Three-cluster dynamics within the ab initio no-core shell model with continuum: How many-body correlations and $\alpha$-clustering shape $^6$He

TL;DR

This paper develops an ab initio method combining the no-core shell model with continuum to accurately describe bound and unbound states of $^6$He, emphasizing the importance of many-body correlations and clustering effects.

Contribution

It introduces a formalism coupling no-core shell model eigenstates with three-cluster continuum states, enabling detailed analysis of $^6$He structure and reactions.

Findings

Successfully reproduces $^6$He binding energy and radii without extrapolation.

Identifies many-body correlations as key to the narrow $2^+$ resonance.

Highlights the role of $^4$He+$n$+$n$ clustering in $^6$He structure.

Abstract

We realize the treatment of bound and continuum nuclear systems in the proximity of a three-body breakup threshold within the ab initio framework of the no-core shell model with continuum. Many-body eigenstates obtained from the diagonalization of the Hamiltonian within the harmonic-oscillator expansion of the no-core shell model are coupled with continuous microscopic three-cluster states to correctly describe the nuclear wave function both in the interior and asymptotic regions. We discuss the formalism in detail and give algebraic expressions for the case of core+$n$+$n$ systems. Using similarity-renormalization-group evolved nucleon-nucleon interactions, we analyze the role of $^4$He+$n$+$n$ clustering and many-body correlations in the ground and low-lying continuum states of the Borromean $^6$He nucleus, and study the dependence of the energy spectrum on the resolution scale of the interaction. We show that $^6$He small binding energy and extended radii compatible with experiment can be obtained simultaneously, without recurring to extrapolations. We also find that a significant portion of the ground-state energy and the narrow width of the first $2^+$ resonance stem from many-body correlations that can be interpreted as core-excitation effects.