Using an explicit analytical expression of the s-wave S matrix for a typical short-range potential barrier we correlate the classical orbiting and corresponding quantum-mechanical barrier states. These are compared with the results of earlier works on this problem and some additional interesting features, such as dependence of width on height of the barrier and spacing between the levels of the barrier region resonances, are pointed out. On this basis, a four-parameter barrier region resonance model is introduced in the analysis of resonances in heavy ion scattering. The model is then applied to fit satisfactorily the large number of resonances observed in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$${+}^{12}$C and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$${+}^{16}$O systems. The present model directly relates the nucleus-nucleus potential barrier generated by the effective nucleus-nucleus potential to heavy ion resonances.

• Received 29 May 1991

DOI:https://doi.org/10.1103/PhysRevC.44.2729