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 , 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.

的过程中α衰变与所述的共振状态固有量子力学源自α +子核二体系统，其中，散射相移在狭窄的存在快速地改变在所述谐振宽度的大小的一小能量范围谐振。我们对这种物理现象进行建模，并通过适当地匹配两个δ电势的壳段内的精确解，从而产生与纯库仑波产生共振的相移能量导数，得出了衰减宽度Γ的清晰表达式。在库仑-核散射现象中起作用。对于这个衰减宽度Γ，使用标准关系T _1/2 = ln 2 ，衰减半衰期T _1/2表示为解析式，计算结果成功地解释了质子数为Z的许多轻，重和超重放射性核的α衰变半衰期为10 ^-7 s–10 ²⁵ s的实验结果= 52–120，质量数A = 106–299。