Isospin-forbidden electric-dipole capture and the $\alpha(d,\gamma)^6$Li reaction

TL;DR

This paper investigates the isospin-forbidden electric-dipole (E1) capture in the $ ext{ }^2$H($ ext{ }^4$He,$ ext{ }^6$Li) reaction, analyzing theoretical contributions and comparing calculations with recent experimental data, emphasizing the role of isovector E1 transitions.

Contribution

The study provides a microscopic analysis of isoscalar and isovector E1 contributions, deriving the dominant operators and confirming the importance of small isospin admixtures in explaining experimental data.

Findings

The calculated astrophysical S factor agrees with recent LUNA data.

The exact-masses prescription is not justified microscopically and should be avoided.

Capture from initial S-wave scattering states significantly impacts the reaction.

Abstract

At the long-wavelength approximation, $E1$ transitions are forbidden between isospin-zero states. Hence $E1$ radiative capture is strongly hindered in reactions involving $N = Z$ nuclei but the $E1$ astrophysical $S$ factor may remain comparable to, or larger than, the $E2$ one. Theoretical expressions of the isoscalar and isovector contributions to $E1$ capture are analyzed in microscopic and three-body approaches in the context of the $\alpha(d,\gamma)^6$Li reaction. The lowest non-vanishing terms of the operators are derived and the dominant contributions to matrix elements are discussed. The astrophysical $S$ factor computed with some of these contributions in a three-body $\alpha+n+p$ model is in agreement with the recent low-energy experimental data of the LUNA collaboration. This confirms that a correct treatment of the isovector $E1$ transitions involving small isospin-one admixtures in the wave functions should be able to provide an explanation of the data without adjustable parameter. The exact-masses prescription which is often used to avoid the disappearance of the $E1$ matrix element in potential models is not founded at the microscopic level and should not be used for such reactions. The importance of capture components from an initial $S$ scattering wave is also discussed.