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\(\alpha\)-cluster states and \(4 \alpha\)-particle Bose condensate in \(^{16}{\text{O}}\). (English) Zbl 1170.81475

Summary: In order to explore the \(4 \alpha\)-particle condensate state in \(^{16}{\text{O}}\), we solve a full four-body equation of motion based on the \(4 \alpha\) OCM (Orthogonality Condition Model) in a large \(4 \alpha\) model space spanned by Gaussian basis functions. A full spectrum up to the \(0^{+}_{6}\) state is reproduced consistently with the lowest six \(0^{+}\) states of experimental spectrum. The \(0_{6}^{+}\) state is obtained at 2 MeV above the \(4 \alpha\) breakup threshold and has a dilute density structure, where the rms radius is more than 5 fm. The state has an appreciably large \(\alpha\) condensate fraction 61 %, and a highly amount of \(\alpha + ^{12}{\text{C}}(0_{2}^{+})\) components, both of which are strong pieces of evidence of the state being the \(4 \alpha\) condensate state.

MSC:

81V35 Nuclear physics
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
82B26 Phase transitions (general) in equilibrium statistical mechanics
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