Beta decay is the process in which a nucleus transforms into a proton, an electron, and a neutrino. The decay rate is estimated by calculating the product of the electron, neutrino, and nuclear current densities. However, the conventional formula is inaccurate for heavy nuclei with large atomic numbers. To address this issue, researchers from Japan developed a new formula by iteratively solving the integral of the electron wave function to obtain the leading order (LO) and next-to-leading order (NLO) approximations.

They showed that the LO approximation, which resembles the conventional formula, overestimated the decay rate, while the NLO approximation provided a more exact result for the transition densities obtained by a nuclear energy-density-functional method. However, it is a general formula that does not consider the effects of velocity-dependent weak currents and induced currents.

In a follow up paper published in Progress of Theoretical and Experimental Physics, the researchers now present the complete formulas for the allowed and first-forbidden transitions of beta decay by considering both the leptonic and hadronic currents. They applied them to the beta decay of the neutron-rich nucleus, tin-160. The conventional formulas overestimated the decay rate by 10–20%, while the NLO corrections reproduced the exact results with high accuracy. Moreover, the induced current terms contributed at most five percent to the rate.

This newly completed formula can be applied not only to various beta-decay processes but also to the shape and angular patterns in beta-decay and neutrino reactions. Thus, it could help control nuclear waste and may unearth new physics beyond the standard model of particle physics.