Analysis of $M1$ capture in the $\alpha(d,\gamma)^6$Li reaction

TL;DR

This paper analytically and numerically investigates the $M1$ contribution to the $oldsymbol{ m ^{6}Li}$ radiative capture reaction, revealing the dominant transition pathways and clarifying discrepancies in previous $M1$ $S$-factor calculations.

Contribution

It introduces an effective $M1$ operator approach to analyze the reaction, showing isoscalar $M1$ transitions are forbidden and identifying the main transition contributions.

Findings

Isoscalar $M1$ transitions are forbidden without initial state distortion.

Negligible $M1$ $S$-factor at low energies in a three-body model.

Main $M1$ contribution from initial $S$ wave to isospin 1 components.

Abstract

An effective operator is exactly equivalent to the long-wavelength form of the $M1$ operator in transition matrix elements. It allows us to analytically and numerically analyze the $M1$ contribution to the $\alpha(d,\gamma)^6$Li reaction. Isoscalar $M1$ transitions from an initial $S$ wave are shown to be forbidden in radiative capture reactions when distortion is neglected in the initial state. A calculation in a three-body model with proton, neutron, and a structureless $\alpha$ interacting through effective forces leads to a negligible $M1$ $S$-factor at small energies. The dominant $M1$ contribution comes from transitions from an initial $S$ wave to isospin 1 components of the $^6$Li ground state. It is suggested that using this effective $M1$ operator in other models should clarify the origin of large discrepancies between $M1$ $S$-factors appearing in the literature.