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NEW INSIGHT ON THE CHAIN STATES AND BOSE-EINSTEIN CONDENSATE IN THE LIGHT NUCLEI

NEW INSIGHT ON THE CHAIN STATES AND BOSE-EINSTEIN CONDENSATE IN THE LIGHT NUCLEI. K.A. Gridnev, S. Yu. Torilov, W. Greiner. Saint-Petersburg State University. Light self-conjugated nuclei. Structure (Two possibilities). α. α. α. α. α. nucleons. α. α. α. α. 8. Be. D.

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NEW INSIGHT ON THE CHAIN STATES AND BOSE-EINSTEIN CONDENSATE IN THE LIGHT NUCLEI

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  1. NEW INSIGHT ON THE CHAIN STATES AND BOSE-EINSTEIN CONDENSATE IN THE LIGHT NUCLEI K.A. Gridnev, S. Yu. Torilov, W. Greiner Saint-Petersburg State University

  2. Light self-conjugated nuclei Structure (Two possibilities) α α α α α nucleons α α α α

  3. 8 Be D Θ= const. ρ ρ ρ p tot n P. Arumugan, et al. Phys. Rev. C71 064308 (2005)

  4. <T> ~ number of kinds of Jacobi coordinates <V> ~ number of bonds Binding energy ~ <T> + <V> (H. Horiuchi, K. Ikeda, Cluster model of the nuclei) Binding energy Binding energy

  5. E Bind MeV 20 15 10 5 L.R. Hafstad, E. Teller, Phys. Rev. 54 (1938) 681 2 4 6 8 N Bonds

  6. Spin-isospin alpha-like combinations of nucleons in nuclei D Alpha-particle

  7. Energy levels of an harmonic-oscillator potential for prolate deformation P. Ring, P. Schuk “The nuclear many-body problem”

  8. Chain configurations in light nuclei 2 Efr – fragmentation energy Eb – binding energy of the configuration

  9. The breaking up of bonds 1 Bond ~ 3 MeV 3 Bonds ~ 9 MeV + < 4 Bonds + 5 Bonds > ~ 13.5 MeV

  10. Shell-model calculations with Strutinsky corrections

  11. Classification of the alpha-particle states in 20Ne

  12. Radial density distribution of 8Be ρ [fm-3] R

  13. Bose-Einstein Condensation description A) Nonlinear Schrödinger equation – Gross-Pitaevskii equation (K. A. Gridnev et al., Cond . Matter. Theor. 15, Nova Science, Ney-York, 2000) B) Linear Schrödinger equation (S. Mishra, P. Pfeifer, J. Phys. A40 (2007) F243) • Conditions for BEC • No nodes • The same value of momentum for every α’s • λα~ D • ρnucl ~ ⅓ρ0

  14. Folding potential “Nucleons-clusters” phase transition (Brink ) Alpha-particles density distribution (Hofstadter) Alpha-alpha interaction (Yamada, Schuck Phys. Rev. C69 (2004) 024309 ) One-particle energy

  15. Cluster density distribution 12 C Nucleons Phase transition (ρ ~ 1/3ρ0) BEC

  16. The solution of the Schrödinger equation with a folding potential for 12C,16O and 20Ne EBEC=ESch (Nα-1)

  17. Results

  18. Conclusion Though we do not think that the model here presented is good enough to give a detailed account of experimental facts, we believe that it is not worse than the Hartree model. L.R. Hafstad, E. Teller, Phys. Rev. v54 (1938) 681 BEC is a new state of the nuclear matter. It manifests itself for high excitations and small values of the alpha’s momentum in the momentum space.

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