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The production of $^7$Be and $^7$Li nuclei plays an important role inprimordial nucleosynthesis, nuclear astrophysics, and fusion energy generation.The $^3\mathrm{He}(\alpha , \gamma) ^7\mathrm{Be}$ and $^3\mathrm{H}(\alpha ,\gamma) ^7\mathrm{Li}$ radiative-capture processes are important to determinethe $^7$Li abundance in the early universe and to predict the correct fractionof pp-chain branches resulting in $^7$Be versus $^8$B neutrinos. In this workwe study the properties of $^7$Be and $^7$Li within the no-core shell modelwith continuum (NCSMC) method, using chiral nucleon-nucleon interactions as theonly input, and analyze all the binary mass partitions involved in theformation of these systems. The NCSMC is an ab initio method applicable tolight nuclei that provides a unified description of bound and scattering statesand thus is well suited to investigate systems with many resonances andpronounced clustering like $^7$Be and $^7$Li. Our calculations reproduce allthe experimentally known states of the two systems and provide predictions forseveral new resonances of both parities. Some of these new possible resonancesare built on the ground states of $^6$Li and $^6$He, and thus represent arobust prediction. We do not find any resonance in the p${+}^6$Li masspartition near the threshold. On the other hand, in the p${+}^6$He masspartition of $^7$Li we observe an $S$-wave resonance near the thresholdproducing a very pronounced peak in the calculated S factor of the$^6\mathrm{He} (\mathrm{p},\gamma) ^7\mathrm{Li}$ radiative-capture reaction,which could be relevant for astrophysics and its implications should beinvestigated.

$^7$Be and $^7$Li nuclei within the no-core shell model with continuum