# The ${}_{\Lambda\Lambda}^{\,\,\,\,4}n$ system

## TL;DR

This study investigates whether a hypothetical hypernucleus, ${}_{\Lambda\Lambda}^{4}n$, can exist as a bound state, using realistic nuclear interactions, and concludes it is likely unbound, just above the threshold.

## Contribution

The paper applies updated Nijmegen potentials and Yukawa-type interactions to assess the existence of the ${}_{\Lambda\Lambda}^{4}n$ hypernucleus, providing new insights into its unbound nature.

## Key findings

- ${}_{\Lambda\Lambda}^{4}n$ is unbound, just above threshold.
- The $^1S_0$ $nn$ repulsive term influences binding.
- Updated potentials do not support bound ${}_{\Lambda\Lambda}^{4}n$.

## Abstract

Using local central Yukawa-type Malfliet-Tjon interactions reproducing the low-energy parameters and phase shifs of the $nn$ system and the latest updates of the $n\Lambda$ and $\Lambda\Lambda$ Nijmegen ESC08c potentials we study the possible existence of a ${}_{\Lambda\Lambda}^{\,\,\,\,4}n$ bound state. Our results indicate that the ${}_{\Lambda\Lambda}^{\,\,\,\,4}n$ is unbound, being just above threshold. We discuss the role played by the $^1S_0$ $nn$ repulsive term of the Yukawa-type Malfliet-Tjon interaction.