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The Study of Nuclear Structures with the Brueckner-AMD

The Study of Nuclear Structures with the Brueckner-AMD. Tomoaki Togashi and Kiyoshi Kato. Department of Physics, Hokkaido University. P. ｎ. ｎ. ｎ. ｎ. INPC2007, Tokyo June 6, 2007. P. P. ｎ. Purposes.

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The Study of Nuclear Structures with the Brueckner-AMD

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  1. The Study of Nuclear Structures with the Brueckner-AMD Tomoaki Togashi and Kiyoshi Kato Department of Physics, Hokkaido University P ｎ ｎ ｎ ｎ INPC2007, Tokyo June 6, 2007 P P ｎ

  2. Purposes - We develop a new ab initio calculation framework based on the antisymmetrized molecular dynamics (AMD) and the Brueckner theory. Brueckner-AMD; the Brueckner theory + Antisymmetrized molecular dynamics (AMD) T.Togashi and K.Kato; Prog. Theor. Phys. 117 (2007) 189

  3. H.Bando, Y.Yamamoto , S.Nagata , PTP 44 (1970) 646 Framework of the Brueckner-AMD ( Gaussian wave packet ) ｎ P ｎ ｎ ｎ ｎ P ｎ P P ｎ P P ｎ The state at the energy minimum A.Dote, H.Horiuchi, PTP 103 (2000) 91 A.Dote, Y.Kanada-En’yo, H.Horiuchi, PRC56 (1997) 1844 1. AMD wave function ( Slater determinant ) 2. Single particle orbits are constructed with the AMD-HF 4. The frictional cooling method ( B-matrix ) ( diagonalization ) single particle orbit* 3. G-matrix is calculated with the single particle orbits ( Bethe-Goldstone equation ) self-consistent *The single particle orbits should be Hartree-Fock hamiltonian eigen states, however, in the case that those state are adopted as the single particle orbits, the results have scarcely been changed until now.

  4. Intrinsic Density (４He) Brueckner-AMD Results ρ(r) Ｙ Av8’; P.R.Wringa and S.C.Pieper, PRL89 (2002), 182501. *In the case of 8Be and 12C, the Gaussian width parameter is the same value as the case of 4He. Ｘ Intrinsic Density (8Be) Intrinsic Density (12C) ρ(r) ρ(r) Ｙ Ｙ Ｘ Ｘ

  5. Parity- & Jπ- projection in the Brueckner-AMD Ex) Parity Projection Parity-projected state : parity Space inversion operator ⇒the liner combination of two Slater determinants The G-matrix between the different Slater determinants is necessary. ⇒ Bethe-Goldstone Equation Correlation function Model (AMD) wave function Y. Akaishi, H. Bando, and S. Nagata,PTP. Suppl. No.52 (1972), 339. The G-matrix is constructed with the correlation functions.

  6. Results of 4He with variation after projection (VAP) Argonne v8’ （ｎｏ　Ｃｏｕｌｏｍｂ　ｆｏｒｃｅ） A. Variation (cooling) with no projection 4He (Parity +) Ｙ ρ(r) Binding Energy (4He)： -22.5(MeV) B. Variation after projection (VAP): parity+ Binding Energy (4He: +)： -23.6(MeV) + Projection after variation (PAV): J=0 Ｘ Binding Energy (4He: 0+)： -24.7(MeV) The result is comparable with that of the benchmark calculations benchmark calculations† : -25.9(MeV) †Ref: H. Kamada et al. , PRC64 (2001) 044001

  7. Results of Be isotopes with VAP (Parity) Argonne v8’ 8Be (Parity +) 9Be (Parity -) Ｙ ρ(r) Ｙ ρ(r) （ｎｏ　Ｃｏｕｌｏｍｂ　ｆｏｒｃｅ） Ｘ Ｘ 10Be (Parity +) Binding energy: -37.2(MeV) Binding energy: -36.5(MeV) ρ(r) Ｙ Ｘ Binding energy: -39.6(MeV) *The Gaussian width parameter is the optimized value of 8Be in the case with no projection.

  8. Intrinsic density of 9Be (Parity -) （ proton ） Ｙ ρ(r) （ matter ） Ｙ ρ(r) Ｘ （ neutron ） ρ(r) Ｙ Ｘ π-orbit Argonne v8’ （ｎｏ　Ｃｏｕｌｏｍｂ　ｆｏｒｃｅ） Binding energy: -36.5(MeV) *The Gaussian width parameter is the optimized value of 8Be in the case with no projection. Ｘ

  9. Intrinsic density of 9Be (Parity +) （ proton ） ρ(r) Ｙ （ matter ） Ｙ ρ(r) Ｘ （ neutron ） Ｙ ρ(r) Ｘ σ-orbit Argonne v8’ （ｎｏ　Ｃｏｕｌｏｍｂ　ｆｏｒｃｅ） Binding energy: -34.0(MeV) *The Gaussian width parameter is the optimized value of 8Be in the case with no projection. Ｘ

  10. Intrinsic density of 10Be (Parity +) （ proton ） ρ(r) Ｙ （ matter ） ρ(r) Ｙ Ｘ （ neutron ） ρ(r) Ｙ Ｘ Argonne v8’ （ｎｏ　Ｃｏｕｌｏｍｂ　ｆｏｒｃｅ） Binding energy: -39.6(MeV) *The Gaussian width parameter is the optimized value of 8Be in the case with no projection. Ｘ

  11. Intrinsic density of 10C (Parity +) （ proton ） ρ(r) Ｙ （ matter ） ρ(r) Ｙ Ｘ （ neutron ） ρ(r) Ｙ Ｘ Argonne v8’ （ｎｏ　Ｃｏｕｌｏｍｂ　ｆｏｒｃｅ） Binding energy: -39.6(MeV) *The Gaussian width parameter is the optimized value of 8Be in the case with no projection. Ｘ

  12. Summary & Future works Summary ・ We constructed the framework of AMD with realistic interactions based on the Brueckner theory. ・ Furthermore, we proposed the projection method in the Brueckner-AMD with the correlation functions based on the Bethe-Goldstone equation. ・ With the Brueckner-AMD and the variation(cooling) after projection, we obtained the reasonable results for light nuclei starting with the realistic interaction. Future works ・ Systematic calculations inlight nuclei : Calculated : Calculating ・ Calculations with other realistic interactions: Argonne v18, CD-Bonn, ・・・ ・ Three-body force http://wwwndc.tokai-sc.jaea.go.jp/CN04/CN001.html

  13. IKEDA Diagram Nuclear Cluster Structures Threshold rules Molecular structures will appear close to the respective cluster threshold. Unstable nuclei Ground states of drip-line nuclei are observed near the thresholds. Threshold Physics It is desired to understand exotic properties of drip-line nuclei and various kinds of cluster structures in light nuclei from more basic points of view, namely with a realistic nuclear force and a wide model space.

  14. Intrinsic density of 9B (Parity -) ( preliminary) （ proton ） ρ(r) Ｙ （ matter ） ρ(r) Ｙ Ｘ （ neutron ） ρ(r) Ｙ Ｘ Argonne v8’ （ｎｏ　Ｃｏｕｌｏｍｂ　ｆｏｒｃｅ） Binding energy: -36.5(MeV) *The Gaussian width parameter is the optimized value of 8Be in the case with no projection. Ｘ

  15. Intrinsic density of 7Li (Parity -) （ proton ） ρ(r) Ｙ （ matter ） ρ(r) Ｙ Ｘ （ neutron ） ρ(r) Ｙ Ｘ Argonne v8’ （ｎｏ　Ｃｏｕｌｏｍｂ　ｆｏｒｃｅ） Binding energy: -25.1(MeV) *The Gaussian width parameter is the optimized value of 8Be in the case with no projection. Ｘ

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