Astrophysical S-factor for ${}^6$Li$(p,\gamma )$${}^7$Be in the coupled-channel Gamow shell model

We have applied the Gamow shell model (GSM) in the coupled-channel representation to study the astrophysical $S$-factor for the proton radiative capture reaction of ${}^6$Li. Reaction channels are built by coupling the proton wave function expanded in different partial waves with the GSM wave functions of the ground state ($1^{+}$) and the excited states ($3_1^{+}$, $0_1^{+}$ and $2_1^{+}$) of ${}^6$Li. All relevant $E1$, $M1$, and $E2$ transitions from the initial continuum states in ${}^7$Be to the final bound states (${3\mathrm{/}2}_1^{-}$ and ${1\mathrm{/}2}_1^{-}$) states are included. It is found that the calculated total astrophysical $S$ factor for this reaction agrees well with the experimental data.