Algebraic model studies of the structure and reactions of 12C and 16O

The role of algebraic models and geometric cluster models of alpha clusters in the structure of ground and first excited 0(+) and second excited 2(+) states in C-12 are evaluated with the aim of establishing if the rotational bands are compatible with rigid structures or if they are instead overlaps of different configurations. A rigid equilateral triangle shape is assumed in Ref.[2, 3]: the energy spectrum, electromagnetic observables are calculated and the transition densities are compared with elastic and inelastic cross-sections for various processes. In a different approach [4, 5], we solve the three-body quantum problem for 3 alphas using the orthogonality condition and the stochastic variational method with correlated Gaussian basis functions. The two-body density distributions indicate that the main configurations of both the second 0(+) and 2(+) states are acute iscosceles triangle shapes with a Be-8(0(+))+alpha configuration. We also find clues that the second 2(+) state is probably not a member of the rigid rotational band built on the Hoyle state.