Although they are among the lightest nuclei, the hydrogen isotopes are not well understood both experimentally and theoretically. Indeed, besides the deuteron and triton, all known hydrogen isotopes are resonances of complex structure. Even more elusive is ${}^7\mathrm{H}$, which may have been observed experimentally and has been claimed to be a narrow resonance. Nevertheless, even its existence is controversial, and its theoretical study is difficult due to both its unbound character and large number of interacting valence nucleons. It is then the object of this paper to theoretically study the hydrogen isotopes ${}^{4–7}\mathrm{H}$ with the Gamow shell model and to perform, to our knowledge, the first direct calculation of unbound resonance hydrogen isotopes up to ${}^7\mathrm{H}$. As the Gamow shell model includes both continuum coupling and internucleon correlations, useful information can be obtained about poorly known unbound hydrogen isotopes. Our present calculations indicate that ${}^{4,6}\mathrm{H}$ ground states are fairly broad resonances, whereas those of ${}^{5,7}\mathrm{H}$ are narrow, which is in accordance with current experimental data. The results then suggest that, in particular, ${}^{5,7}\mathrm{H}$ should be more heavily studied, as they might well be among the most narrow neutron resonances of the light nuclear chart.

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• Lifetimes & widths
• Nuclear binding
• Nuclear many-body theory
• Shell model
• 6 ≤ A ≤ 19
• A ≤ 5