O Fusion Between Light and Medium - Light Heavy Ions.

We present here a theoretical description for fusion between two light and medium-light heavy ions. To this end, we first analyse the ('12)C + ('12)C elastic scattering data (angular distributions and excitation functions) using a molecular potential to see if such a potential could also be used to explain the experimentally measured fusion cross sections. Parameters of the real part of this potential are obtained from scaling the potential used for ('16)O + ('16)O case. As expected, the calculated reaction cross section using the potential determined from elastic scattering do not account for the fusion data. We then develop a model which describes the fusion mechanism between two heavy ions as quantum mechanical penetration through a parabolic barrier in the presence of a proper Coulomb interaction with appropriate boundary conditions. The parabolic potential is matched to the Coulomb potential in order to avoid any discontinuity of the potential surface. The Schrodinger equations in the exterior and interior regions containing, respectively, the Coulomb and parabolic potentials are solved and the penetrability function is calculated from the logarithmic derivative at the matching radius. The theory is then applied to calculate the energy dependence of the fusion cross section and the astrophysical S-factor for a wide class of systems at energies both below and above the Coulomb barrier. The theory is valid at all energies and can explain the overall shape, magnitude, and gross features of fusion data remarkably well. It is, however, not suitable for understanding structures in the cross sections. To explain the structures in the data, we formulate a coupled channel theory involving bound states embedded in the continuum (BSEC). In particular, we consider the effects of interaction of bound states among themselves as well as coupling of the continuum channels with these interacting bound states. Within the context of BSEC, we show that the S-matrix for each partial wave can be expressed as the sum of a smooth background term and a resonance term which is of the Breit-Wigner type. The formalism is then used to analyse the fusion cross sections for the reactions ('12)C + ('28,29,30)Si and is found to account for the structures in the data quite well.