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Nuclear Dynamics in Time-Dependent Picture

Nuclear Dynamics in Time-Dependent Picture. Takashi Nakatsukasa University of Tsukuba Collaborator: Kazuhiro Yabana (U.T.). The 6 th China-Japan Joint Nuclear Physics Symposium, May 16-20, 2006. Time-dependent approach to quantum mechanical problems. Time rep. vs Energy rep.

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Nuclear Dynamics in Time-Dependent Picture

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  1. Nuclear Dynamicsin Time-Dependent Picture Takashi Nakatsukasa University of Tsukuba Collaborator: Kazuhiro Yabana (U.T.) The 6th China-Japan Joint Nuclear Physics Symposium, May 16-20, 2006

  2. Time-dependent approach to quantum mechanical problems Time rep. vs Energy rep. Nuclear TDDFT (TDHF) Giant resonances Nuclear screening effects at drip line

  3. Basic equations Time-dep. Schroedinger eq. Time-dep. Kohn-Sham eq. Energy resolution ΔE〜ћ/T All energies Boundary Condition No need for BC Approximate BC Easy for complex systems Basic equations Time-indep. Schroedinger eq. Static Kohn-Sham eq. (Eigenvalue equation) Energy resolution ΔE〜0 A single energy point Boundary condition Exact scattering boundary condition is possible Difficult for complex systems Energy Domain Time Domain

  4. Applications of the time-dependent framework Fusion reactions: NPA722 (2003) 261c; PTPS154 (2004) 85; nucl-th/0506073 (PLB) Linear response in molecules: JCP114 (2001) 2550; CPL374 (2003) 613 Linear response in nuclei: PTPS146 (2002) 447; EPJA20 (2004) 163; PRC71 (2005) 024301 In this talk, we focus on the linear density response (RPA). TDHF with effective interactions

  5. Skyrme TDHF in real space Time-dependent Hartree-Fock equation 3D space is discretized in lattice Single-particle orbital: N: Number of particles Mr: Number of mesh points Mt: Number of time slices y [ fm ] Spatial mesh size is about 1 fm. Time step is about 0.2 fm/c Nakatsukasa, Yabana, Phys. Rev. C71 (2005) 024301 X [ fm ]

  6. Real-time calculation of response functions • Weak instantaneous external perturbation • Calculate time evolution of • Fourier transform to energy domain ω [ MeV ]

  7. 300 BKN with continuum IS Octupole Strength [ fm6/MeV ] SGII without continuum 0 10 20 30 40 50 E [ MeV ] Exp for HEOR LEOR & HEOR in 16O Perrin et al. (1977) Low-lying 3–state SGII int.→ E ≈ 7, 13, 14 MeV Exp . → E ≈ 6.1, 11.6, 13, 14 MeV

  8. 50 16O E1 resonances in 16,22,28O Leistenschneider et al, PRL86 (2001) 5442 σ [ mb ] 0 50 22O Berman & Fultz, RMP47 (1975) 713 SGII parameter set Г=0.5 MeV Note: Continnum is NOT taken into account ! σ [ mb ] 0 50 28O σ [ mb ] 0 0 20 40 E [ MeV ]

  9. Giant dipole resonance instable and unstable nuclei Classical image of GDR p n

  10. Neutrons Time-dep. transition density δρ> 0 28O 16O δρ< 0 Protons

  11. Skyrme HF for 8,14Be z y z x x x 8Be 14Be Neutron Proton S.Takami, K.Yabana, and K.Ikeda, Prog. Theor. Phys. 94 (1995) 1011.

  12. δρ> 0 8Be δρ< 0 Solid: K=1 Dashed: K=0 14Be

  13. Giant dipole resonance p p “Screening” Neutron-rich N=Z nuclei n n

  14. E1 polarizability 8Be 8Be No dynamical screening Dynamical screening Protons Protons Neutrons Neutrons Total Total No dynamical screening With dynamical screening 14Be 14Be Neutrons Protons Protons Neutrons Total Total Negative polarization of weakly-bound neutrons

  15. + － － + + － － + － + － + + － Electronic dynamical screening Nuclear dynamical screening p n

  16. Summary • TDDFT(TDHF)+ABC to study dynamical aspects of nuclear response in the continuum • Neutron-proton attractive correlation leads to a complex dipole motion (“screening”) for neutron-rich nuclei • …, though the frequency decomposition is necessary for a definite answer. Stable (N=Z) Neutron-rich (N >> Z)

  17. Boundary Condition Absorbing boundary condition (ABC) Absorb all outgoing waves outside the interacting region How is this justified? All the scattering information resides in the interacting region. Localized w.f.

  18. + － － + － + － + － + － + + － Linear optical absorption TDDFT accurately describe optical absorption Dynamical screeningeffect is significant PZ+LB94 with Dynamical screening without TDDFT Exp Without dynamical screening (frozen Hamiltonian) T. Nakatsukasa, K. Yabana, J. Chem. Phys. 114(2001)2550.

  19. Damping width of GDR near drip line Enhancement of escape width : Г↑ Phase space Threshold effect Enhancement of Landau damping : ГL↓ Large diffuseness of the mean-field potential → Many 1p-1h states with the same symmetry 1p-1h 2 ω0 excitations ωGDR ≈ 79 A-1/3 MeV ≈ 2 ω0 Positive-parity

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