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ISTANBUL-06

ISTANBUL-06. Covariant Density Functionals with Spectroscopic Properties and Quantum Phase Transitions in Finite Nuclei. Vietri sul Mare, May 24, 2010. Peter Ring. Technical University Munich. Publications: Niksic , Vretenar, Lalazissis, P.R., PRL 99 , 092502 (2007)

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ISTANBUL-06

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  1. ISTANBUL-06 Covariant Density Functionals with Spectroscopic Propertiesand Quantum Phase Transitions in Finite Nuclei Vietri sul Mare, May 24, 2010 Peter Ring Technical University Munich Publications: Niksic, Vretenar, Lalazissis, P.R., PRL 99, 092502 (2007) Niksic, Li, Vretenar, Prochniak, Meng, P.R., PRC 79, 034303 (2009) Li, Niksic, Vretenar, Meng, Lalazissis, P.R., PRC 79, 054301 (2009) X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  2. Covariant density functional theory Calculations of Spectra Content: Quantum phase transitions - Generator Coordinate Method - axial symmetric calculations of the Nd-chain - 5-dimensional Bohr Hamiltonian Order parameters - R42, B(E2), - isomer shifts, - E0-strength Conclusions X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  3. X(5) 152Sm Quantum phase transitions and critical symmetries: Interacting Boson Model Casten Triangle E(5): F. Iachello, PRL 85, 3580 (2000) X(5): F. Iachello, PRL 87, 52502 (2001) R.F. Casten, V. Zamfir, PRL 85 3584, (2000) X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  4. Transition U(5) → SU(3) in Nd-isotopes: R. Krücken et al, PRL 88, 232501 (2002) R = BE2(J→J-2) / BE2(2→0) X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  5. Quantum phase transitions in the Interacting Boson Model: E(5) X(5) E(5): F. Iachello, PRL 85, 3580 (2000) X(5): F. Iachello, PRL 87, 52502 (2001) X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  6. Critical E Spherical PES Spectrum β • First and second order QPT can • occur between systems characterized • by different ground-state shapes. • Control Parameter: Number of nucleons Deformed X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  7. Mean field: Eigenfunctions: Interaction: Density functional theory in nuclei: Density functional theory Extensions: Pairing correlations, Covariance Relativistic Hartree Bogoliubov (RHB) theory Walecka model: g(ρ) X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  8. ω ω ρ ρ σ σ Point-coupling models with derivative terms: gσ(ρ) gω(ρ) gρ(ρ) Manakos and Mannel, Z.Phys.330, 223 (1988) Bürvenich, Madland, Maruhn, Reinhard, PRC 65, 044308 (2002): PC-F1 Niksic, Vretenar, P.R., PRC 78, 034318 (2008): DD-PC1 Effective density dependence: The basic idea comes from ab initio calculations density dependent coupling constants include Brueckner correlations and threebody forces non-linear meson coupling: NL3 gσ(ρ) gω(ρ) gρ(ρ) adjusted to ground state properties of finite nuclei Typel, Wolter, NPA 656, 331 (1999) Niksic, Vretenar, Finelli, P.R., PRC 66, 024306 (2002): DD-ME1 Lalazissis, Niksic, Vretenar, P.R., PRC 78, 034318 (2008): DD-ME2 X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  9. Comparison with ab initio calculations: ab initio (Baldo et al) neutron matter DD-ME2 (Lalazissis et al) nuclear matter we find excellent agreement with ab initio calculations of Baldo et al. X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  10. data from ab initio calculations are in the fit: point coupling model is fittedto microscopic nuclear matter andto masses of 66 deformed nuclei: av = 16,04 av = 16.06 av = 16,08 av = 16,10 av = 16,12 av = 16,14 av = 16.16 ρsat= 0.152 fm-3 m* = 0.58m Knm = 230 MeV a4 = 33 MeV DD-PC1 A. Akmal, V.R. Pandharipande, and D.G. Ravenhall, PRC. 58, 1804 (1998). X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  11. Problems: • no fluctuation in transitional nuclei • noenergy dependence of the self energy • symmetry violations are difficult to restore • no spectroscopy Advantages of density functional methods: • they are defined in the full model space (no valence particles) • the functional is universal and applicable throughout the periodic chart. • the results are easy to visualize (e.g. single particle motion) • pure vibrational excitations can be calculated by selfconsistent RPA • pure rotational excitations can be calculated in the Cranking Model X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  12. Can a universal density functional, adjusted to ground state properties, at the same time reproduce critical phenomena in spectra ? We need a method to derive spectra: GCM, ATDRMF We consider the chain of Nd-isotopes with a phase transition from spherical (U(5)) to axially deformed (SU(3)) X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  13. Generator Coordinate Method (GCM) (Hill & Wheeler 1952) Constraint Hartree Fock produces wave functions depending on agenerator coordinate q GCM wave functionis a superposition of Slater determinants Hill-Wheeler equation: with projection: X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  14. X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  15. R. Krücken et al, PRL 88, 232501 (2002) Niksic et al PRL 99, 92502 (2007) F. Iachello, PRL 87, 52502 (2001) GCM: only one scale parameter: E(21) X(5): two scale parameters: E(21), BE2(22→01) Problem of GCM at this level: restricted to γ=0 X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  16. X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  17. X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  18. X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  19. X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  20. potential energy suface: First relativictic full 3D GCM calculations in 24Mg Yao et al, PRC 81,044311 (2010) collective wave functions: 24Mg X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  21. 1) good agreement in BE2-values (no effective charges) 2) theoretical spectrum is streched 3) β-band has no rotational character 24Mg X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  22. triaxial GCM in q=(β,γ) is approximated by the diagonalization of a 5-dimensional Bohr Hamiltonian: the potential and the inertia functions are calculated microscopically from rel. density functional Theory: Giraud and Grammaticos (1975) (from GCM) Baranger and Veneroni (1978) (from ATDHF) Skyrme: J. Libert,M.Girod, and J.-P. Delaroche (1999) RMF: L. Prochniak and P. R. (2004) Niksic, Li, et al (2009) X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  23. Potential energy surfaces: X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  24. Microscopic analysis of nuclear QPT: • Spectum GCM: only one scale parameter: E(21) X(5): two scale parameters: E(21), BE2(22→01) No restriction to axial shapes X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  25. neutron levels X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  26. Conclusions 1 ------- questions: - How much are the discontinuities smoothed out in finite systems ? - How well can the phase transition be associated with a certain value of the control parameter that takes only integer values ? - Which experimental data show discontinuities in the phase transition? X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  27. Sharp increase of R42=E(41)/E(21) and B(E2;21-01) X(5) 4 X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  28. Isomeric shifts in the charge radii X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  29. Properties of 0+ excitations X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  30. Monopol transition strength ρ(E0; 02 – 01) X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  31. Fission barrier andsuper-deformed bandsin 240Pu X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  32. Conclusions 1 ------- Conclusions: GCM calculations for spectra in transitional nuclei - J+N projection is important, - triaxial calculations so only for very light nuclei possible Derivation of a collective Hamiltonian - allows triaxial calculations - nuclear spectroscopy based on density functionals - open question of inertia parameters The microscopic framework based on universal density functionals provides a consistent and (nearly) parameter free description of quantum phase transitions The finiteness of the nuclear system does not seem to smooth out the discontinuities of these phase transitions X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

  33. Collaborators: T. Niksic (Zagreb) D. Vretenar (Zagreb) G. A. Lalazissis (Thessaloniki) L. Prochniak (Lublin) Z.P. Li (Beijing) J.M. Yao (Chonqing) J. Meng (Beijing) X International Spring Meeting on Nuclear Physics, Vietri sul Mare, May 2010

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