Understanding the fundamental excitations of many-fermion systems is of significant current interest. In atomic nuclei with even numbers of neutrons and protons, the low-lying excitation spectrum is generally formed by nucleon pair breaking and nuclear vibrations or rotations. However, for certain numbers of protons and neutrons, a subtle rearrangement of only a few nucleons among the orbitals at the Fermi surface can result in a different elementary mode: a macroscopic shape change. The first experimental evidence for this phenomenon came from the observation of shape coexistence in 16O (ref. 4). Other unexpected examples came with the discovery of fission isomers and super-deformed nuclei. Here we find experimentally that the lowest three states in the energy spectrum of the neutron deficient nucleus 186Pb are spherical, oblate and prolate. The states are populated by the alpha-decay of a parent nucleus; to identify them, we combine knowledge of the particular features of this decay with sensitive measurement techniques (a highly efficient velocity filters with strong background reduction, and an extremely selective recoil-alpha-electron coincidence tagging methods). The existence of this apparently unique shape triplet is permitted only by the specific conditions that are met around this particular nucleus.

In the centres of stars where the temperature is high enough, three alpha-particles (helium nuclei) are able to combine to form 12C because of a resonant reaction leading to a nuclear excited state. (Stars with masses greater than approximately 0.5 times that of the Sun will at some point in their lives have a central temperature high enough for this reaction to proceed.) Although the reaction rate is of critical significance for determining elemental abundances in the Universe, and for determining the size of the iron core of a star just before it goes supernova, it has hitherto been insufficiently determined. Here we report a measurement of the inverse process, where a 12C nucleus decays to three alpha-particles. We find a dominant resonance at an energy of approximately 11 MeV, but do not confirm the presence of a resonance at 9.1 MeV (ref. 3). We show that interference between two resonances has important effects on our measured spectrum. Using these data, we calculate the triple-alpha rate for temperatures from 10(7) K to 10(10) K and find significant deviations from the standard rates. Our rate below approximately 5 x 10(7) K is higher than the previous standard, implying that the critical amounts of carbon that catalysed hydrogen burning in the first stars are produced twice as fast as previously believed. At temperatures above 10(9) K, our rate is much less, which modifies predicted nucleosynthesis in supernovae.

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Using decays of a clean source of 12 N produced at the IGISOL facility, we have measured the breakup of the 12 C (12.71 MeV) state into three particles with a segmented particle detector setup. The high quality of the data permits solving the question of the breakup mechanism of the 12.71 MeV state, a longstanding problem in few-body nuclear physics. Among existing models, a modified sequential model fits the data best, but systematic deviations indicate that a three-body description is needed.