The two protons emitted in the decay of ${}^{54}\mathrm{Zn}$ have been individually observed for the first time in a time projection chamber. The total decay energy and the half-life measured in this work agree with the results obtained in a previous experiment. Angular and energy correlations between the two protons are determined and compared to theoretical distributions of a three-body model. Within the shell model framework, the relative decay probabilities show a strong contribution of the $p^2$ configuration for the two-proton emission. After ${}^{45}\mathrm{Fe}$, the present result on ${}^{54}\mathrm{Zn}$ constitutes only the second case of a direct observation of the ground state two-proton decay of a long-lived isotope.

Forbidden nonunique $\beta$ decays feature shape functions that are complicated combinations of different nuclear matrix elements and phase-space factors. Furthermore, they depend in a very nontrivial way on the values of the weak coupling constants, $g_{\mathrm{V}}$ for the vector part and $g_{\mathrm{A}}$ for the axial-vector part. In this work we include also the usually omitted second-order terms in the shape functions to see their effect on the computed decay half-lives and electron spectra ($\beta$ spectra). As examples we study the fourth-forbidden nonunique ground-state-to-ground-state ${\beta }^{-}$ decay branches of ${}^{113}\mathrm{Cd}$ and ${}^{115}\mathrm{In}$ using the microscopic quasiparticle-phonon model and the nuclear shell model. A striking new feature that is reported in this paper is that the calculated shape of the $\beta$ spectrum is quite sensitive to the values of $g_{\mathrm{V}}$ and $g_{\mathrm{A}}$ and hence comparison of the calculated with the measured spectrum shape opens a way to determine the values of these coupling constants. This article is designed to show the power of this comparison, coined spectrum-shape method (SSM), by studying the two exemplary $\beta$ transitions within two different nuclear-structure frameworks. While the SSM seems to confine the $g_{\mathrm{V}}$ values close to the canonical value $g_{\mathrm{V}}=1.0$, the values of $g_{\mathrm{A}}$ extracted from the half-life data and by the SSM emerge contradictory in the present calculations. This calls for improved nuclear-structure calculations and more measured data to systematically employ SSM for determination of the effective value of $g_{\mathrm{A}}$ in the future.

A significant fraction of stars between 7 and 11 solar masses are thought to become supernovae, but the explosion mechanism is unclear. The answer depends critically on the rate of electron capture on ${}^{20}\mathrm{Ne}$ in the degenerate oxygen-neon stellar core. However, because of the unknown strength of the transition between the ground states of ${}^{20}\mathrm{Ne}$ and ${}^{20}\mathrm{F}$, it has not previously been possible to fully constrain the rate. By measuring the transition, we establish that its strength is exceptionally large and that it enhances the capture rate by several orders of magnitude. This has a decisive impact on the evolution of the core, increasing the likelihood that the star is (partially) disrupted by a thermonuclear explosion rather than collapsing to form a neutron star. Importantly, our measurement resolves the last remaining nuclear physics uncertainty in the final evolution of degenerate oxygen-neon stellar cores, allowing future studies to address the critical role of convection, which at present is poorly understood.

In the noisy intermediate-scale quantum era, variational algorithms have become a standard approach to solving quantum many-body problems. Here, we present variational quantum eigensolver results of selected oxygen isotopes within the shell-model description. The aim of the present work is to locate the neutron drip line of the oxygen chain using unitary coupled cluster type Ansätze with different microscopic interactions (DJ16, JISP16, and N3LO), in addition to a phenomenological USDB interaction. While initially infeasible to execute on contemporary quantum hardware, the size of the problem is reduced significantly using qubit tapering techniques in conjunction with custom circuit design and optimization. The optimal values of Ansatz parameters from classical simulation are taken for the DJ16 interaction, and the tapered circuits are run on IonQ's Aria, a trapped-ion quantum computer. After applying gate error mitigation for three isotopes, we reproduced exact ground-state energies within a few percent error. The postprocessed results from hardware also clearly show ${}^{24}\mathrm{O}$ as the drip line nucleus of the oxygen chain. Future improvements in quantum hardware could make it possible to locate drip lines of heavier nuclei.

The $T_z=-\frac{3}{2}$ nucleus ${}^{21}\mathrm{Mg}$ has been studied by Coulomb excitation on ${}^{196}\mathrm{Pt}$ and ${}^{110}\mathrm{Pd}$ targets. A 205.6(1)-keV $\gamma$-ray transition resulting from the Coulomb excitation of the ${\frac{5}{2}}^{+}$ ground state to the first excited ${\frac{1}{2}}^{+}$ state in ${}^{21}\mathrm{Mg}$ was observed for the first time. Coulomb excitation cross-section measurements with both targets and a measurement of the half-life of the ${\frac{1}{2}}^{+}$ state yield an adopted value of $B(E2;{\frac{5}{2}}^{+}\to {\frac{1}{2}}^{+})=13.3\left(4\right)$ W.u. A new excited state at 1672(1) keV with tentative ${\frac{9}{2}}^{+}$ assignment was also identified in ${}^{21}\mathrm{Mg}$. This work demonstrates a large difference in the $B(E2;{\frac{5}{2}}^{+}\to {\frac{1}{2}}^{+})$ value between $T=\frac{3}{2}, A=21$ mirror nuclei. The difference is investigated in the shell-model framework employing both isospin conserving and breaking USD interactions and using modern ab initio nuclear structure calculations, which have recently become applicable in the $sd$ shell.