# Influence of orthogonalization procedure on astrophysical S-factor for the direct $\alpha+d$ $\rightarrow$ $^6$Li + $\gamma $ capture process in a three-body model

## TL;DR

This study investigates how different orthogonalization methods affect the calculated astrophysical S-factor for the alpha+d to Li-6 + gamma reaction within a three-body model, revealing significant differences in E1 contributions and better data agreement with the OPP method.

## Contribution

It compares the effects of orthogonalization procedures on the astrophysical S-factor in a three-body model, highlighting the impact on E1 and E2 components and data agreement.

## Key findings

- OPP yields larger isotriplet components than SUSY.
- E1 S-factor energy dependence is similar, but absolute values differ.
- OPP matches low-energy experimental data better.

## Abstract

The astrophysical S-factor for the direct $ \alpha(d,\gamma)^{6}{\rm Li}$ capture reaction is calculated in a three-body model based on the hyperspherical Lagrange-mesh method. A sensitivity of the E1 and E2 astrophysical S-factors to the orthogonalization method of Pauli forbidden states in the three-body system is studied. It is found that the method of orthogonalising pseudopotentials (OPP) yields larger isotriplet ($T=1$) components than the supersymmetric transformation (SUSY) procedure. The E1 astrophysical S-factor shows the same energy dependence in both cases, but strongly different absolute values. At the same time, the E2 S-factor does not depend on the orthogonalization procedure. As a result, the OPP method yields a very good description of the direct data of the LUNA collaboration at low energies, while the SUSY transformation strongly underestimates the LUNA data. \keywords{three-body model; orthogonalization method; astrophysical S factor.