Astrophysical reaction rate for $^9$Be formation within a three-body approach

TL;DR

This paper develops a three-body approach to accurately calculate the astrophysical reaction rate for $^9$Be formation, highlighting differences between sequential and direct capture processes across temperature ranges.

Contribution

It introduces an analytical three-body method for $^9$Be formation, providing more accurate reaction rates especially at low temperatures where direct capture dominates.

Findings

At high temperatures, results agree with sequential process calculations.

At low temperatures, direct capture yields higher reaction rates.

The method is reliable for systems with multiple charged particles.

Abstract

The structure of the Borromean nucleus $^9$Be ($\alpha+\alpha+n$) is addressed within a three-body approach using the analytical transformed harmonic oscillator method. The three-body formalism provides an accurate description of the radiative capture reaction rate for the entire temperature range relevant in Astrophysics. At high temperatures, results match the calculations based on two-step sequential processes. At low temperatures, where the particles have no access to intermediate two-body resonances, the three-body direct capture leads to reaction rates larger than the sequential processes. These results support the reliability of the method for systems with several charged particles.