On Fliessbach's approaches to direct reactions

The conventional models of direct cluster reactions treat the nuclear wave-function overlaps or reduced-width amplitudes as single-particle wave functions, which is contrary to the Pauli principle. The motivation of Fliessbach's two approaches reviewed in this paper is to improve on these models by a proper treatment of antisymmetrization. Fliessbach's approaches involve redefined reduced-width amplitudes, which can be regarded as single-particle wave functions. We show, however, that in the approach specialized to transfer reactions the antisymmetrization is in fact treated incorrectly, and the more general approach seems applicable only to processes that involve just two nuclear fragments, like a decay or radiative capture. We outline how single-particle wave functions can be used correctly in approximating reduced-width amplitudes. We show that our approach helps to bring the phenomenological spectroscopic factors into agreement with the nuclear structure models.