Isospin-symmetry breaking is responsible for the energy difference of excited states in mirror nuclei. It also influences the coefficient of the isobaric multiplet mass equation. In the present work, we extensively investigate isospin-symmetry breaking in medium-mass nuclei within ab initio frameworks. For this, we employ the ab initio valence-space in-medium similarity renormalization group approach, in which charge-symmetry and charge-independence breakings are included in the adopted nuclear force. The mirror energies of $sd$- and $pf$-shell nuclei are computed for that matter. The effects of single-particle states on weakly bound and unbound nuclear states, especially those of the $s$ wave, are discussed. Predictions are also made concerning proton drip-line nuclei bearing large mirror energy difference. Finally, the coefficient of the isobaric multiplet mass equation in $T=1/2$ and $T=1$ isospin multiplets for $A=18$ to $A=76$ is calculated.

The Gamow shell model (GSM) is a powerful method for the description of the exotic properties of drip line nuclei. Internucleon correlations are included via a configuration interaction framework. Continuum coupling is directly included at basis level by using the Berggren basis, in which, bound, resonance, and continuum single-particle states are treated on an equal footing in the complex momentum plane. Two different types of Gamow shell models have been developed: its first embodiment is that of the GSM defined with phenomenological nuclear interactions, whereas the GSM using realistic nuclear interactions, called the realistic Gamow shell model, was introduced later. The present review focuses on the recent applications of the GSM to drip line nuclei.

Proton-rich nuclei possess unique properties in the nuclear chart. Due to the presence of both continuum coupling and Coulomb interaction, phenomena such as halos, Thomas-Ehrman shift, and proton emissions can occur. Relevant experimental data are difficult to obtain, so that theoretical calculations are needed to understand nuclei at drip lines and to guide experimentalists. In particular, the ${}^{16}\mathrm{Ne}$ and ${}^{18}\mathrm{Mg}$ isotopes are supposed to be one-proton and/or two-proton emitting nuclei, but associated experimental data are either incomplete or even unavailable. Consequently, we performed Gamow shell model calculations of carbon isotones bearing $A=15\text{–}18$. Isospin-symmetry breaking occurring in carbon isotones and isotopes is also discussed. It is hereby shown that the mixed effects of continuum coupling and Coulomb interaction at drip lines generate complex patterns in isospin multiplets. Added to that, it is possible to determine the one-proton and two-proton widths of ${}^{16}\mathrm{Ne}$ and ${}^{18}\mathrm{Mg}$. Obtained decay patterns are in agreement with those obtained in previous experimental and theoretical works. Moreover, to our knowledge, this is the first theoretical calculation of binding energy and partial decay widths of ${}^{18}\mathrm{Mg}$ in a configuration interaction picture.

We report here the first observation of the $0_2^{+}$ state of ${}^8\mathrm{He}$, which has been predicted to feature the condensatelike $\alpha +{}^{2}n+{}^{2}n$ cluster structure. We show that this state is characterized by a spin parity of $0^{+}$, a large isoscalar monopole transition strength, and the emission of a strongly correlated neutron pair, in line with theoretical predictions. Our finding is further supported by the state-of-the-art microscopic $\alpha +4n$ model calculations. The present results may lead to new insights into clustering in neutron-rich nuclear systems and the pair correlation and condensation in quantum many-body systems under strong interactions.

Using the Bρ-defined isochronous mass spectrometry technique, we conducted the first mass measurement of the proton dripline nucleus ^{22}Si. We confirm that ^{22}Si is bound against particle emission with S_{p}/S_{2p}=+1412(114)/+229(54) keV, fixing the proton dripline location for the Si element. By analyzing the mass differences of the neighboring sd-shell nuclei, we find that ^{22}Si exhibits a doubly magic character similar to its mirror partner ^{22}O, and that the mirror energy difference of ^{22}Si-^{22}O deviates from the predictions assuming mirror symmetry. Gamow shell-model calculations reveal that the average occupations of valence protons in ^{22}Si are nearly identical to those of valence neutrons in ^{22}O, supporting the Z=14 magicity in ^{22}Si. The observed mirror-symmetry breaking is attributed to the extended proton distribution in ^{22}Si arising from a small contribution of the unbound π2s_{1/2} orbital.