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

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)6Li 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 reactions of N = Z nuclei. The importance of capture components from an initial S scattering wave is also discussed.