Decay of three-body resonances in a discrete basis

TL;DR

This paper develops a theoretical method to analyze the decay properties of three-body resonances using a discrete basis, with applications to neutron decay in beryllium-16, revealing dominant decay pathways and neutron correlations.

Contribution

It introduces a new formalism combining inhomogeneous Schrödinger equations and hyperspherical expansion to accurately compute three-body resonance decay characteristics.

Findings

Decay dominated by lowest hypermomentum components.

Neutron-neutron correlations observed in energy distributions.

Results align with direct two-neutron emission experiments.

Abstract

We present a theoretical framework for calculating the asymptotic properties and decay dynamics of three-body resonances described in a discrete basis. The method involves solving an inhomogeneous Schr\"odinger equation to determine the non-normalizable resonant state by identifying a normalizable source state, which captures the short-range internal structure. The long-range behavior is then calculated using the free three-body propagator, providing accurate asymptotic coefficients necessary for describing decay correlations. We apply this formalism to the two-neutron decay of the 0$^{+}$ ground-state and the 2$^{+}$ excited-state resonances of $^{16}\text{Be}$ ($^{14}\text{Be}+n+n$), working within the hyperspherical expansion method with an analytical transformed harmonic oscillator basis. Our results show that the decay is strongly dominated by the lowest hypermomentum components at large separations, reflecting effective three-body barrier penetration dynamics that shape the final state. The calculated relative-energy distributions exhibit clear neutron-neutron correlations for both states, arising from mixing between different asymptotic channels, and are consistent with a direct two-neutron emission mechanism, in agreement with recent experimental observations. This work provides a reliable tool for linking the internal structure of three-body resonances to their decay properties.