Jacobi Transformations in Four-cluster Systems

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The matter in many-body quantum systems is not always uniformly distributed. Particles inside it, whether they are molecules, atoms or nucleons, can gather together forming clusters. In light atomic nuclei, many states are known in which nucleons gather into two of three clusters. Recently, experimentalists from Birmingham, Surrey and York have studied nuclear states that behave like four-cluster systems, namely, the carbon isotope 10C which is made of two alpha-particles and two protons, and some excited states in 16O that behave like systems of four individual alpha-particles. The present proposal is to begin a theoretical model to deal with four-cluster states and to apply this model to 10Be, 10C and 16O. This will later enable us find out if any of the 4-alpha states in 16O can be considered as a Bose-Einstein condensate of four individual alpha-particles.