics under quasi-free conditions. The results validate high-energy (p,pα) measurements as precise, quantitative probes of α clustering and pave the way for broader systematic studies in stable and unstable nuclei.

Abstract

The \( (p,pα) \) reaction offers a direct means to probe preformed \( α\)-cluster structures in nuclei under quasi-free scattering conditions. Previous studies around \SI{100}{MeV} provided valuable insights into \( α\) clustering, but quantitative comparison with microscopic cluster wave functions remained limited due to strong distortion effects. At higher energies, the reaction mechanism becomes simpler and the distorted-wave impulse approximation (DWIA) provides a more reliable framework for quantitative analysis. In the present work, the \isotope[40]{Ca}\( (p,pα) \) reaction was measured at an incident energy of \SI{392}{MeV} using the high-resolution Grand Raiden and LAS spectrometers at RCNP. Despite the small cross section in this energy region, the achieved resolution allowed clear separation of the ground and excited states of the residual \isotope[36]{Ar} nucleus, and corresponding momentum distributions were extracted. %These results provided the first direct evidence of the \( α\)-cluster component in \isotope[40]{Ca} at high energy. DWIA calculations using a Woods--Saxon \( α+ \isotope[36]{Ar} \) bound-state wave function yielded an experimental spectroscopic factor of \( S_{\mathrm{FAC}}^{\mathrm{WS}} = 0.51 \pm 0.05 \), consistent with the previous result at \SI{101.5}{MeV} (\(0.52 \pm 0.23 \)). This agreement demonstrates that the reaction mechanism is well described across a wide energy range. The present study establishes the feasibility of high-precision \( (p,pα) \) measurements at several hundred MeV and highlights their potential as a quantitative probe of \( α\) clustering in medium-mass nuclei, forming the basis for systematic studies in both stable and unstable systems.

Figures (7)

• Figure 1: Schematic layout of the experimental setup with the double-arm spectrometer used for the $(p,p\alpha)$ measurement at RCNP.
• Figure 2: Particle identification at the focal planes of GR (a) and LAS (b). In each panel, the left plot shows the two-dimensional correlation used for particle identification (horizontal position vs. light output in GR, or horizontal position vs. TOT in LAS), while the right plot displays the corresponding projected spectrum after correcting for the position dependence. Distinct bands of protons, deuterons, and $\alpha$ particles are clearly identified.
• Figure 3: Time-difference spectrum between the timing signals of GR and LAS. Multiple peaks appear, reflecting the bunch structure of the cyclotron. The prompt-peak selection window and background-selection windows are indicated. The red line represents the contribution of accidental coincidences evaluated from the side peaks.
• Figure 4: Energy correlation between the proton and the $\alpha$ particle in each coincidence window. Panel (a) shows the prompt-peak selection, where the events are distributed along a line corresponding to constant $T_p + T_\alpha$, demonstrating energy conservation in the $(p,p\alpha)$ reaction. Panel (b) shows the background selection, where the background originating from accidental coincidences exhibits no structure.
• Figure 5: $S_\alpha$ energy spectra constructed under two different coincidence timing conditions. The black line corresponds to the prompt-peak selection, and the red line shows the background estimated from accidental coincidences.