A nucleus, initially in a bound state akin to a Dirac δ well potential, under severe action of reflection from a repulsive electrostatic interaction at very small separation between the newly born α cluster and the daughter nucleus goes to the quasistationary state from which the decay of α sets in. The energy derivative of the phase-shift of the $S$-matrix of transition scattering from an isolated quasibound state to a scattering state is related to the width (${\Gamma}$)of the resonance and hence the half-life T$_{1/2}$= ln 2$\bar{h}$/${\Gamma}$of α-decay. Using exact solutions of the delta well driven Coulomb potential, we derive a compact expression for log10 T$_{1/2}$ in terms of Q-value and the mass and charge numbers of the α emitter with a radius parameter specifying the sum of the charge radii of α and daughter nuclei or the radius of the parent emitter. The computed results of half-lives successfully explain the experimental values of α-decay half-lives ranging from 10$^{−7}$s to 10$^{25}$s in many light, heavy and super heavy radioactive nuclei with charge number Z = 52–120 and mass number A = 106–299. Showing uniformity in the applications of formulation to the decay of positive ions, namely α and cluster ions, the universal nature of the decay rule is established.