Gamow shell model description of the hypernuclei

Hypernuclear physics studies baryon interactions and the structure of exotic atomic nuclei, where strangeness plays a key role in dense matter. High-resolution $\gamma$-ray spectroscopy (e.g., Hyperball at BNL/KEK) and upcoming facilities (J-PARC, JLab) have provided precise data on $p$-shell hypernuclei, constraining $YN$ potentials. We applied the Gamow shell model to $p$-shell hypernuclei to systematically investigate the role of the $\Lambda N$ interaction and its components, and how it affects the mean field of nucleons. The Gamow shell model extends the standard shell model by replacing the harmonic oscillator basis with the Berggren ensemble, treating bound, resonant, and continuum states on equal footing. The effective Hamiltonian includes Woods-Saxon core potentials and two-body interactions (central, spin-orbit, tensor) optimized to experimental data. Our calculations reproduce and predict binding energies, excitation spectra, and densities for hypernuclei from ${}^{5}_{\Lambda}\mathrm{He}$ to ${}^{16}_{\Lambda}\mathrm{O}$ using the same $\Lambda N$ interaction. The tensor force significantly impacts excited-state splittings in bound systems, while its effect is suppressed in unbound cases due to the continuum coupling. The Gamow shell model provides a unified framework for hypernuclei, capturing the interplay between bound, resonant, and continuum states. This work lays the foundation for extending the model to heavier and multi-strange systems.