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 ${}^4\mathrm{He}{(d,\gamma )}^6\mathrm{Li}$ 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. An illustrative 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 ${}^6\mathrm{Li}$ ground state. The importance of the orthogonality between initial and final states is emphasized. 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.

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• H & He induced nuclear reactions
• Nuclear astrophysics
• Nuclear reactions
• Radiative capture
• 6 ≤ A ≤ 19