A Formulation of the Theory of Alpha-particle Decay from Time-independent Equations

Abstract

The theory of alpha-particle decay is formulated from the time-independent R-matrix theory of nuclear reactions. It is shown that the most appropriate proper solutions are the ones with radial nodes near the channel radii, and therefore the Teichmann-Wigner sum rules involving the alpha-particle kinetic energy may be applied. Exact and approximate relations are given for the dependence on the angular momentum of the decay rate for the square well model. Barrier penetration formulas are given which include estimates of the effects of an external nuclear exponential potential and the atomic electron screening.