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Fully self-consistent calculation of isovector dipole response: Systematic study up to A=50

Tsunenori Inakura Takashi Nakatsukasa Kazuhiro Yabana. ( Univ. of Tsukuba ) ( RIKEN ) ( Univ. of Tsukuba ). Fully self-consistent calculation of isovector dipole response: Systematic study up to A=50. First FIDIPRO-JSPS Workshop on Energy Density Functionals in Nuclei

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Fully self-consistent calculation of isovector dipole response: Systematic study up to A=50

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  1. Tsunenori Inakura Takashi Nakatsukasa Kazuhiro Yabana (Univ. of Tsukuba) (RIKEN) (Univ. of Tsukuba) Fully self-consistent calculationof isovector dipole response:Systematic study up to A=50 First FIDIPRO-JSPS Workshop on Energy Density Functionals in Nuclei Keurusselka, (Jyväskylä) FINLAND October 25-27, 2007.

  2. 3 distinct computational methodsfor fully self-consistent linear-response calculation in 3D grid representation Diagonalization • Obtain eigenfunction X, Y directly. • Time-consuming (to go to high energy region). • Not suitable to be parallelized. Real-time TDHF (Impulse response) • Easy to obtain overall strength. • Not easy to extract eigenfunction X, Y. • Isovector only. • Parallelization: Coordinate, Orbit, …. Energy-fixed response • Obtain solution at arbitrary (complex) energy. • Many calculations to obtain overall strength. • Parallelization: Energy, Coordinate, Orbit, ….

  3. Lowest negative-parityexcited states 3- SGII SIII SkM* Exp. 1-

  4. TDHF+ABC 16O SkM* SGII

  5. Adaptive Coordinate Nakatsukasa & Yabana, PRC71, 024301 # = 27736 # = 11760

  6. Finite Amplitude Method (FAM) Phys. Rev. C76, 024318

  7. TDHF eq. Perturbation is weak. Linear-response eq. Fourier Transformation Linear-response eq. in w-representation Introducing single-particle orbit. RPA eq. to be solved

  8. RPA eq. Residual interaction is …

  9. Diagonalization vs. Energy-fixed response with FAM 16O SIII G = 2 MeV Lbox= 10 fm

  10. TDHF vs. Energy-fixed response with FAM 16O SkM* TDHF+ABC TDHF FAM G = 1 MeV Rbox = 15fm

  11. IVGDR in 16O

  12. Isovector dipole strengths up to Ar isotopes SkM* Rbox= 15 fm G = 1 MeV

  13. 16O spherical 18O prolate Exp. data : http://cdfe.sinp.msu.ru/services/

  14. 24Mg prolate 26Mg triaxial Exp. data : http://cdfe.sinp.msu.ru/services/

  15. 12C spherical 40Ca spherical Exp. data : http://cdfe.sinp.msu.ru/services/

  16. Peak position of IVGDR Si C O S Ar Be Ne Mg Cal. vs. Exp. No clear relation between evolution of peak positionand deformation. 14C 22Ne

  17. Peak splitting by deformation

  18. Low-lying dipole strength in deformed nucleus 26Ne J. Gibelin, Ph. D thesis.

  19. IV dipole responses in Ne isotopes 26Ne SkM*

  20. 26Ne Exp. SkM* G = 1MeV K=0 K=1

  21. Low-lying K=1 state

  22. Particle states in low-lying K=1 state

  23. N=16 (2s1/2) Energy Weighted Sum value up to 10 MeV C Be O Ne Mg Si S Ar

  24. ( 2s1/2 ) N=12 N=14 N=18 N=16 N=20

  25. PACS-CS @ Univ. of Tsukuba Xeon 2.8GHz, 3D Hyper-Crossbar, 2560 CPUs, 14.3TFlops.

  26. Summary • Fully self-consistent linear response calculation in 3D mesh. • Finite Amplitude Method (FAM). • adaptive coordinate. • Systematic study up to Ar isotopes. • underestimate peak position of IVGDR. • peak splitting by deformation. • Applied to pygmy resonance in 26Ne. • neutron emission from 2s1/2. • Perspective. • heavier nuclei. • Absorbing Boundary Condition (ABC).

  27. Low-lying K=0 state

  28. Particle states in low-lying K=0 state

  29. Gogny-QRPA calc. Peru et al., Nucl. Phys. A788, 44c K=0 Skyrme-RPA K=1

  30. 12C 14C 10 20 30 40 Ex [ MeV ] 10 20 30 40 Ex [ MeV ]

  31. 18O 16O Prolate 10 20 30 40 Ex [ MeV ] 40

  32. 26Mg 24Mg Triaxial Prolate 10 20 30 40 10 20 30 40 Ex [ MeV ] Ex [ MeV ]

  33. 28Si 30Si Oblate Oblate 10 20 30 40 Ex [ MeV ] 10 20 30 40 Ex [ MeV ]

  34. 32S 34S Prolate Oblate 10 20 30 40 10 20 30 40 Ex [ MeV ] Ex [ MeV ]

  35. 44Ca Prolate 48Ca 40Ca 10 20 30 Ex [ MeV ] 10 20 30 40 Ex [ MeV ] 10 20 30 40 Ex [ MeV ]

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