Neutron-neutron scattering length from the $^6$He$(p,p\alpha)nn$ reaction

TL;DR

This paper introduces a new method to measure the neutron-neutron scattering length using the $^{6}$He$(p,peta)nn$ reaction, leveraging final state interactions and Halo EFT to improve precision and estimate uncertainties.

Contribution

The paper develops a novel experimental approach combined with Halo EFT calculations to extract the neutron-neutron scattering length with quantified uncertainties.

Findings

The neutron-neutron relative energy distribution is sensitive to the scattering length.

Halo EFT provides uncertainty estimates for the ground-state wave function of $^6$He.

Comparison of FSI models shows the distribution depends weakly on the effective range.

Abstract

We propose a novel method to measure the neutron-neutron scattering length using the $^{6}$He$(p,p\alpha)nn$ reaction in inverse kinematics at high energies. The method is based on the final state interaction (FSI) between the neutrons after the sudden knockout of the $\alpha$ particle. We show that the details of the neutron-neutron relative energy distribution allow for a precise extraction of the $s$-wave scattering length. We present the state-of-the-art in regard to the theory of this distribution. The distribution is calculated in two steps. First, we calculate the ground-state wave function of $^6$He as a $\alpha n n$ three-body system. For this purpose we use Halo effective field theory (Halo EFT), which also provides uncertainty estimates for the results. We compare our results at this stage to model calculations done with the computer code FaCE. In a second step we determine the effects of the $nn$ FSI using the $nn$ t-matrix. We compare these FSI results to approximate FSI approaches based on standard FSI enhancement factors. While the final distribution is sensitive to the $nn$ scattering length, it depends only weakly on the effective range. Throughout we emphasize the impact of theoretical uncertainties on the neutron-neutron relative energy distribution, and discuss the extent to which those uncertainties limit the extraction of the neutron-neutron scattering length from the reaction $^{6}$He$(p,p\alpha)nn$.