# Astrophysical $S$-factor of the direct $\alpha(d,\gamma)^6$Li capture reaction in a three-body model

## TL;DR

This paper calculates the astrophysical S-factor for the (,Li) reaction using a three-body model, achieving agreement with experimental data without adjustable parameters.

## Contribution

It introduces a three-body +n+p model that accurately predicts the S-factor, addressing limitations of previous potential models.

## Key findings

- The model reproduces experimental S-factor data from LUNA.
- Electric dipole transitions are forbidden at long wavelengths in isospin-zero states.
- Using exact masses avoids the disappearance of E1 transitions in potential models.

## Abstract

At the long-wavelength approximation, electric dipole transitions are forbidden between isospin-zero states. In an $\alpha+n+p$ model with $T = 1$ contributions, the $\alpha(d,\gamma)^6$Li astrophysical $S$-factor is in agreement with the experimental data of the LUNA collaboration, without adjustable parameter. The exact-masses prescription used to avoid the disappearance of $E1$ transitions in potential models is not founded at the microscopic level.