Analytical transformed harmonic oscillator basis for three-body nuclei of astrophysical interest: Application to 6He

TL;DR

This paper introduces an analytical transformed harmonic oscillator basis for three-body nuclei, demonstrating its effectiveness through application to 6He and suggesting potential for studying other complex Borromean nuclei in astrophysics.

Contribution

The paper generalizes a previously successful two-body basis method to three-body systems, enabling simpler calculations for complex nuclei like 6He.

Findings

Accurate capture reaction rate for 6He obtained

Method compares well with existing three-body continuum calculations

Encourages application to other Borromean nuclei

Abstract

Recently, a square-integrable discrete basis, obtained performing a simple analytical local scale transformation to the harmonic oscillator basis, has been proposed and successfully applied to study the properties of two-body systems. Here, the method is generalized to study three-body systems. To test the goodness of the formalism and establish its applicability and limitations, the capture reaction rate for the nucleosynthesis of the Borromean nucleus 6He (4He + n + n) is addressed. Results are compared with previous publications and with calculations based on actual three-body continuum wave functions, which can be generated for this simple case. The obtained results encourage the application to other Borromean nuclei of astrophysical interest such as 9Be and 12C, for which actual three-body continuum calculations are very involved.