The Complex Scaling Method for Many-Body Resonances and Its Applications to Three-Body Resonances

TLDR

Resonance phenomena are well known in quantum physics, yet a complete physical, mathematical, or computational description of many-body resonances remains elusive, especially after recent experimental focus on unstable nuclei and heavy‑ion reactions. This article summarizes recent studies of the complex scaling method for treating many‑body resonances and its applications to three‑body resonant states in two‑neutron halo nuclei and three‑cluster systems. The complex scaling method is applied to many‑body systems, enabling resonant states of three‑body systems to be treated in the same way as two‑body systems. The method now allows resonant states of three‑body systems to be treated equivalently to two‑body systems.

Abstract

Resonance phenomena in quantum physics are very familiar in many fields of physics, but we have not yet obtained a complete physical understanding, mathematical description or computational treatment, especially in the case of many-body resonances. Recently, in experimental developments concerning unstable nuclear physics and heavy-ion nuclear reactions, much interest has been concentrated on many-body resonance problems. In the last quarter century, theoretical and mathematical treatments of many-body resonances have experienced great development through application of the complex scaling method (CSM). We can now treat resonant states of three-body systems in the same way as those of two-body systems. In this article, starting from the definition of a resonant state and discussion of its norm, we present a summary of recent studies of CSM to treat many-body resonances and applications to three-body resonant states in two-neutron halo nuclei and three-cluster systems.