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Andreas Krugmann

Comparison of the confined β -soft Rotor Model and a microscopic collective Hamiltonian based on the relativistic mean field model in 150,152 Nd *. Andreas Krugmann. Motivation Theoretical framework Comparison of the model calculations Summary. SFB 634.

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Andreas Krugmann

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  1. Comparison of the confined β-soft Rotor Model and a microscopic collective Hamiltonian based on the relativistic mean field model in 150,152Nd * Andreas Krugmann • Motivation • Theoretical framework • Comparison of the model calculations • Summary SFB 634 *Supported by the DFG within SFB 634 24. März 2011 | TU Darmstadt | Institut für Kernphysik | Andreas Krugmann | 1

  2. Motivation • Description of nuclei in the A=150 phase shape transitional region • CBS model has a very simple macroscopic potential ansatz for solving • the Bohr Hamiltonian (square well potential) • Has the CBS model a microscopic justification? • In 150,152Nd microscopic calculations based on Relativistic Mean Field • approach are available • Comparison of both models 24. März 2011 | TU Darmstadt | Institut für Kernphysik | Andreas Krugmann | 2

  3. Model Potentials • Study impact on the • evolution of nuclear • structure originating in • the shift of the inner • potential wall • To what extend the use of • square well potentials is • microscopically justified? 24. März 2011 | TU Darmstadt | Institut für Kernphysik | Andreas Krugmann | 3

  4. The collective Hamiltonian • Very general form: • Vibrational kinetic energy: • Rotational kinetic energy: • Discuss two different approaches for Vcoll 24. März 2011 | TU Darmstadt | Institut für Kernphysik | Andreas Krugmann | 4

  5. Confined β-Soft (CBS) Rotor Model • Analytical wave functions in deformation coordinate β • Very good description of B(E2) strengths & g.s. band energies in transitional nuclei • Prediction for E0 transition strengths Probability density distribution of g.s. Probability density distribution of 0+2 state N. Pietralla and O. Gorbachenko, Phys. Rev. C 70, 011304(R) (2004) 0 J. Bonnet et al. Phys. Rev. C 79, 034307 (2009) 24. März 2011 | TU Darmstadt | Institut für Kernphysik | Andreas Krugmann | 5

  6. Relativistic mean field Hamiltonian • Moments of inertia • Mass Parameters • collective potential • Potential Vcoll: • Subtracting zero-point energy corrections from total energy • (corresponds to solution of constrained RMF+BCS equations • at each point of the triaxial deformation plane) microscopic nuclear energy-density functional NikšićT, Li Z P, Vretenar D, Prochniak L, Meng J and Ring P 2009 Phys. Rev. C 79, 034303 24. März 2011 | TU Darmstadt | Institut für Kernphysik | Andreas Krugmann | 6

  7. Level Scheme in 150Nd 24. März 2011 | TU Darmstadt | Institut für Kernphysik | Andreas Krugmann | 7

  8. Level Scheme in 152Nd 24. März 2011 | TU Darmstadt | Institut für Kernphysik | Andreas Krugmann | 8

  9. Centrifugal stretching • Relative dynamic • moment of inertia: • Stretching parameter: 24. März 2011 | TU Darmstadt | Institut für Kernphysik | Andreas Krugmann | 9

  10. Wave functions of the g.s. band • Wave functions are very • similar • Centroids at the same • deformation β • Similar amount of centrifugal • stretching in the two models • Potential stiffens with • increasing neutron number 24. März 2011 | TU Darmstadt | Institut für Kernphysik | Andreas Krugmann | 10

  11. Wave functions of the g.s. band • Wave functions are very • similar • Centroids at the same • deformation β • Similar amount of centrifugal • stretching in the two models • Potential stiffens with • increasing neutron number 24. März 2011 | TU Darmstadt | Institut für Kernphysik | Andreas Krugmann | 11

  12. Wave functions of the β-band • Large overlap between • both models • Centroids coincide for • 152Nd • For 150Nd RMF • potential more • repulsive for small • deformations 24. März 2011 | TU Darmstadt | Institut für Kernphysik | Andreas Krugmann | 12

  13. Summary • Two solutions of the collective Hamiltonian have been • tested and compared in the nuclei 150,152Nd • Remarkable similarity of the two models in: • energies, intra- and interband B(E2)-values and centrifugal • stretching • Centroids of the wave functions almost exactly coincide • Ansatz in CBS: • outer potential wall stays almost constant with • varying number of valence neutrons • inner wall that shifts to higher deformations • Microscopically justified for 150,152Nd 24. März 2011 | TU Darmstadt | Institut für Kernphysik | Andreas Krugmann | 13

  14. Thank you for your attention! • Collaborators: • IKP Darmstadt:Southwest University Chonquing: • - Peter von Neumann-Cosel - Zhipan P. Li • - Norbert Pietralla • Peking University:University of Zagreb: • - Jie Meng - Dario Vretenar • Results submitted to Journal of Physics G. 24. März 2011 | TU Darmstadt | Institut für Kernphysik | Andreas Krugmann | 14

  15. Backup 1: CBS Model 13. März 2011 | TU Darmstadt | Institut für Kernphysik | Andreas Krugmann |

  16. Backup 1: CBS operators E0-transition operator E0-transition operator 13. März 2011 | TU Darmstadt | Institut für Kernphysik | Andreas Krugmann |

  17. Backup 2: RMF Hamiltonian Moments of inertia calculated microscopically from Inglis-Belyaev Mass parameters are calculated in the cranking approximation 13. März 2011 | TU Darmstadt | Institut für Kernphysik | Andreas Krugmann |

  18. Backup 3: RMF Projections Probability density distribution in the (β,γ)-plane Normalization: Projection to the (β)-plane for comparing with CBS: 13. März 2011 | TU Darmstadt | Institut für Kernphysik | Andreas Krugmann |

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