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According to standard stellar evolution, lithium abundance is believed to bea useful indicator of the stellar age. However, many evolved stars like redgiants show huge fluctuations around expected theoretical abundances that arenot yet fully understood. The better knowledge of nuclear reactions thatcontribute to the creation and destruction of lithium can help to solve thispuzzle. In this work we apply the Gamow shell model (GSM) formulated in thecoupled-channel representation (GSM-CC) to investigate the mirror radiativecapture reactions $^6$Li$(p,\gamma)$$^7$Be and $^6$Li$(n,\gamma)$$^7$Li. Thecross-sections are calculated using a translationally invariant Hamiltonianwith the finite-range interaction which is adjusted to reproduce spectra,binding energies and one-nucleon separation energies in $^{6-7}$Li, $^7$Be. Allrelevant $E1$, $M1$, and $E2$ transitions from the initial continuum states tothe final bound states $J={3/2}_1^-$ and $J={1/2}^-$ of $^7$Li and $^7$Be areincluded. We demonstrate that the $s$-wave radiative capture of proton(neutron) to the first excited state $J^{\pi}=1/2_1^+$ of $^7$Be ($^7$Li) iscrucial and increases the total astrophysical $S$-factor by about 40 \%.

Gamow shell model description of radiative capture reactions $^6$Li$(p,\gamma)$$^7$Be and $^6$Li$(n,\gamma)$$^7$Li