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Highly deformed modes in the ab initio symplectic no-core shell model
T Dytrych, K D Sviratcheva, C Bahri, J P Draayer and J P Vary 2008 J. Phys. G: Nucl. Part. Phys. 35 095101 (12pp)   doi: 10.1088/0954-3899/35/9/095101

Analysis of previous microscopic calculations for the second 0⁺ state in ¹²C in terms of 3- alpha particle Bose-condensed state

Abstract. The wave function of the second 0⁺ state of ¹²C, which was obtained a long time ago by solving the microscopic 3 alpha problem, is shown to be almost completely equivalent to the wave function of the 3 alpha condensed state, which has been proposed recently by the present authors. This equivalence of the wave functions is shown to hold in two cases where different effective two-nucleon forces are adopted. This finding gives strong support for interpreting the second 0⁺ state of ¹²C, which is the key state for the synthesis of ¹²C in stars ("Hoyle" state), and which is one of the typical mysterious 0⁺ states in light nuclei, as a gaslike structure of three alpha particles, Bose condensed into an identical s-wave function

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