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Microscopic Cluster Model for Exotic Nuclei

Microscopic Cluster Model for Exotic Nuclei. M. Tomaselli a,b Th. Kühl a , D. Ursescu a. a Gesellschaft für Schwerionenforschung, D-64291 Darmstadt,Germany b Technical University Darmstadt, D-64289 Darmstadt, Germany. Motivation. Perturbative cluster theory.

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Microscopic Cluster Model for Exotic Nuclei

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  1. Microscopic Cluster Model for Exotic Nuclei M. Tomasellia,b Th. Kühla, D. Ursescua a Gesellschaft für Schwerionenforschung, D-64291 Darmstadt,Germany b Technical University Darmstadt, D-64289 Darmstadt, Germany

  2. Motivation Marco Tomaselli

  3. Perturbative cluster theory Correlations can be introduced via eiS method ..... Perturbation approximation possible. We prefer to calculate the effective operators. The perturbative terms of the correlation operators Si correspond to the diagram of the dynamic theory. The particle–hole terms generated by the S3 operator are put to zero in the ladder perturbation. Marco Tomaselli

  4. Effective Hamiltonian S2 Marco Tomaselli

  5. The wavefunction of the deuteron wavefunction amplitude radius (fm) Marco Tomaselli

  6. From UMO to DCM Marco Tomaselli

  7. The Equation of Motion (EoM) in the zero order dynamic linearization (GLA) Marco Tomaselli

  8. The Hamilton's Operator Marco Tomaselli

  9. The Equation of Motion (EoM)-III Marco Tomaselli

  10. The Equation of Motion (EoM) in the second order GLA-IV Marco Tomaselli

  11. The Equation of Motion (EoM)-V Marco Tomaselli

  12. The Non-Linear Eigenvalue Equation Marco Tomaselli

  13. Configuration mixing wave functions (CMWF) for 2 dressed particles Marco Tomaselli

  14. Cluster model based on Dynamic Correlation Model (DCM) ...... Marco Tomaselli

  15. Theory of correlated operators I: Magnetic Moment (mm) Marco Tomaselli

  16. Theory of correlated operators II: Single particle distribution Marco Tomaselli

  17. Theory of correlated operators III: Distribution in BDCM Marco Tomaselli

  18. Effect of linearisation on commutator chain for one body Within the GLA the higher order terms (3p-2h) are calculated with the Wick's theorem by neglecting the normal order. Collect the resulting terms Dynamic eigenvalue equations for mixed mode amplitudes 1 particle => 2 particles – 1 hole The generalization for 1h case is straightforward Marco Tomaselli

  19. Application to 15O and the additional commutator. Magnetic moment (mm) of the ground state Marco Tomaselli

  20. Application to 17O and the additional commutator. Magnetic moment (mm) of the ground state Marco Tomaselli

  21. Effect of linearisation on commutator chain for two body clusters Within the GLA the higher order terms (4p-2h) are calculated with the Wick's theorem by neglecting the normal order. Collect the resulting terms Dynamic eigenvalue equations for mixed mode amplitudes 2 particles => 3 particles – 1 hole Marco Tomaselli

  22. Dynamics eigenvalue equation for one dressed dressed nucleon clusters which is solvable self-consistently Marco Tomaselli

  23. Degree of spuriousity Marco Tomaselli

  24. Application to light nuclei: charge distributions of 6He Marco Tomaselli

  25. Charge radii of 6He Marco Tomaselli

  26. Charge distributions of 6Li Marco Tomaselli

  27. Positive and Negative parity states in 18O Marco Tomaselli

  28. Comparison with Vlow-k potential: 18O Marco Tomaselli

  29. Medium effects on the two body matrix elements (18O) Marco Tomaselli

  30. Application to 14C and the additional commutator. Marco Tomaselli

  31. The EoM of the Three Nucleon Clusters Marco Tomaselli

  32. Three particle Dynamic model Marco Tomaselli

  33. Application to light nuclei: nuclear results for Li isotopes Marco Tomaselli

  34. Summary of Charge Radii Rc = charge radius Rp = point radius References: Method: [1] I. Tanihata, Phys. Lett B 206,592 (1988) Interaction Cross Sections with Glauber model, HO distributions [2] P. Navratil, PRC 57,3119 (1998) Large-basis shell-model calculations [3] S. Pieper, Annu.Rev.Nucl.Part.Sci. 51, 53 (2001) Greens Function Monte Carlo AV18/IL2 [4] S. Pieper, PRC 66, 044310 (2002) Greens Function Monte Carlo AV18/IL2 [5] Suzuki, Progr.Theo.Phys.Suppl. 146, 413 (2002) Stochastic Variational Multicluster Method on a correlated gaussian basis [6] M. Tomaselli et al., Can. J. Phys. 80, 1347 (2002) Dynamic Correlation model [7] Penionzhkevich, Nucl.Phys. A 616, 247 (1997) coupled channel calculations, double-folding optical potential, M3Y effective interaction [8] C.W. de Jager, At.Dat.Nucl.Dat.Tab. 14, 479 (1974) Electron Scattering

  35. Application to 19O and the additional commutator. Marco Tomaselli

  36. Application to 15C and the additional commutator. Marco Tomaselli

  37. Application to 20O and the additional commutator. Marco Tomaselli

  38. Energy splitting and BE(E2;2+ 0+) transition for 16C Marco Tomaselli

  39. Cluster Factorization Theory I Marco Tomaselli

  40. Cluster Factorization Theory II Marco Tomaselli

  41. Cluster Factorization Theory III Marco Tomaselli

  42. Cluster Factorization Theory IV Marco Tomaselli

  43. Factorisation of the model CMWFs in terms of cluster coefficients The factorisation method is presently applied to reduce complex Feynman diagrams to simple form Interaction between nucleons Particle line Hole line Marco Tomaselli

  44. Thank You! Marco Tomaselli

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