Limitations of the Geiger-Nuttall law in heavy cluster decay

Geiger-Nuttall law is the simplest relation in radioactive decay relating half-life and energy. Initially restricted to $\ensuremath{\alpha}$ of individual isotopes, generalizations unifying different isotopes modes under a single set constant coefficients were subsequently achieved. This motivates investigating what extent such are possible. We also examine whether there exists universal that can simultaneously describe all nuclei including heavy clusters. show validity its hinges on assumption be approximated linearly as function square root ratio energy Coulomb barrier height. Systematic calculation across nuclear chart for 12 reveals it varies over whole range between 0 1. Consequently, no linear approximation unify coefficients, thus possible contrast previous claims. In cluster decay, within 0.6--1 where nonlinearity becomes significant generalized description clusters ongoing attempts unification, might necessary go beyond incorporate additional terms proportional and/or root.