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

¹ Dip. Fisica e Astronomia “G.Galilei”, Univ. Padova (Italy)
² I.N.F.N. Sez. Padova, Padova (Italy)

^* e-mail: fortunat@pd.infn.it

Published online: 28 October 2024

Abstract

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 ¹²C 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 ⁸Be(0⁺)+α 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.