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ISTANBUL-06

ISTANBUL-06. Density functional theory and nuclear shape transitions. Sofia, Oct. 8, 2015. Peter Ring. Technical University Munich Excellence Cluster “Origin of the Universe” Peking University, Beijing. X(5). 152 Sm. Quantum phase transitions and critical symmetries.

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ISTANBUL-06

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  1. ISTANBUL-06 Density functional theory and nuclear shape transitions Sofia, Oct. 8, 2015 Peter Ring Technical University Munich Excellence Cluster “Origin of the Universe” Peking University, Beijing „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  2. 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) „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  3. Transition U(5) → SU(3) in Ne-isotopes R. Krücken et al, PRL 88, 232501 (2002) R = BE2(J→J-2) / BE2(2→0) „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  4. 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) „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  5. Courtesy: Zhipan Li 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 „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  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 Can we descibe such phenomena in a microscopic picture, with nucleonic degrees of freedom,free of phenomenological parameters? Deformed „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  7. Motivation: proton number Z Density functional Theory (DFT) Shell model Coupled cluster Ab initio neutron number N „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  8. Density functional theory (DFT) for manybody quantum systems The manybody problem is mapped onto a one-body problem: Density functional theory starts from the Hohenberg-Kohn theorem: „The exact ground state energy E[ρ] is a universal functional for the local density ρ(r)“ Kohn-Sham theory starts with a density dependent self-energy: and the single particle equation: with the exact density: : In Coulombic systems the functional is derived ab initio „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  9. Basic problems of density functional theory in nuclei: ● Nuclei are selfbound systems ●Symmetry breaking is important: Advantage: Problems: Correlations can be no good quantum numbers taken into account no spectroscopy in simple wave functions projection required translational, rotational, gauge symmetry, ……. momentum P spin J particle number N ●Shape coexistence: transitional nuclei, shape transitions ●Energy dependence of self energy ● at present all successful functionals are phenomenological Janus „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  10. 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: Generator coordinate method (GCM), Adiabatic time-dependent relativistic mean field (ATDRMF) We consider the chain of Ne-isotopes with a phase transition from spherical (U(5)) to axially deformed (SU(3)) „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  11. DFT beyond mean field: GCM-method Constraint Hartree Fock produces wave functions depending on agenerator coordinate q GCM wave functionis a superposition of Slater determinants Hill-Wheeler equation: with projection: „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  12. GCM: „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  13. Spectra in 24Mg Mg-24 spectrum „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  14. Spectra in 24Mg Mg-24 spectrum „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  15. „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  16. 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 „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  17. „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  18. „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  19. „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  20. „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  21. 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) „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  22. B Inertia of Thouless Valatin: Moment of inertia Zhipan Li et al PRC 86 (2012) 1.32 „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  23. Potential energy surfaces: „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  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 „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  25. 5D-benchmark calculations for 76Kr Generator-Coordinates: q = (β,γ) Projection on J and N: (5 angles) J.M. Yao, K. Hagino, Z.P. Li, P.R. , J. Meng PRC (2014) „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  26. Spectra: GCM (7D) Bohr Hamiltonian (5DCH) PC-PK1 J.M. Yao et al, PRC (2014) „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  27. quasi-βband ground state band wave functions J.M. Yao et al, PRC (2014) quasi-γband „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  28. Fission barrier andsuper-deformed bandsin 240Pu Zhipan Li et al, PRC (2010) „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  29. Static DFT in nuclei has is limits: no good quantum numbers (spectroscopic data) no fluctuations (shape coexistence, transitions) Generator-Coordinate Method succesful, but complicated, problem with moment of inertia Derivation of a collective Hamiltian (from GCM, from ATDHF) benchmark calculations show excellent agreement Application for Quantum Phase Transitions (QPT) Conclusions Limitations:number and nature of the collective variables q „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  30. Thanks to my collaborators: Jiangming Yao (Chongqing,Sendai) Zhipan Li (Chongqing) Jie Meng (Beijing) T. Niksic (Zagreb) D. Vretenar (Zagreb) G. A. Lalazissis (Thessaloniki) L. Prochniak (Lublin) „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  31. 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? „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  32. Sharp increase of R42=E(41)/E(21) and B(E2;21-01): X(5) 4 „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  33. Properties of 0+ excitations „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  34. Monopol transition strength ρ(E0; 02 – 01) „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  35. T.Niksic (2011) „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  36. T.Niksic (2011) „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  37. T.Niksic (2011) „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  38. T.Niksic (2011) „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  39. T.Niksic (2011) „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  40. Derivation of a collective Hamiltonian from GCM: Gaussian overlap approach: „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  41. Yoccoz-inertia: „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

  42. time-odd Adiabatic TDHF: Baranger+Veneroni (1978) time-even „Shapes and Dynamics of Atomic Nuclei: Contemporary Apects“, Sofia, Oct. 8-10, 2015

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