Description of light-ion collisions in the time-dependent cluster model

The time-dependent cluster model is applied to the description of light-ion reactions of various types. Special emphasis is placed on the quantitative description of the fusion excitation function in the ${}_{}{}^{12}{}_{}{}^{}\mathrm{-}_{}^{12}{}_{}{}^{}$C system and the qualitative discussion of l matching for different binary reactions in the ${}_{}{}^{12}{}_{}{}^{}\mathrm{-}_{}^{16}{}_{}{}^{}$O system. The Euler-Lagrange equations of the time-dependent cluster model are generalized to the multideterminantal case, and in this form they are applied to describe the evolution of parity-projected wave functions in the α${\mathrm{-}}^{12}$C reaction. For this reaction, the results for various assumptions about the trial wave function and the initial geometry of the reaction are qualitatively discussed.