# Two- and three-cluster decays of light nuclei with the hyperspherical harmonics

## TL;DR

This paper investigates the effectiveness of hyperspherical harmonics in modeling two- and three-cluster decay processes in light nuclei, demonstrating their capability to describe bound and scattering states with a limited basis.

## Contribution

It evaluates the applicability of hyperspherical harmonics for describing two-body and three-body continuum states in light nuclear systems with at least one binary decay channel.

## Key findings

- Hyperspherical harmonics can describe bound states in three-cluster systems.
- A restricted set of hyperspherical harmonics suffices for two-body continuum states.
- The method's applicability depends on the system's specific decay channels.

## Abstract

We consider a set of three-cluster systems ($^{4}$He, $^{7}$Li, $^{7}$Be, $^{8}$Be, $^{10}$Be) within a microscopic model which involves the hyperspherical harmonics to represent intercluster motion. We selected such three-cluster systems which have at least one binary channel. Our aim is to study whether the hyperspherical harmonics are able and under what conditions to describe two-body channel(s) (nondemocratic motion) or they are suitable for describing three-cluster continuum only (democratic motion). It is demonstrated that a rather restricted number of the hyperspherical harmonics allows us to describe bound states and scattering states in two-body continuum for a three-cluster system.