We report a measurement of a new high spin J π = 5 − state at 22.4(0.2) MeV in 12 C which fits very well to the predicted (ground state) rotational band of an oblate equilateral triangular spinning top with a D 3h symmetry characterized by the sequence 0 + , 2 + , 3 − , 4 ± , 5 − with almost degenerate 4 + and 4 − (parity doublet) states. Such a D 3h symmetry was observed in triatomic molecules and it is observed here for the first time in nuclear physics. We discuss a classification of other rotation-vibration bands in 12 C such as the (0 + ) Hoyle band and the (1 − ) bending mode band and suggest measurements in search of the predicted ("missing") states that may shed new light on clustering in 12 C 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-particle composing the Hoyle state at 7.654 MeV in 12 C.

We have studied three different 2n-transfer reactions on a 12 C target, the 2p pick-up reaction on 16 O and the 5 He transfer in the reaction 9 Be( 7 Li, d) 14 C. Combined with a systematic search through experimental results for transfer reactions, inelastic excitations and other data, we have established an almost complete spectroscopy for 14 C up to 18 MeV excitation. We identify states with single-particle structure that have oblate shapes and states corresponding to proton excitations that are connected to oblate (triangular) cluster states. Further we list states of prolate shape which have no simple structure related to the low-lying oblate states of 12 C. These are proposed to have strong α-clustering and to form rotational bands as a parity inversion doublet, with high moment of inertia. With these results it is possible for the first time to identify chain states expected in the isotope 14 C.

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We investigate the existence of weakly coupled gas-like states comprised of three α particles around an 16 O core in 28 Si. We calculate the excited states in 28 Si using the multi-configuration mixing method based on the 16 O + 3α cluster model. We also include the 16 O + 12 C and 24 Mg + α basis wave functions prepared by the generator coordinate method. To identify the gas-like states, we calculate the isoscalar monopole transition strengths and the overlap of the obtained states with the geometrical cluster wave function and the TohsakiHoriuchi-Schuck-Röpke (THSR) wave function. The results show that the obtained fourth and twelfth states significantly overlap with the THSR wave function. These two states clearly coexist with the 16 O + 12 C cluster states, emerging at similar energies. The calculated isoscalar monopole strengths between those two states are significantly large, indicating that the states are members of the excitation mode. Furthermore, the calculated root-mean-squared (RMS) radii for these states also suggest that a layer of gas-like three α particles could exist around the surface of the 16 O core, which can be described as a "two-dimensional gas" in the intermediate state before the Hoyle-like three α states emerge. 21.60.Gx,27.20.+n,27.30.+t The investigations of excited states in light-mass nuclei provide a good opportunity to study the rich variety of nuclear structures of quantum many-body systems. One of these states is the well known Hoyle state in 12 C * [1]. The Hoyle state is the second 0 + state in 12 C * , with an excitation energy of 7.65 MeV, just above the 3 α decay threshold energy. Many theoretical attempts have been performed to reproduce its energy and geometrical properties. It was found, that it is difficult to reproduce those values by calculations based only on the shell model. On the other hand, the microscopic three α cluster models successfully describe the properties of the Hoyle state (such as the observed α-decay width) and indicate that the three α state develops well in the 0 + 2 state [2,3]. Recent calculations, using the α cluster model suggest that in the Hoyle state, the three "gas-like" α particles are weakly coupled with each other at near the three α-decay threshold energy [4,5]. Based on this picture, the Tohsaki-HoriuchiSchuck-Röpke (THSR) wave function was proposed. This wave function describes the α particles as independent, with their center-of-mass motion, in the same 0S state of the harmonic oscillator, having a large oscillator parameter. Using this wave function, Tohsaki et al. proposed the extremely large RMS nuclear radius for the 0 + 2 state in 12 C [4]. Those studies have triggered interest in whether such gaslike states exist in heavier-mass nuclei. Funaki et al. searched for gas-like four α states in 16 O * using the microscopic α cluster model coupled with the THSR wave function [6,7]. In this connection, the existence of weakly coupled gas-like α cluster states around a core has been recently suggested [8][9][10][11][12]. To study...