Resonances of A=4 T=1 isospin triplet states within the ab initio no-core Gamow shell model

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 ${1}^{\ensuremath{-}}$ excited state almost degenerates with the ${2}^{\ensuremath{-}}$ 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.