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

The $(p,p α)$ reaction offers a direct means to probe preformed $α$-cluster structures in nuclei under quasi-free scattering conditions. Previous studies around 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 $^{40}$Ca$(p,pα)$ reaction was measured at an incident energy of 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 $^{36}$Ar nucleus, and corresponding momentum distributions were extracted. DWIA calculations using a Woods-Saxon $α+ ^{36}$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 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.

💡 Research Summary

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The paper reports a high‑energy (p,pα) experiment performed on 40Ca at an incident proton energy of 392 MeV, aiming to establish the reaction as a quantitative probe of pre‑formed α‑cluster structures under quasi‑free scattering (QFS) conditions. Historically, (p,pα) studies around 100 MeV have provided valuable qualitative information on α clustering, but strong distortion effects and final‑state interactions (FSI) limited the reliability of distorted‑wave impulse approximation (DWIA) analyses. By moving to several hundred MeV, the authors exploit the reduced absorption of optical potentials, the suppression of FSI, and a kinematic regime that closely mimics free p–α elastic scattering, thereby simplifying the reaction mechanism.

The experiment was carried out at the Research Center for Nuclear Physics (RCNP) in Osaka using the Ring Cyclotron to deliver a 392 MeV proton beam with an energy spread of <200 keV (FWHM) and a spot size of ~1 mm. A self‑supporting natural Ca target (11.8 mg cm⁻², 96.9 % 40Ca) was placed perpendicular to the beam. The outgoing proton and α particle were detected in coincidence with the Grand Raiden (GR) and Large Acceptance Spectrometer (LAS), positioned at laboratory angles of 46.26° and 58.56°, respectively. This configuration corresponds to a p–α center‑of‑mass scattering angle of 60°, chosen to achieve recoil‑less kinematics for the residual 36Ar nucleus (Q = −7.038 MeV). The central kinetic energies after the spectrometers were 318.59 MeV for protons and 66.37 MeV for α particles. High‑resolution focal‑plane detectors (multi‑wire drift chambers and plastic scintillators) provided precise tracking and energy‑loss information; α energies between 50 and 90 MeV were accepted, and low‑energy α detection was facilitated by using time‑over‑threshold signals from the drift chambers.

Data were accumulated for 8 hours (50 nA for 4 h, 100 nA for 4 h). The overall energy resolution, dominated by target thickness effects, was about 0.4 MeV (σ), sufficient to resolve the ground state of 36Ar and its low‑lying excited states (e.g., 2.0 MeV, 3.3 MeV). Momentum distributions of the knocked‑out α clusters were extracted for each final state. DWIA calculations employed optical potentials scaled from the well‑tested 100 MeV parametrizations and a Woods‑Saxon α + 36Ar bound‑state wave function. The calculated momentum profiles reproduced the measured spectra, and the extracted spectroscopic factor for the α cluster, S_FAC^WS = 0.51 ± 0.05, is in excellent agreement with the previously reported value at 101.5 MeV (0.52 ± 0.23). This consistency across a factor of four in beam energy demonstrates that the DWIA framework remains robust at several hundred MeV and that the reaction mechanism is dominated by a single‑step quasi‑free knockout.

The authors emphasize several implications. First, the successful high‑resolution measurement at 392 MeV proves that (p,pα) reactions can be performed with sufficient statistics despite the rapidly decreasing cross section, provided a high‑intensity beam and thin target are used. Second, the agreement of spectroscopic factors validates the use of simple Woods‑Saxon bound‑state wave functions and DWIA for quantitative extraction of α‑cluster strengths, opening the way to compare directly with microscopic cluster models such as AMD or GCM. Third, the methodology is readily extendable to heavier or more exotic nuclei (e.g., Sn isotopes, neutron‑rich systems), where α clustering is of current theoretical interest. The authors note that similar setups have already been applied to tin isotopes at 400 MeV, but limited resolution prevented state‑by‑state analyses; the present work shows that with optimized target thickness and spectrometer settings, such limitations can be overcome.

In conclusion, the paper establishes the 40Ca(p,pα) reaction at 392 MeV as a reliable, high‑precision tool for probing α‑cluster components in medium‑mass nuclei under quasi‑free conditions. The demonstrated consistency with low‑energy data validates the DWIA approach across a wide energy range and provides a solid experimental foundation for systematic studies of α clustering in both stable and radioactive nuclei. Future work will likely focus on mapping the mass and isotopic dependence of α‑cluster spectroscopic factors, thereby offering stringent tests for modern nuclear structure theories.