Subjecting a physical system to extreme conditions is one of the means often used to obtain a better understanding and deeper insight into its organization and structure. In the case of the atomic nucleus, one such approach is to investigate isotopes that have very different neutron-to-proton (N/Z) ratios than in stable nuclei. Light, neutron-rich isotopes exhibit the most asymmetricN/Zratios and those lying beyond the limits of binding, which undergo spontaneous neutron emission and exist only as very short-lived resonances (about 10⁻²¹ s), provide the most stringent tests of modern nuclear-structure theories. Here we report on the first observation of²⁸O and²⁷O through their decay into²⁴O and four and three neutrons, respectively. The²⁸O nucleus is of particular interest as, with theZ = 8 andN = 20 magic numbers^1,2, it is expected in the standard shell-model picture of nuclear structure to be one of a relatively small number of so-called ‘doubly magic’ nuclei. Both²⁷O and²⁸O were found to exist as narrow, low-lying resonances and their decay energies are compared here to the results of sophisticated theoretical modelling, including a large-scale shell-model calculation and a newly developed statistical approach. In both cases, the underlying nuclear interactions were derived from effective field theories of quantum chromodynamics. Finally, it is shown that the cross-section for the production of²⁸O from a²⁹F beam is consistent with it not exhibiting a closedN = 20 shell structure.

We perform large-scale shell-model calculations of $\beta$-decay properties for neutron-rich nuclei with $13\le Z\le 18$ and $22\le N\le 34$, taking the first-forbidden transitions into account. The natural-parity and unnatural-parity states are calculated in the $0\hslash \omega$ and $1\hslash \omega$ model spaces, respectively, within the full $sd+pf+sdg$ valence shell. The calculated $\beta$-decay half-lives and $\beta$-delayed neutron emission probabilities show good agreement with the experimental data. The first-forbidden transitions make a non-negligible contribution to the half-lives of $N\gtrsim 28$ nuclei. The low-lying Gamow-Teller strengths of even-even nuclei are considerably larger than those of the neighboring odd-$A$ and odd-odd nuclei, strongly affecting the half-lives and neutron emission probabilities. It is shown that this even-odd effect is caused by the $J^{\pi }=1^{+}$ proton-neutron pairing interaction. We derive a formula to represent the positions of the Gamow-Teller giant resonances from the calculated strength distributions.

The cross sections of the ${}^7\mathrm{Be}(n,\alpha ){}^4\mathrm{He}$ reaction for $p$-wave neutrons were experimentally determined at $E_{\mathrm{c}.\mathrm{m}.}=0.20–0.81\mathrm{MeV}$ slightly above the big bang nucleosynthesis (BBN) energy window for the first time on the basis of the detailed balance principle by measuring the time-reverse reaction. The obtained cross sections are much larger than the cross sections for $s$-wave neutrons inferred from the recent measurement at the n_TOF facility in CERN, but significantly smaller than the theoretical estimation widely used in the BBN calculations. The present results suggest the ${}^7\mathrm{Be}(n,\alpha ){}^4\mathrm{He}$ reaction rate is not large enough to solve the cosmological lithium problem, and this conclusion agrees with the recent result from the direct measurement of the $s$-wave cross sections using a low-energy neutron beam and the evaluated nuclear data library ENDF/B-VII.1.

We systematically measured the differential cross sections of inelastic $\alpha$ scattering off self-conjugate $A=4n$ nuclei at two incident energies $E_{\alpha }=130\mathrm{MeV}$ and $386\mathrm{MeV}$ at Research Center for Nuclear Physics, Osaka University. The measured cross sections were analyzed by the distorted-wave Born-approximation (DWBA) calculation using the single-folding potentials, which are obtained by folding macroscopic transition densities with the phenomenological $\alpha N$ interaction. The DWBA calculation with the density-dependent $\alpha N$ interaction systematically overestimates the cross sections for the $\mathrm{\Delta }L=0$ transitions. However, the DWBA calculation using the density-independent $\alpha N$ interaction reasonably well describes all the transitions with $\mathrm{\Delta }L=0$–4. We examined uncertainties in the present DWBA calculation stemming from the macroscopic transition densities, distorting potentials, phenomenological $\alpha N$ interaction, and coupled channel effects in ${}^{12}\mathrm{C}$. It was found that the DWBA calculation is not sensitive to details of the transition densities nor the distorting potentials, and the phenomenological density-independent $\alpha N$ interaction gives reasonable results. The coupled-channel effects are negligibly small for the $2_1^{+}$ and $3_1^{-}$ states in ${}^{12}\mathrm{C}$, but not for the $0_2^{+}$ state. However, the DWBA calculation using the density-independent interaction at $E_{\alpha }=386\mathrm{MeV}$ is still reasonable even for the $0_2^{+}$ state. We concluded that the macroscopic DWBA calculations using the density-independent interaction are reliably applicable to the analysis of inelastic $\alpha$ scattering at $E_{\alpha }\sim 100\mathrm{MeV}/\mathrm{u}$.

The uncertainty quantifications of theoretical results are of great importance in making meaningful comparisons of those results with experimental data and making predictions in experimentally unknown regions. By quantifying uncertainties, one can make more solid statements about, e.g., origins of discrepancy in some quantities between theory and experiment. We propose a novel method for uncertainty quantification for the effective interactions of nuclear shell-model calculations as an example. The effective interaction is specified by a set of parameters, and its probability distribution in the multidimensional parameter space is considered. This enables us to quantify the agreement with experimental data in a statistical manner and the resulting confidence intervals show unexpectedly large variations. Moreover, we point out that a large deviation of the confidence interval for the energy in shell-model calculations from the corresponding experimental data can be used as an indicator of some exotic property, e.g., $\alpha$ clustering. Other possible applications and impacts are also discussed.