# Momentum-space probability density of ${}^6$He in Halo Effective Field Theory

## TL;DR

This paper calculates the momentum-space probability density of the halo nucleus ${}^6$He using Halo Effective Field Theory, treating it as a three-body system and analyzing the effects of energy-dependent interactions.

## Contribution

It introduces a leading-order Halo EFT framework for ${}^6$He and examines the normalization and regulator independence of the probability density.

## Key findings

- Probability density is regulator independent within EFT validity.
- Small effects from energy-dependent $nc$ t-matrix modifications.
- Framework applicable to other halo nuclei.

## Abstract

We compute the momentum-space probability density of ${}^6$He at leading order in Halo EFT. In this framework, the ${}^6$He nucleus is treated as a three-body problem with a ${}^4$He core ($c$) and two valence neutrons ($n$). This requires the $nn$ and $nc$ t-matrices as well as a $cnn$ force as input in the Faddeev equations. Since the $nc$ t-matrix corresponds to an energy-dependent potential, we consider the consequent modifications to the standard normalization and orthogonality conditions. We find that these are small for momenta within the domain of validity of Halo EFT. In this regime, the ${}^6$He probability density is regulator independent, provided the cutoff is significantly above the EFT breakdown scale.