Reaction-rate function of proton-deuteron radiative capture within potential model

The proton-deuteron ($p$D) radiative capture reaction plays a crucial role in primordial nucleosynthesis. The astrophysical $S$-factor is calculated using a phenomenological potential model, considering both electric dipole ($E1$) and magnetic dipole ($M1$) transitions. The resulting $S$-factor is found to be in good agreement with recent experimental data. In addition, an approximate polynomial expression for the reaction-rate function is provided.