# Emergence of clusters: Halos, Efimov states, and experimental signals

## TL;DR

This paper models the emergence of nuclear halos and Efimov-like states in neutron-rich nuclei, showing halos form near the binding threshold and Efimov states are unlikely, with implications for experimental detection.

## Contribution

It introduces a combined self-consistent mean-field and three-body model to study halos and Efimov states, providing new insights into their formation and observability in nuclei.

## Key findings

- Halo configurations emerge at low three-body binding energies (~100 keV)
- Efimov states are unlikely to exist in nuclei
- Large-distance wave function decay properties can differ from short-distance behavior

## Abstract

We investigate emergence of halos and Efimov states in nuclei by use of a newly designed model which combines self-consistent mean-field and three-body descriptions. Recent interest in neutron heavy calcium isotopes makes $^{72}$Ca ($^{70}$Ca+n+n) an ideal realistic candidate on the neutron dripline, and we use it as a representative example that illustrates our broadly applicable conclusions. By smooth variation of the interactions we simulate the crossover from well-bound systems to structures beyond the threshold of binding, and find that halo-configurations emerge from the mean-field structure for three-body binding energy less than $\sim 100$keV. Strong evidence is provided that Efimov states cannot exist in nuclei. The structure that bears the most resemblance to an Efimov state is a giant halo extending beyond the neutron-core scattering length. We show that the observable large-distance decay properties of the wave function can differ substantially from the bulk part at short distances, and that this evolution can be traced with our combination of few- and many-body formalisms. This connection is vital for interpretation of measurements such as those where an initial state is populated in a reaction or by a beta-decay.