Complex-Energy Shell-Model Description of Alpha Decay

Abstract

In his pioneering work of alpha decay, Gamow assumed that the alpha particle formed inside the nucleus tunnels through the barrier of the alpha-daughter potential. The corresponding metastable state can be viewed as a complex-energy solution of the time-independent Schroedinger equation with the outgoing boundary condition. The formation of the alpha cluster, missing in the original Gamow formulation, can be described within the R-matrix theory in terms of the formation amplitude. In this work, the alpha decay process is described by computing the formation amplitude and barrier penetrability in a large complex-energy configuration space spanned by the complex-energy eigenstates of the finite Woods-Saxon (WS) potential. The proper normalization of the decay channel is essential as it strongly modifies the alpha-decay spectroscopic factor. The test calculations are carried out for the ^{212}Po alpha decay.