Inelastic scattering from12 C has been measured at the extremely forward angles including 0• using 386 MeV α particles to study the α-cluster states around Ex ∼ 10 MeV, especially the 2 + state predicted by the α-cluster model. We have analyzed the (α,α ′ ) cross-section data using both the peak-fitting and the multipole decomposition techniques. A 2 + state at Ex = 9.84 ± 0.06 MeV with a width of 1.01 ± 0.15 MeV is found to be submerged in the broad 0 + state at Ex = 9.93 ± 0.03 MeV with a width of 2.71 ± 0.08 MeV. This 2 + state may be interpreted as the 2 + excitation of the Hoyle state and the α-condensate state.

The Technical Design for the COMET Phase-I experiment is presented in this paper. COMET is an experiment at J-PARC, Japan, which will search for neutrinoless conversion of muons into electrons in the field of an aluminum nucleus ($\mu$–$e$ conversion, $\mu^{-}N \rightarrow e^{-}N$); a lepton flavor-violating process. The experimental sensitivity goal for this process in the Phase-I experiment is $3.1\times10^{-15}$, or 90% upper limit of a branching ratio of $7\times 10^{-15}$, which is a factor of 100 improvement over the existing limit. The expected number of background events is 0.032. To achieve the target sensitivity and background level, the 3.2 kW 8 GeV proton beam from J-PARC will be used. Two types of detectors, CyDet and StrECAL, will be used for detecting the $\mu$–$e$ conversion events, and for measuring the beam-related background events in view of the Phase-II experiment, respectively. Results from simulation on signal and background estimations are also described.

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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.

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