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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Fine structure has been shown to be a general phenomenon of nuclear giant resonances of different multipolarities over a wide mass range. In this article we assess various techniques that have been proposed to extract quantitative information from the fine structure in terms of characteristic scales. These include the so-called local scaling dimension, the entropy index method, Fourier analysis, and continuous and discrete wavelet transforms. As an example, results on the isoscalar giant quadrupole resonance in 208 Pb from high-energy-resolution inelastic proton scattering and calculations with the quasiparticle-phonon model are analyzed. Wavelet analysis, both continuous and discrete, of the spectra is shown to be a powerful tool to extract the magnitude and localization of characteristic scales.

The 12 C excitation energy spectra populated in both proton and α-particle inelastic scattering measurements are examined. The data indicate the existence of a 2 + state at Ex=9.75(0.15) MeV with a width of 750(150) keV. It is believed that this state corresponds to the 2 + excitation of the 7.65 MeV, 0 + , Hoyle-state, which acts as the main path by which carbon is synthesised in stars. A simultaneous R-matrix analysis of the two sets of data indicates that the 2 + state possesses a very large α-reduced width, approaching the Wigner limit. This would indicate that the state is associated with a highly clustered structure. The potential geometric arrangements of the clusters is discussed.