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Problems and Ideas at the Dawn of Three-Body Force Effects in the Shell Model

Problems and Ideas at the Dawn of Three-Body Force Effects in the Shell Model. Takaharu Otsuka University of Tokyo / MSU. ECT* workshop “Three-Nucleon Forces in Vacuum and in the medium” Trento, Italy July 11 (11-15), 20 11. Outline. 1. Monopole problem in the shell model.

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Problems and Ideas at the Dawn of Three-Body Force Effects in the Shell Model

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  1. Problems and Ideasat the Dawn ofThree-Body Force Effects in the Shell Model Takaharu Otsuka University of Tokyo / MSU ECT* workshop “Three-Nucleon Forces in Vacuum and in the medium” Trento, Italy July 11 (11-15), 2011

  2. Outline 1. Monopole problem in the shell model 2. Shell evolution in exotic nuclei 3. Solution by three-body force Introduction to talks by J. Holt, A. Schwenk and T. Suzuki

  3. Spectra of Ca isotopes calculated by most updated NN interaction microscopically obtained By Y. Tsunoda and N. Tsunoda N3LO Vlow-k with L=2.0 fm-1 2nd and 3rd order Q-box 4hw and 6hw GXPF1A KB3G for comparison s.p.e. used Present GXPH1A KB3G

  4. Two-body matrix elements (TBME) may be calculated to a rather good accuracy 40Ca core is not very stable yet -> 0+ energy lowered

  5. 48Ca

  6. As N or Z is changed to a large extent in exotic nuclei, the shell structure is changed (evolved) by • Monopole component of the NN interaction • Averaged over possible orientations Linearity: Shift nj’: # of particles in j’ <nj’ > can be ~ 10 in exotic nuclei -> effect quite relevant to neutron-rich exotic nuclei Strasbourg group made a major contribution in initiating systematic use of the monopole interaction. (Poves and Zuker, Phys. Rep. 70, 235 (1981))

  7. 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 What’s this ? Repulsive corrections to G-matrix j = j’

  8. 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 Repulsivecorrections to G-matrix j = j’ j = j’

  9. T=0 monopole interaction The correction is opposite !

  10. f-p f-f p-p T=0 monopole interactions in the pf shell Tensor force (p+r exchange) GXPF1A G-matrix (H.-Jensen) “Local pattern”  tensor force

  11. T=0 monopole interactions in the pf shell Tensor force (p+r exchange) GXPF1A shell-model int. G-matrix (H.-Jensen) Tensor component is subtracted Correction is attractive

  12. Outline 1. Monopole problem in the shell model 2. Shell evolution in exotic nuclei 3. Solution by three-body force

  13. Treatment of tensor force by V low k and Q box (3rd order) Monopole component of tensor interactions in pf shell Bare(AV8’) short-range correlation by V low k in-medium correction with intermediate states (> 10 hw, 3rd order) only for comparison

  14. Systematic description of monopole properties of exotic nuclei can be obtained by an extremely simple interaction as monopole component of tensor force in nuclear medium Parameters are fixed for all nuclei almost equal ? monopole component of tensor force in free space

  15. Shell evolution due to proton-neutron tensor + central forces Changes of single-particle properties due to these nuclear forces

  16. exotic nucleus with neutron skin proton stable nucleus neutron r dr/dr T=1NN interaction more relevant to ls splitting change ls splitting smaller

  17. From RIA Physics White Paper

  18. Neutron single-particle energies at N=20 for Z=8~20 solid line : full VMU (central + tensor) p3/2 low 20 14 8 16 Z dashed line : central only Tensor force makes changes more dramatic. 20 16 These single-particle energies are “normal” f7/2-p3/2 2~3 MeV N=20 gap ~ 6 MeV energy (MeV) d5/2 s1/2 d3/2 Z PRL 104, 012501 (2010) more exotic

  19. Increase of 2+ excitation energy 2+ level (MeV) Neutron number

  20. Outline 1. Monopole problem in the shell model 2. Shell evolution in exotic nuclei 3. Solution by three-body force

  21. Nuclear Chart - Left Lower Part - Why is the drip line of Oxygen so near ? Proton number  Neutron number 

  22. Single-Particle Energy for Oxygen isotopes by phenomenological eff. int. by microscopic eff. int. - G-matrix + fit - G-matrix+ core-pol. : Kuo, Brown Utsuno, O., Mizusaki, Honma, Phys. Rev. C 60, 054315 (1999) SDPF-M Vlow-k : Bogner, Schwenk, Kuo Brown and Richter, Phys. Rev. C 74, 034315 (2006) USD-B trend trend

  23. A solution within bare 2-body interaction is very unlikely (considering efforts made so far) Zuker, Phys. Rev. Lett. 90, 042502 (2003)  3-body interaction What is the origin of the repulsivemodificationof T=1 monopole matrix elements ? The same puzzle as in the pf shell

  24. The clue : Fujita-Miyazawa 3N mechanism (D-hole excitation) D particle m=1232 MeV S=3/2, I=3/2 p D p Miyazawa, 2007 N N N

  25. 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

  26. 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

  27. 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.

  28. Most important message with Fujita-Miyazawa 3NF m’ m Effective monopole repulsive interaction m + D m’ D m m’ m’ m m D Pauli blocking Renormalization of single particle energy same m’ m Monopole part of Fujita-Miyazawa 3-body force

  29. (i) D-hole excitation in a conventional way • EFT with D D-hole dominant role in determining oxygen drip line -> J.Holt, A. Schwenk, T. Suzuki (iii) EFT incl. contact terms (N2LO)

  30. O, Suzuki, Holt, O, Schwenk, Akaishi, PRL 105 (2010) Ground-state energies of oxygen isotopes NN force + 3N-induced NN force (Fujita-Miyazawa force) Drip line

  31. What was wrong with “microscopic theories” ? N Observed in NN scattering N N N D (Effective) two-body interaction N N N N If the origin is “forgotten”, present picture constant change of single-particle energy This is what happened in “microscopic theories”, leading to wrong drip line. or

  32. states below Fermi level k For neutron matter : attractive k k repulsive k Brown and Green, Nucl.Phys. A137, 1 (1969 Fritsch, Kaiser and Weise, Nucl. Phys. A750, 259 (2005); Tolos, Friman and Schwenk, Nucl.Phys. A806}, 105 (2008); Hebeler and Schwenk, arXiv:0911.0483 [nucl-th]

  33. For valence neutrons: states outside the core Attractive (single-particle energy renormalization) repulsive (valence neutron interaction)

  34. Quick Summary More from J. Holt, A. Schwenk and T. Suzuki Major monopole forces are due to FM 3NF + + V m=1 fm variation of shell structure limit of existence, shell structure at far stability basic binding (T=0), repulsive (T=1) except for j=j’

  35. Casablanca mechanism Love = attractive force* This love is reduced by the presence of Victor This love is reduced by the presence of Rick Rick Victor repulsion *This equation has no proof.

  36. E N D

  37. The central force is modeled by a Gaussian function V = V0exp( -(r/m) 2) (S,T dependences) with V0 = -166 MeV, m=1.0 fm, (S,T) factor (0,0) (1,0) (0,1) (1,1) -------------------------------------------------- relative strength 1 1 0.6 -0.8 Can we explain the difference between f-f/p-p and f-p ?

  38. 5hw 4hw 3hw 2hw 1hw Magic numbers Mayer and Jensen (1949) Eigenvalues of HO potential 126 82 50 28 20 8 2 Spin-orbit splitting

  39. density saturation + short-range NN interaction + spin-orbit splitting Mayer-Jensen’s magic number with rather constant gaps (except for gradual A dependence) robust feature -> nuclear forces not included in the above can change it -> tensor force

  40. Brief history on our studies on tensor force Magic numbers may change due to spin-isospin nuclear forces Tensor force produces unique and sizable effect Tensor and central forces -> Weinberg-type model

  41. s . s . Tensor Interaction by pion exchange VT = (t1t2) ( [s1s2](2)Y(2)(W) )Z(r) contributes only to S=1 states relative motion p meson : primary source p Yukawa r meson (~ p+p) : minor (~1/4) cancellation Ref:Osterfeld, Rev. Mod. Phys. 64, 491 (92)

  42. V ~ Y2,0~ 1 – 3 cos2q q=p/2 q=0 repulsion attraction How does the tensor force work ? Spin of each nucleon is parallel, because the total spin must be S=1 The potential has the following dependence on the angle qwith respect to the total spin S. q S relative coordinate

  43. Monopole effects due to the tensor force - An intuitive picture - wave function of relative motion spin of nucleon large relative momentum small relative momentum repulsive attractive j> = l + ½, j< = l – ½ TO et al., Phys. Rev. Lett. 95, 232502 (2005)

  44. wave function when two nucleons interact - approx. by linear motion - k1 k2 k = k1 – k2 , K= k1 + k2 k1 k2 large relative momentum k small relative momentum k strong damping loose damping k1 k2 wave function of relative coordinate wave function of relative coordinate k2 k1

  45. TO. et al., Phys. Rev. Lett. 95, 232502 (2005) j< = l – ½ neutron j> = l + ½ j’< proton j’> General rule of monopole interaction of the tensor force Identity for tensor monopole interaction ( j’j>) ( j’j<) (2j> +1) vm,T+ (2j<+1)vm,T= 0 vm,T: monopole strength for isospin T

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