Fumitaka Endo

We report systematic data on the quasi-free $(p,pt)$ and $(p,p{^{3}{\rm He}})$ reactions of $\mathrm{^{40\text{-}48}Ca}$ isotopes at an incident proton energy of 226 MeV under recoil-less conditions, with the aim of investigating t and ${^{3}{\rm He}}$ cluster correlations in medium-mass nuclei. In addition, data on $\mathrm{^{12}C}$ and $\mathrm{^{16}O}$ were taken to estimate the contribution of $\mathrm{^{16}O}$ impurities originating from surface oxidation of the Ca targets and to provide benchmark data for light $N=Z$ systems. From the experimental data, state-resolved triple differential cross-sections were extracted, together with separation-energy-integrated triple differential cross-sections as a complementary observable. The state-resolved triple differential cross-sections were analyzed within a distorted wave impulse approximation (DWIA) framework, and experimental spectroscopic factors were deduced using Woods–Saxon wave functions. In addition, theoretical triple differential cross-sections were obtained from DWIA calculations employing cluster wave functions derived from generalized relativistic density functional theory (grDFT) and were compared with the experimental results. For the Ca isotopes, pronounced low-lying S-wave peaks are observed in the separation-energy spectra for both the $(p,pt)$ and $(p,p{^{3}{\rm He}})$ channels. The corresponding low-lying S-wave triple differential cross-sections and experimental spectroscopic factors decrease systematically with increasing neutron number for both the t and ${^{3}{\rm He}}$ clusters. Comparisons with grDFT-based DWIA calculations show that the calculated triple differential cross-sections are of the same order of magnitude as the experimental low-lying S-wave triple differential cross-sections and capture their global decreasing trend toward neutron-rich Ca isotopes. The separation-energy-integrated triple differential cross-sections exhibit a clear channel-dependent behavior: the integrated strength decreases for the $(p,p{^{3}{\rm He}})$ channel, whereas it remains nearly constant for the $(p,pt)$ channel. Overall, the present results demonstrate that quasi-free $(p,pX)$ reactions provide a sensitive and versatile probe of cluster correlations in finite nuclei, and strongly motivate further experimental and theoretical studies of t and ${^{3}{\rm He}}$ cluster formation across a wide range of nuclei.

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 Large Acceptance Spectrometer 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 ($0.52 \pm 0.11$). 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.

Deuteron inelastic scattering on $^{86}$Kr was measured in inverse kinematics with the gaseous active target CAT-M, as part of a systematic investigation aimed at determining the nuclear-matter incompressibility. The isoscalar monopole strength distribution was extracted via a multipole decomposition analysis, and the energy of the isoscalar giant monopole resonance was determined to be $17 \pm 1$ MeV. The nuclear incompressibility of $^{86}$Kr and the isospin-dependent term of the nuclear-matter incompressibility are discussed in Section 5.