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Structure of exotic nuclei

Structure of exotic nuclei. Takaharu Otsuka University of Tokyo / RIKEN / MSU. A presentation supported by the JSPS Core-to-Core Program 　“ International Research Network for Exotic Femto Systems (EFES)”. 7 th CNS-EFES summer school Wako, Japan August 26 – September 1, 2008. Day 3.

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Structure of exotic nuclei

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  1. Structure of exotic nuclei Takaharu OtsukaUniversity of Tokyo / RIKEN / MSU A presentation supported by the JSPS Core-to-Core Program　“International Research Network for Exotic Femto Systems (EFES)” 7th CNS-EFES summer school Wako, Japan August 26 – September 1, 2008 Day 3

  2. Summary of Day2-1 Single-particle properties (shell structure) are one of the most dominant elements of nuclear structure. Example : The deformation (of low-lying states) is a Jahn-Teller effect to a good extent. We discussed on how single-particle levels change (shell evolution) as functions of Z and N in exotic nuclei due to various components of the nuclear force. • Tensor force • Central force

  3. Summary of Day2 - 2 Some components of NN interactions show characteristic patterns of the shell evolution Tensor force : - variation of spin-orbit splitting - strong  unexpected oblate deformation of a doubly-magic 42Si Central force : - differentiates different radial nodal structure of single-particle orbits - stronger (< tensor) Tensor + Central combined (typically in the ratio 2:1)  lowering of neutron f5/2 in Ca-Cr-Ni inversion of proton f5/2 and p3/2 in Cu for N~46 54Ca,78Ni, 100Sn Day-One experiments of RIBF

  4. Outline Section 1: Basics of shell model Section 2: Construction of effective interaction and an example in the pf shell Section 3: Does the gap change ? - N=20 problem - Section 4: Force behind Section 5: Is two-body force enough ? Section 6: More perspectives on exotic nuclei

  5. From Day 2 lecture T=1 monopole interaction

  6. j = j’ T=1monopole interactions in the pf shell GXPF1A G-matrix (H.-Jensen) Tensor force (p+r exchange) Basic scale ~ 1/10 of T=0 Repulsive corrections to G-matrix j = j’

  7. T=1monopole interactions in the sd shell SDPF-M(~USD) G-matrix (H.-Jensen) Tensor force (p+r exchange) Basic scale ~ 1/10 of T=0 Repulsive corrections to G-matrix j = j’ j = j’

  8. Origin and implication of repulsive modification of T=1 monopole components

  9. nuclei (mass number) stable exotic -- with halo A Proton number  Neutron number  Stable Nuclei Nuclear Chart - Left Lower Part - proton halo F (Z=9) O (Z=8) Why is the drip line of Oxygen so near ? Drip Line (Existence Limit of Nuclei) 11Li リチウム１１ neutron halo neutron skin

  10. This is because the neutron d3/2 orbit is high for Oxygen. Neutron orbits in Fluorineisotopes Neutron orbits inOxygenisotopes 1d3/2 neutron threshold 23O15 ~ 24O16 2s1/2 Proton-neutron force, Incl. strong tensor force, due to a proton in d5/2 17O9 ~ 22O14 1d5/2 16O core 16O core

  11. Neutron orbits in Fluorineisotopes Neutron orbits inOxygenisotopes 1d3/2 neutron threshold 23O15 ~ 24O16 2s1/2 17O9 ~ 22O14 1d5/2 Why do those neutrons NOT pull down d3/2 ? 16O core 16O core

  12. Kuo-Brown G-matrix + core-pol. d3/2 d5/2 5 10 15 20 Neutron number (N) Wrong drip line Effective Single-Particle Energy for Oxygen isotopes narrowing

  13. Effective Single-Particle Energy for Oxygen isotopes Kuo-Brown G-matrix + core-pol. Empirical correction USD Less steep d3/2 d5/2 5 10 15 20 5 10 15 20 Neutron number (N) Neutron number (N) Additional repulsion between d5/2 and d3/2 Wrong drip line Not enough narrowing

  14. Effective Single-Particle Energy for Oxygen isotopes Kuo-Brown G-matrix + core-pol. Empirical correction Final correction SDPF-M USD Less steep d3/2 d5/2 5 10 15 20 Neutron number (N) Neutron number (N) Finally flat, d3/2 kept high  correct drip line Neutron number (N) Y. Utsuno, T.O., T. Mizusaki, and M. Honma, Phys. Rev. C 60, 054315 (1999). narrowing

  15. A solution within bare 2-body interaction is very unlikely (considering efforts made so far)  3-body interaction Question What is the origin of the repulsive modification to T=1 monopole matrix elements ? However 3NF -> attractive effects systematics in results of GFMC, NCSM CC (Hagen et al., Phys. Rev. C76, 034302 (2007)

  16. GFMC(Green Function Monte Carlo) by Argonne group 3-body force 3-body force increases binding energies 3-body force included

  17. Nucleons in valence orbits (of low momenta) Nucleons in higher shell (of high momenta) Nucleons in valence orbits (of low momenta) One reason : 3N force with short range produces basically more attraction from the 2nd order perturbation

  18. The key : Fujita-Miyazawa 3N mechanism (D-hole excitation) p D particle m=1236 MeV S=3/2, I=3/2 D p N N N

  19. D Renormalization of NNinteraction due to D excitation in the intermediate state Modification to bare NN interaction (for NN scattering) T=1 attraction between NN effectively

  20. D-hole excitation effect on single-particle energy N N D D N N D N core N N valence particle Renormalization of single particle energy due to D-hole excitation attractive (more bound)

  21. Pauli blocking effect on the renormalization of single-particle energy m m single particle states m’ m’ m’ D D m m Another valence particle in state m’ Renormalization of single particle energy due to D-hole excitation  more binding (attractive) Pauli Forbidden The effect is suppressed

  22. Inclusion of Pauli blocking m m’ m m’ m’ D D m m’ m Pauli forbidden (from previous page) This Pauli effect is included automatically by the exchange term.

  23. Realization in terms of 3-body interaction m’ m m + D m’ D m m’ m’ m m D Pauli blocking Renormalization of single particle energy same m’ m A part of Fujita-Miyazawa 3-body force

  24. Fujita-Miyazawa 3N mechanism (D-hole excitation) p D particle m=1236 MeV S=3/2, I=3/2 D p N N N

  25. Incorporation of this effect into effective interaction We look at this effect as an effective interaction between states m and m’. m’ m This effect is monopole, because it is about single-particle energies. m m’ D This effect is repulsive, because it is suppression of more binding. veff m m’ m’ m Effective monopole repulsive interaction reproduces the effect. <mm’ |veff| mm’>> 0

  26. D Other diagram included Pauli blocking Related effect was discussed by Frisch, Kaiser and Weise for neutron matter See also Nishizaki, Takatsuka and Hiura PTP 92, 93 (1994) Particle in the inert core T=1 interaction between valence particles

  27. D-hole excitation may be crucial to neutron matter property Chiral Perturbation incl. D : Frisch, Kaiser and Weise

  28. Back to the question of high-lying d3/2 Neutron orbits inOxygenisotopes Central : attractive (generally) 1d3/2 neutron threshold Tensor : attractive - 0.9 MeV (next page) 2s1/2 17O9 ~ 22O14 1d5/2 D-hole induced repulsion ( > tensor ) Next page 16O core

  29. Repulsive effective monopole interaction assuming 16O core pexchange with radial cut-off at 0.7 fm , ΔE =293 MeV f_{πNΔ｝/f_{πNN} = \sqrt{9/2} Monopole interaction j j' pion tensor d5/2 d3/2 250 keV d3/2 single-particle energy relative to N=8 +1 MeV S.P.E. +2 MeV neutron number (N) 8 14 D-hole-induced repulsion Tensor

  30. More binding by 3NF Is this always true ?

  31. EFT (Vlow-k) result for D~ conventional p-N-D calculation Contact terms can be evaluated as well Pairing cases Effects may be larger with higher order diagrams. 2-body empirical fit (~SDPF-M)

  32. From EFT (Effective Field Theory) sd shell pf shell

  33. j = j’ T=1monopole interactions in the pf shell GXPF1A G-matrix (H.-Jensen) Tensor force (p+r exchange) Basic scale ~ 1/10 of T=0 Repulsive corrections to G-matrix j = j’

  34. (Effective) single-particle energies n-n p-n new magic numbers ? 34 KB3G 32 Lowering of f5/2 from Ca to Cr : ~ 1.6 MeV = 1.1 MeV (tensor) + 0.5 MeV (central) Rising of f5/2 from 48Ca to 54Ca : p3/2-p3/2 attraction p3/2-f5/2 repulsion KB interactions : Poves, Sanchez-Solano, Caurier and Nowacki, Nucl. Phys. A694, 157 (01)

  35. KB3 interaction and its family By Strasbourg – Madrid group Started from Kuo-Brown’s G-matrix Monopole part and pairing part are empirically adjusted Recent versions : KBF, KB3G, .... good for lighter pf-shell nuclei

  36. N  D If another nucleon (X) is in state m’and wave functions are coupled antisymmetric , the effect is vanished.  Repulsive force Density dependent repulsive force - Long-ranged due to p exchange - m’ p m p

  37. m3 m4 D m1 m2 Multipole parts Remark : Multipole interactions …different story m m’ D m m’ Effective repulsion for monopole

  38. Contact terms in 3N force Back-ground attraction : still not completely known

  39. Effect of higher order diagram Important next order diagram Effective monopole repulsive interaction m’ m <mm’ |veff| mm’>> 0 D Other terms of 3-body force cancel this effect to a certain effect m’ Tensor force m Cancellation strong for T=0 weak T=1 included in EFT calc. Larger correction to T=0

  40. Outline Section 1: Basics of shell model Section 2: Construction of effective interaction and an example in the pf shell Section 3: Does the gap change ? - N=20 problem - Section 4: Force behind Section 5: Is two-body force enough ? Section 6: More perspectives on exotic nuclei

  41. Can the shell evolution change the deformation ? If so, how much ?

  42. Application to controversial 42Si Nature 435 (2005), Florida/MSU 44S -> 42Si cross section small deformed PRL accepted (2007), GANIL 44S prolate 42Si oblate Cauier et al. Shell Model, Werner et al. Skyrme model, Lalazissis et al. RMF, Peru et al. Gogny model, Rodriguez-Guzman et al. Gogny model

  43. Exp. New SM f7/2 d3/2 neutron Strong oblate Deformation ? s1/2 d5/2 proton full Potential Energy Surface 4214Si28 Tensor force removed from cross-shell interaction Z=28 gap is reduced also by tensor force Otsuka, Suzuki and Utsuno, Nucl. Phys. A805, 127c (2008)

  44. S isotopes Potential Energy Surface of 44S (triaxial) full Tensor removed from cross shell int. Tensor force may not be so crucial for S isotopes.

  45. Effect of tensor force on (spherical) superheavy magic numbers 1k17/2 2h11/2 N=184 Neutron Tensor force added Woods-Saxon potential Occupation of neutron 1k17/2 and 2h11/2 Proton single particle levels Otsuka, Suzuki and Utsuno, Nucl. Phys. A805, 127c (2008)

  46. Skyrme, Gogny, RMF, … Mean field theories - Inclusion of tensor Stancu, Brink and Flocard, Phys. Lett. 68B, 108 (1077) d-func. Tensor into Skyrme, no prospect for systematic effect Otsuka, Matsuo and Abe, Phys. Rev. Lett. 97, 162501 (2006) Tensor force with Gogny interaction First systematic studies along with the shell evolution idea due to the tensor force, new parameter being searched Brown, Duguet, Otsuka, Abe and Suzuki, Phys. Rev. C 74, 061303, (2006). Re-visit to SBF, systematics, strange T=1 tensor from fit + many other works afterwards e.g. Zalewski, Satula and Dobaczewski, Phys. Rev. C (2008) - Inclusion of 3-body force open for Fujita-Miyazawa type

  47. Does the shell evolution remain in continuum ? Tsukiyama has given a short presentation. The nuclear force shifts resonance-type peaks of neutron spectra. The width changes also. More to be done in a close connection to the nuclear force. (Some works have been done with simpler forces.)

  48. 1+ and 2+ states of 24O to be seen in charge exchange from 24F Tsukiyama, Otsuka, Fujimoto 2008

  49. Summary of Day-3 Three-body force : - repulsive monopole modification for T=1 channel - suppression of D-hole excitation (monopole part of Fujita-Miyazawa force) - effect seen in single-particle energies (Ca) and drip lines (O) in neutron-rich exotic nuclei with high T (isospin) same physics as neutron matter (through NNN force) - features consistent with modern nuclear forces, e.g. EFT (Effective Field Theory)  oxygen drip line closer to the b stability line new magic N=34 in (or maybe only around) Ca

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