Three-body calculations of β decay applied to Li11

Abstract

A novel practical few-body method is formulated to include isospin symmetry for nuclear halo structures. The method is designed to describe $\ensuremath{\beta}$ decay, where the basic concept of isospin symmetry facilitates a proper understanding. Both isobaric analog and antianalog states are treated. We derive general and explicit formulas for three-body systems using hyperspherical coordinates. The example of the $\ensuremath{\beta}$ decaying $^{11}\mathrm{Li}$ ($^{9}\mathrm{Li}+n+n$) 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 analog and antianalog states are situated in the daughter nucleus. An interpretation of the decay pattern at lower excitation energies is suggested. Decays of the $^{9}\mathrm{Li}$ core and the two halo neutrons are individually treated and combined with 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.