Current and Future Tests of the Algebraic Cluster Model of¹²C

A new theoretical approach to clustering in the frame of the Algebraic Cluster Model (ACM) has been developed. It predicts, in¹²C, rotation-vibration structure with rotational bands of an oblate equilateral triangular symmetric spinning top with a D _3h symmetry characterized by the sequence of states: 0⁺, 2⁺, 3⁻, 4^±, 5⁻ with a degenerate 4⁺ and 4⁻ (parity doublet) states. Our newly measured $2_2^{+}$ state in¹²C allows the first study of rotation-vibration structure in¹²C. The newly measured 5⁻ state and 4⁻ states fit very well the predicted ground state rotational band structure with the predicted sequence of states: 0⁺, 2⁺, 3⁻, 4^±, 5⁻ with almost degenerate 4⁺ and 4⁻ (parity doublet) states. Such a D _3h symmetry is characteristic of triatomic molecules, but it is observed in the ground state rotational band of¹²C for the first time in a nucleus. We discuss predictions of the ACM of other rotation-vibration bands in¹²C such as the (0⁺) Hoyle band and the (1⁻) bending mode with prediction of ("missing 3⁻ and 4⁻") states that may shed new light on clustering in¹²C and light nuclei. In particular, the observation (or non observation) of the predicted ("missing") states in the Hoyle band will allow us to conclude the geometrical arrangement of the three alpha particles composing the Hoyle state at 7.6542 MeV in¹²C. We discuss proposed research programs at the Darmstadt S- DALINAC and at the newly constructed ELI-NP facility near Bucharest to test the predictions of the ACM in isotopes of carbon. (paper)