Nuclear reaction theory, such as deuteron-alpha radiative capture, has been an essential part of developing nuclear physics. This reaction is the only process that leads to the production of 6Li. The deuteron-alpha radiative capture reaction has been investigated under the framework of Effective Field Theory, up to next to leading order (NLO). In this study, alpha particles were considered structureless and the Coulomb effects were assumed as a Coulomb correction for E1 and E2 electric multipole transitions, up to NLO. By inserting three-body forces, the scattering amplitude was computed at the initial state of the deuteron-alpha P-wave for the sum of both multipole transitions E1 and E2. Two of the low-energy photonuclear observables, including the astrophysical S-factor and reaction rate of deuteron-alpha radiative capture reaction, are calculated. The calculated photonuclear observables are in satisfactory agreement with the other theoretical methods and the available experimental data, with energies relevant to Big-Bang Nucleosynthesis.
