Establishing the $^{40}$Ca$(p,p \alpha)$ reaction at 392 MeV under quasi-free scattering conditions
The $(p,p \alpha)$ reaction offers a direct means to probe preformed $\alpha$-cluster structures in nuclei under quasi-free scattering conditions. Previous studies around 100 MeV provided valuable insights into $\alpha$ 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$(p,p\alpha)$ 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 $\alpha + ^{36}$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 $(p,p\alpha)$ measurements at several hundred MeV and highlights their potential as a quantitative probe of $\alpha$ clustering in medium-mass nuclei, forming the basis for systematic studies in both stable and unstable systems.