Improved Geiger-Nuttall law for one- and two-proton radioactivity

Proton radioactivity, a rare decay mode occurring in proton-rich nuclei beyond the proton drip line, provides valuable insights into nuclear structure, nuclear stability, and the limits of nuclear existence. Building upon the Geiger–Nuttall (GN) law and recent developments in one-proton and two-proton radioactivity systematics, this work proposes an improved GN law that explicitly separates the effects of the daughter-nucleus charge Z d and the orbital angular momentum l . Previous empirical formulas typically couple or add these two contributions, despite their fundamentally different physical origins—the long-range Coulomb interaction and the relatively shorter-range centrifugal potential. By introducing an additional parameter to independently scale the l -dependent contribution, we quantify their separate roles on the decay half-life. Using experimental data from 44 proton emitters and available two-proton emitters, we determine the optimal parameter sets for both one-proton and two-proton radioactivity. The improved GN law yields a smaller standard deviation σ=0.357 for one-proton emission and reproduces experimental two-proton radioactive half-lives within one order of magnitude. The resulting law provides enhanced predictive power and a physically transparent interpretation of Coulomb and centrifugal contributions, offering reliable theoretical support for future studies and experimental searches of exotic proton-rich nuclei.