Alpha-Decay Theory and a Surface Well Potential

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Abstract
A discussion is given of the escape of an alpha particle from a square-well potential which is in the form of a spherical shell surrounding the daughter nucleus. In the present approximation the alpha particle, as such, is excluded from the interior of the nucleus by making the one-body potential infinite in that region. The usual Coulomb barrier is used. It is found that the properties of this model differ in several important respects from those of the usual square-well one-body model, in which the well is located at the origin of coordinates. Arguments are presented which lead to the representation of the many-body decay constant as the product of a dimensionless "preformation factor" and a one-body decay constant, as opposed to the usual product of an intrinsic nonbarrier decay constant and a dimensionless barrier transmission coefficient. The preformation factor involves an "intrinsic" alpha-decay probability and, in addition, the probability per sec that an alpha particle at the nucleus will be absorbed as nucleons. The nuclear physics problem of deriving expressions for these latter two probabilities is not considered, but examples are given which can be used to show expected ranges of numerical values of the preformation factor when the one-body model is either the present one or the usual one.