The existence of multineutron systems has always been a debatable question. Indeed, both internucleon correlations and a large continuum coupling occur in these states. We then employ the ab initio no-core Gamow shell model to calculate the resonant energies and widths of the trineutron and tetraneutron systems with realistic interactions. Our results indicate that trineutron and tetraneutron are both unbound and bear broad widths. The calculated energy and width of tetraneutron are also comparable with recent experimental data. Moreover, our calculations suggest that the energy of trineutron is lower than that of tetraneutron, while its resonance width is also narrower. This strongly suggests that trineutron is more likely to be experimentally observed than tetraneutron. We thus suggest experimentalists to search for trineutron at low energy.

We apply the Gamow shell model to study ${}^{25–31}\mathrm{F}$ isotopes. As both internucleon correlations and continuum coupling are properly treated therein, the structure shape of ${}^{31}\mathrm{F}$ at large distance can be analyzed precisely. For this, one-nucleon densities, root-mean-square radii, and correlation densities are calculated in neutron-rich fluorine isotopes. It is then suggested that ${}^{31}\mathrm{F}$ exhibits a two-neutron halo structure, built from both continuum coupling and nucleon-nucleon correlations.

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 $A=4$ nuclei, i.e., ${}^4\mathrm{H}, {}^4\mathrm{He}$, and ${}^4\mathrm{Li}$, establish an interesting isospin $T=1$ isobaric system. ${}^4\mathrm{H}$ and ${}^4\mathrm{Li}$ are unbound broad resonances, whereas ${}^4\mathrm{He}$ is deeply bound in its ground state but unbound in all its excited states. The present situation is that experiments so far have not given consistent data on the resonances. Few-body calculations have well studied the scatterings of the $4N$ systems. In the present work, we provide many-body calculations of the broad resonance structures, in an ab initio framework with modern realistic interactions. It occurs that, indeed, ${}^4\mathrm{H}, {}^4\mathrm{Li}$, and excited ${}^4\mathrm{He}$ are broad resonances, which is in accordance with experimental observations. The calculations also show that the first $1^{-}$ excited state almost degenerates with the $2^{-}$ ground state in the pair of mirror isobars of ${}^4\mathrm{H}$ and ${}^4\mathrm{Li}$, which may suggest that the experimental data on energy and width are the mixture of the ground state and the first excited state. The $T=1$ isospin triplet formed with an excited state of ${}^4\mathrm{He}$ and ground states of ${}^4\mathrm{H}$ and ${}^4\mathrm{Li}$ is studied, focusing on the effect of isospin symmetry breaking.

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.