  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.
