A high-energy-resolution magnetic spectrometer has been used to measure the 12 C excitation energy spectrum to search for the 2 + excitation of the 7.65 MeV, 0 + Hoyle state. By measuring in the diffractive minimum of the angular distribution for the broad 0 + background, evidence is found for a possible 2 + state at 9.6(1) MeV with a width of 600(100) keV. The implications for the 8 Be + 4 He reaction rate in stellar environments are discussed.One of the mysteries of nuclear structure is the nature of the 7.65 MeV, 0 + state in 12 C. Its existence is innately tied to that of organic life as it is the portal through which the most abundant isotope of carbon ( 12 C) is synthesized. The existence of the state was originally proposed by Hoyle [1] to address the question as to the abundance of 12 C, which could only be accounted for if a resonance were to lie close to the Gamow window. The anthropic power of this argument was demonstrated when the state was discovered by Cook and co-workers [2] with precisely the predicted properties.The structure of this state has, however, remained something of a mystery. What is known is that it must have an unusual nature, which is probably a well-developed 3α-cluster structure. Evidence for this comes from several sources. First, it is known that the optimal conditions for the formation of clusters is that a state should lie close to the associated cluster decay threshold [3]; in the present instance, the Hoyle state lies just 375 keV above the 3α-decay threshold. Shell model calculations, for example, those of Ref.[4], reproduce rather well the energy of the first 2 + (4.44 MeV) excitation. However, in the region of the second 0 + state (0 + 2 ), the Hoyle state, there is a void in the calculations; the energy of this state cannot be reproduced. A similar conclusion is reached in the no-core shell model calculations [5]. Analysis of electron inelastic-scattering data [6,7] indicates that the Hoyle state has a volume some 3.4 times larger than the ground state. This larger volume reduces the overlap of the α particles and may allow them to obtain their quasifree characteristics in something approaching an α-particle gas or perhaps a bosonic condensate (BEC) [8]. This latter possibility is intriguing, as it would correspond to a new form of nuclear matter in which the bosonic nature of the α particles would allow the constituents to all occupy the lowest energy level of the mutual interaction potential-unlike fermions. Fermionic molecular dynamics (FMD) calculations also find that the 7.65 MeV state has a similar structure [9].From an experimental perspective, one key ingredient in pinning down the structural properties of the state is finding the location of its collective (2 + ) excitation. A state in which the three α particles are arranged in a linear fashion (3α chain) would have a 2 + excitation at 0.8 MeV above the 0 + state [10]. On the other hand, BEC calculations predict an energy difference of 1.3 MeV [11], the FMD predict 2.3 MeV [9], and the separation is 1.6-2.8 MeV...

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