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Nuclear three-body problem in the complex energy plane: Complex-Scaling-Slater method

The physics of open quantum systems is an interdisciplinary area of research. The nuclear "openness" manifests itself through the presence of the many-body continuum representing various decay, scattering, and reaction channels. As the radioactive nuclear beam experimentation extends the known nuclear landscape towards the particle drip lines, the coupling to the continuum space becomes exceedingly more important. Of particular interest are weakly bound and unbound nuclear states appearing around particle thresholds. Theories of such nuclei must take into account their open quantum nature. To describe open quantum systems, we introduce a Complex Scaling (CS) approach in the Slater basis. We benchmark it with the complex-energy Gamow Shell Model (GSM) by studying energies and wave functions of the bound and unbound states of the two-neutron halo nucleus 6He viewed as an $α$+ n + n cluster system. In the CS approach, we use the Slater basis, which exhibits the correct asymptotic behavior at large distances. To extract particle densities from the back-rotated CS solutions, we apply the Tikhonov regularization procedure, which minimizes the ultraviolet numerical noise. While standard applications of the inverse complex transformation to the complex-rotated solution provide unstable results, the stabilization method fully reproduces the GSM benchmark. We also propose a method to determine the smoothing parameter of the Tikhonov regularization. The combined suite of CS-Slater and GSM techniques has many attractive features when applied to nuclear problems involving weakly-bound and unbound states. While both methods can describe energies, total widths, and wave functions of nuclear states, the CS-Slater method, if it can be applied, can provide an additional information about partial energy widths associated with individual thresholds.