An Attempt to Unify Half-Lives of Proton Decay, Beta Decay and Electron Capture Through GN Law

We have made an attempt to unify the decay process such as one and two proton decay, beta(+) and beta(+) decay and electron capture through Geiger-Nuttall law (GNL). As a result of this, we have constructed empirical formula for proton, beta(+), b and electron capture half-lives based on the Geiger-Nuttall law. The variation of logT(1/2) with Z(d)(n)/root Q for the elements with atomic number 1-118 is not perfectly linear instead of that these decays follow different order polynomial rule. The values produced by the present formula for proton and beta decay are close to the experiments than the other formulae available in the literature. Empirical formulae constructed for the electron capture are first of its kind. The constructed pocket formulae produce half-lives with the simple inputs of atomic number of daughter nuclei and decay energy. This pocket formula is independent on spin and deformation of daughter nuclei.

Automated summary

The study established empirical formulas for the processes of proton decay, beta(+), b decay, and electron capture based on the Geiger-Nuttall law. It was found that the decay processes do not follow a simple linear relationship, but instead adhere to different polynomial rules. The new formulas yielded values closer to experimental results, providing important insights for understanding and predicting nuclear decay.