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The nuclear shell structure, which originates in the nearly independent motion of nucleons in an average potential, provides an important guide for our understanding of nuclear structure and the underlying nuclear forces. Its most remarkable fingerprint is the existence of the so-called `magic numbers' of protons and neutrons associated with extra stability. Although the introduction of a phenomenological spin-orbit (SO) coupling force in 1949 helped explain the nuclear magic numbers, its origins are still open questions. Here, we present experimental evidence for the smallest SO-originated magic number (subshell closure) at the proton number 6 in 13-20C obtained from systematic analysis of point-proton distribution radii, electromagnetic transition rates and atomic masses of light nuclei. Performing ab initio calculations on 14,15C, we show that the observed proton distribution radii and subshell closure can be explained by the state-of-the-art nuclear theory with chiral nucleon-nucleon and three-nucleon forces, which are rooted in the quantum chromodynamics., Comment: 7 pages, 5 figures

It is a well-known fact that a cluster of nucleons can be formed in the interior of an atomic nucleus, and such clusters may occupy molecular-like orbitals, showing characteristics similar to normal molecules consisting of atoms. Chemical molecules having a linear alignment are commonly seen in nature, such as carbon dioxide. A similar linear alignment of the nuclear clusters, referred to as linear-chain cluster state (LCCS), has been studied since the 1950s, however, up to now there is no clear experimental evidence demonstrating the existence of such a state. Recently, it was proposed that an excess of neutrons may offer just such a stabilizing mechanism, revitalizing interest in the nuclear LCCS, specifically with predictions for their emergence in neutron-rich carbon isotopes. Here we present the experimental observation of {\alpha}-cluster states in the radioactive 14C nucleus. Using the 10Be+{\alpha} resonant scattering method with a radioactive beam, we observed a series of levels which completely agree with theoretically predicted levels having an explicit linear-chain cluster configuration. We regard this as the first strong indication of the linear-chain clustered nucleus., Comment: 15 pages, 3 figures

We have measured for the first time the charge-changing cross sections ($\sigma_{\text{CC}}$) of $^{12-16}$C on a $^{12}$C target at energies below $100A$ MeV. To analyze these low-energy data, we have developed a finite-range Glauber model with a global parameter set within the optical-limit approximation which is applicable to reaction cross section ($\sigma_{\text{R}}$) and $\sigma_{\text{CC}}$ measurements at incident energies from 10$A$ to $2100A$ MeV. Adopting the proton-density distribution of $^{12}$C known from the electron-scattering data, as well as the bare total nucleon-nucleon cross sections, and the real-to-imaginary-part ratios of the forward proton-proton elastic scattering amplitude available in the literatures, we determine the energy-dependent slope parameter $\beta_{\rm pn}$ of the proton-neutron elastic differential cross section so as to reproduce the existing $\sigma_{\text{R}}$ and interaction-cross-section data for $^{12}$C+$^{12}$C over a wide range of incident energies. The Glauber model thus formulated is applied to calculate the $\sigma_{\text{\tiny R}}$'s of $^{12}$C on a $^9$Be and $^{27}$Al targets at various incident energies. Our calculations show excellent agreement with the experimental data. Applying our model to the $\sigma_{\text{\tiny R}}$ and $\sigma_{\text{\tiny CC}}$ for the "neutron-skin" $^{16}$C nucleus, we reconfirm the importance of measurements at incident energies below $100A$ MeV. The proton root-mean-square radii of $^{12-16}$C are extracted using the measured $\sigma_{\text{CC}}$'s and the existing $\sigma_{\text{R}}$ data. The results for $^{12-14}$C are consistent with the values from the electron scatterings, demonstrating the feasibility, usefulness of the $\sigma_{\text{CC}}$ measurement and the present Glauber model., Comment: 8 pages, 4 figures

The resonance structure in $^{11}$C is particularly of interest with regard to the astrophysical $^{7}$Be($\alpha$, $\gamma$) reaction, relevant at high temperature, and to the $\alpha$-cluster structure in $^{11}$C. The measurement was to determine unknown resonance parameters for the high excited states of $^{11}$C. In particular, the $\alpha$ decay width can be useful information to discuss $\alpha$ cluster structure in $^{11}$C. New measurements of the $^{7}$Be+$\alpha$ resonant scattering and the $^{7}$Be($\alpha$, $p$)$^{10}$B reaction in inverse kinematics were performed for center-of-mass energy up to 5.5 MeV, and the resonances at excitation energies of 8.9--12.7 MeV in the compound $^{11}$C nucleus were studied. Inelastic scattering of $^{7}$Be+$\alpha$ and the $^{7}$Be($\alpha$, $p_1$)$^{10}$B$^*$ reaction were also studied with a simultaneous $\gamma$-ray measurement. The measurements were performed at the low-energy RI beam facility CRIB (CNS Radioactive Ion Beam separator) of the Center for Nuclear Study (CNS), the University of Tokyo. We obtained excitation functions of $^{7}$Be($\alpha$, $\alpha_0$)$^{7}$Be (elastic scattering), $^{7}$Be($\alpha$, $\alpha_1$)$^{7}$Be$^*$ (inelastic scattering), $^{7}$Be($\alpha$, $p_0$)$^{10}$B, and $^{7}$Be($\alpha$, $p_1$)$^{10}$B$^*$. Many resonances including a new one were observed and their parameters were determined by an R-matrix analysis. The resonances we observed possibly enhance the $^{7}$Be($\alpha$, $\gamma$) reaction rate but in a smaller magnitude than the lower-lying resonances. A new negative-parity cluster band, similar to the one previously suggested in the mirror nucleus $^{11}$B, is proposed.

A new measurement of proton resonance scattering on 7Be was performed up to the center-of-mass energy of 6.7 MeV using the low-energy RI beam facility CRIB (CNS Radioactive Ion Beam separator) at the Center for Nuclear Study of the University of Tokyo. The excitation function of 7Be+p elastic scattering above 3.5 MeV was measured successfully for the first time, providing important information about the resonance structure of the 8B nucleus. The resonances are related to the reaction rate of 7Be(p, gamma)8B, which is the key reaction in solar 8B neutrino production. Evidence for the presence of two negative parity states is presented. One of them is a 2- state observed as a broad s-wave resonance, the existence of which had been questionable. Its possible effects on the determination of the astrophysical S-factor of 7Be(p, gamma)8B at solar energy are discussed. The other state had not been observed in previous measurements, and its spin and parity were determined as 1-., Comment: 6 pages, 4 figures