In this work, we present a theory involving bound states embedded in the continuum in order to explain the observed structures in heavy ion fusion data. As opposed to the continuum-continuum coupling considered in the standard coupled channel calculations, we examine here the effects of interaction of bound states among themselves as well as coupling of the continuum channels with these interacting bound states. By making reasonable approximations within the context of bound states embedded in the continuum, we show that the $S$ matrix for each partial wave can be expressed as a sum of a smooth background term and a resonance term. For the case of a single bound state only, the resonant part of the $S$ matrix is shown to reduce to the Breit-Wigner form. The background part of the $S$ matrix is calculated by using a parabolic barrier in the presence of the Coulomb interaction. The theory is then applied to analyze the fusion excitation functions for the reactions ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{28,29,30}{}_{}{}^{}\mathrm{Si}$ and is found to account for the structures in the data quite well.

NUCLEAR REACTIONS Heavy ion fusion; coupled channel calculation; bound states embedded in the continua; resonant structures; application to ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{28,29,30}{}_{}{}^{}\mathrm{Si}$ systems.

• Received 18 July 1983

DOI:https://doi.org/10.1103/PhysRevC.28.2328