Binding two and three $\alpha$ particles in cold neutron matter

TL;DR

This paper investigates how two- and three-alpha particle states, like $^8$Be and the Hoyle state, can become bound in cold neutron matter, revealing their potential importance in astrophysics and neutron-rich nuclei.

Contribution

It introduces a theoretical framework combining alpha cluster models with in-medium properties to study alpha particle states in neutron matter, highlighting their possible bound states.

Findings

$^8$Be and Hoyle states can become bound in neutron-rich environments.

In-medium alpha states may influence astrophysical phenomena.

Alpha cluster states are relevant in neutron-rich nuclei.

Abstract

We elucidate the fate of neighboring two and three-$\alpha$ particles in cold neutron matter by focusing on an analogy between such $\alpha$ systems and Fermi polarons realized in ultracold atoms. We describe in-medium excitation properties of an $\alpha$ particle and neutron-mediated two- and three-$\alpha$ interactions using theoretical approaches developed for studies of cold atomic systems. We numerically solve the few-body Schr\"odinger equation of $\alpha$ particles within standard $\alpha$ cluster models combined with in-medium properties of $\alpha$ particles. We point out that the resultant two-$\alpha$ ground state and three-$\alpha$ first excited state, which correspond to $^8$Be and the Hoyle state, respectively, known as main components in the triple-$\alpha$ reaction, can become bound states in such a many-neutron background although these states are unstable in vacuum. Our results suggest a significance of these in-medium cluster states not only in astrophysical environments such as core-collapsed supernova explosions and neutron star mergers but also in neutron-rich nuclei.