The physics of exotic nuclei, or nuclei with short lifetimes, is often governed by beta decay, a process in which a neutron decays into a proton, an electron, and an antineutrino. The decay rate is estimated by calculating the product of the electron and nuclear current densities. A widely used formula for calculating this rate relies on a leading-order approximation of the electron wave functions distorted by the Coulomb potential. However, for heavy nuclei with large atomic numbers, this simple approximation may no longer be valid.

To address this issue, physicists from Japan developed a simple approach for improving the conventional formula to apply for the case of heavy nuclei. They treated the neutrino wave function as an exact plane wave and numerically solved for the electron wave functions to obtain both leading-order (or LO) and next-to-leading-order (or NLO) approximations. The physicists then showed that the LO approximation led to an overestimation of the decay rate while the NLO approximation better reproduced the exact result for a schematic transition density as well as for the transition densities obtained by a nuclear energy-density functional method.

The proposed formula could significantly impact our understanding of the origin and formation of heavy elements in our universe and perhaps open a window into yet-undiscovered physics lying beyond the standard model of particle physics.