Quantum systems lying close to the decay threshold experience coupling to the scattering environment, hence they belong to a class of open quantum systems (OQSs).The study of OQSs requires proper treatment of non-localized scattering states and resonances. The Gamow shell model (GSM), as an extension of the traditional shell model formulated in the complex-momentum (k) plane, can properly treat the structural and decay properties of these threshold systems by employing the Berggren ensemble as the single-particle (s.p.) basis. In this thesis, GSM has been used to study two types of OQSs:(i) atomic systems such as quadrupolar anions and anions bounded by a multipolar Gaussian potential; and (ii) light nuclei, such as lithium isotopes and their mirror partners. In atomic systems, low-l channels are found to be essential in defining the trajectories of resonant states near the dissociation threshold. In nuclear systems, a finite-range interaction has been optimized to give a realistic description of the spectra, ranging from well-bound systems to unbound nuclei above the decay threshold.
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