On the theory of atomic ionization following alpha decay

The α-decay of a nucleus may cause atomic ionization. One of the basic assumptions of Migdal's original paper, which is the prototype of all later calculations for this process, is to treat the α-particle outside the nuclear region classically as a point charge moving along a definite trajectory. In contrast to this picture, in the standard quantum-mechanical model of the α-decay, the α-particle is represented by a wave function that, after tunneling through the Coulomb barrier at the nuclear surface, propagates outwards as a spherical wave. We compare these two pictures within a three-body model, clarify the conditions under which the full quantum-mechanical calculation and its semiclassical counterpart give similar results and also point out the origin of their possible discrepancies.