Development of an accurate formalism to predict properties of two-neutron halo nuclei: case study of $^{22}$C

TL;DR

This paper develops a new formalism combining hyperspherical harmonics and R-matrix methods to accurately predict properties of two-neutron halo nuclei, specifically 22C, while improving computational efficiency and enforcing the Pauli principle.

Contribution

It introduces a robust three-body calculation framework with improved Pauli exclusion enforcement and reduced computational cost for halo nuclei modeling.

Findings

The projection method is more accurate than the supersymmetric method for Pauli exclusion.

Convergence achieved with Kmax around 40 for bound and scattering states.

A specific channel truncation reduces computational time by 20%.

Abstract

When moving away from stability or in loosely-bound systems, few-body clusterized structures like two-neutron halo nuclei appear. These emerge from the interplay between the many- and few-body degrees of freedom, and/or strong coupling between bound and continuum states. This motivates the development of models that can accurately describe few-body dynamics while enforcing shell effects. This work has two goals: understanding how to accurately enforce the Pauli principle in few-body models, as well as presenting new technical developments that allow for more robust and cheaper three-body calculations. We focus on properties of the two-neutron halo 22C, but expect the conclusions to apply to other few-body systems. We use a three-body, hyperspherical harmonics formalism combined with the R-matrix method. We compare predictions for properties of 22C starting from phenomenological interactions and using two methods to remove Pauli-forbidden states, the projection and supersymmetric methods. We also present the algorithms and derivations used. Additionally, we explore model space truncations that allow for reduced computational time. We show convergence of the calculation of both bound and scattering states for $K_{max}\sim 40$. The two methods to enforce the Pauli-exclusion principle lead to different predictions of 22C properties; the projection method is more accurate. We find one efficient channel truncation that reduces the computational cost of our calculations by 20%. Our study clarifies that the projection method is more accurate than the supersymmetric one to enforce the Pauli-exclusion principle. Technical and algorithmic developments enable accurate and efficient computation of two-neutron halo properties. This development paves the way to robust uncertainty quantification in three-body predictions, and is a useful starting point to tackle more complex systems and observables.