Quantum Resonances in a Complex-Momentum Basis

Abstract

Resonances are important features of open quantum systems. We study, in particular, unbound and loosely bound nuclear systems. We model 5He and 6He in a few-body picture, consisting of an alpha-particle core with one and two valence neutrons respectively. Basis-expansion theory is briefly explained and then used to expand the nuclear system in the harmonic oscillator and momentum bases. We extend the momentum basis into the complex plane, obtaining solutions that form a Berggren basis. With the complex-momentum method we are able to reproduce experimentally observed resonances in 5He. The 5He Berggren basis solutions are used as a single-particle basis to create many-body states in which we expand the 6He system. For the two-body interaction between the neutrons, we use two different phenomenological models: a Gaussian and a Surface Delta Interaction (SDI). The strength of each interaction is fitted to reproduce the 6He ground state energy. With the Gaussian interaction we do not obtain the 6He resonance, whereas with the SDI we do. The relevant parts of the second quantization formalism is summarized, and we briefly discuss a possible implementation.