Two-delta shell resonance description of α-decay: analytic expression of half-life via energy derivative of phase-shift

Abstract

The process of α-decay being intrinsically quantum mechanical originates from the resonance state of the α + daughter nucleus two-body system where the scattering phase-shifts vary rapidly in a small energy range of the size of the resonance width in the presence of narrow resonance. We model this physical phenomenon and derive a clear expression for the decay width, Γ, in terms of energy derivative of phase-shift obtained by properly matching the exact solutions within the segments of a shell of two delta potentials generating resonance with the pure Coulomb wave functions in the Coulomb–nuclear scattering phenomenon. With this decay width Γ, using the standard relation, T 1/2 = ln 2 ℏ Γ , the decay half-life, T 1/2, is expressed analytically and the computed results successfully explain the experimental results of α-decay half-lives ranging from 10−7 s–1025 s in the cases of many light, heavy and super heavy radioactive nuclei with proton number Z = 52–120 and mass number A = 106–299.