Decay of three-body resonances in a discrete basis

TL;DR

The paper addresses how to connect the internal structure of three-body resonances near the dripline to observable decay correlations. It develops an inhomogeneous Schrödinger equation in a discrete three-body basis, identifying a square-normalizable source state via a resonance-operator approach, and propagates the long-range part with a free three-body propagator within a hyperspherical THO framework to obtain asymptotic coefficients. The method is applied to 16Be (14Be + n + n) for the 0^+ ground state and 2^+ first excited state, showing that asymptotics are dominated by the lowest hypermomentum channels and yielding neutron-neutron correlations consistent with direct two-neutron emission. This framework provides a general tool to link short-range three-body dynamics to decay observables in dripline and Borromean nuclei, with potential extensions to core excitations and angular distributions for other two-neutron emitters.

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 Schrödinger 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.

Figures (6)

• Figure 1: Hyperradial wave functions of the source state for the 0$^+$ (top panel) and 2$^+$ (bottom panel) resonances of $^{16}$Be. The different lines correspond to relevant channels labeled by $\beta\equiv\{K,l_x,l_y,l,S_x\}$ in the Jacobi-T set.
• Figure 2: Spatial probability density distribution of the source state for the resonances $0^+$ (top panel) and $2^+$ (bottom panel), as a function of the distances $n$-$n$ ($r_x$) and $^{14}$Be-$nn$ ($r_y$).
• Figure 3: Modified source terms for the 0$^+$ (top panel) and 2$^+$ (bottom panel) resonances. The real (solid) and imaginary parts (dashed) are shown for different channels. The labels are the same as in Fig. \ref{['fig:wfs']}.
• Figure 4: Neutron-neutron relative energy distributions for the 0$^+$ (top panel) and 2$^+$ (bottom panel) resonances. The dashed line corresponds to three-body phase-space decay. Distributions are normalized to unity.
• Figure 5: Contributions to the neutron-neutron relative-energy distribution of the 2$^+$ state. The singlet dineutron ($K=2, l_x=0,S_x=0$, red solid line), helicopter ($l_x=2,S_x=0$, dashed blue) and triplet ($S_x=1$, dot-dashed magenta) components are shown. See the text.