Three-body calculations of beta decay applied to $^{11}$Li

TL;DR

This paper introduces a new three-body computational method incorporating isospin symmetry to analyze beta decay in nuclear halo structures, demonstrated on $^{11}$Li, with results aligning well with experimental data.

Contribution

A novel practical three-body method using hyperspherical coordinates that includes isospin symmetry for studying beta decay in halo nuclei.

Findings

Good agreement with experimental data at high excitation energies.

Predicted isospin symmetry breaking of about 0.4%.

Provided detailed decay property predictions for future testing.

Abstract

A novel practical few-body method is formulated to include isospin symmetry for nuclear halo structures. The method is designed to describe beta decay, where the basic concept of isospin symmetry facilitates a proper understanding. Both isobaric analogue and anti-analogue states are treated. We derive general and explicit formulas for three-body systems using hyperspherical coordinates. The example of the beta decaying $^{11}$Li ($^{9}$Li+$n$+$n$) is chosen as a challenging application for numerical calculations of practical interest. The detailed results are compared to existing experimental data and good agreement is found at high excitation energies, where the isobaric analogue and anti-analogue states are situated in the daughter nucleus. An interpretation of the decay pattern at lower excitation energies is suggested. Decays of the $^{9}$Li-core and the two halo-neutrons are individually treated and combined to the daughter system with almost unique isospin, which we predict to be broken by about $0.4\%$ probability. Properties of decay products are predicted as possible future tests of this model.