First Observation of Mirror t and 3He Clusters in Stable Ca Isotopes via Quasi-free ( p , pt ) and ( p , p 3He) Reactions

Abstract 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.