Double pole $S$-matrix singularity in the continuum of ${}^7$Be

The double pole singularity of the $S$-matrix, the so-called exceptional point, associated with the $5\mathrm{/}{2}^{-}$ doublet of resonances in the spectrum of ${}^7$Be has been identified in the framework of the Gamow shell model. The exceptional point singularity is demonstrated by the coalescence of wave functions and spectral functions of the two resonances, as well as by the singular behavior of spectroscopic factors and electromagnetic transitions.