Realistic effective YN interactions in hypernuclear models

1. 2011/8/23 APFB2011 Realistic effective YN interactions in hypernuclear models Development from NSC97 to ESC08 Y. Yamamoto (RIKEN) Th.A. Rijken (Nijmegen)

2. In structure calculations based on realistic nuclear interactions Full-space approach : Ab initio calculations with realistic free-space interactions short-range & tensor correlations are included in wave functions Full-space calculations with simplified interactions Pioneering work by Malfliet-Tjon (1969): Faddeev calculation with two-range Yukawa potential

3. Model-space approach : Short-range & tensor correlations are renormalized into effective interactions In model-space wave functions, short-range correlations are not included Structure calculations with effective interactions Most convenient (traditional) way to derive effective interaction is to use G-matrix theory All results in this talk are based on G-matrix interactions

4. Our approach to hypernuclear physics Free-space YN/YY interactions based on SU(3)-symmetry Nijmegen interactions G-matrix theory Effective YN/YY interaction in nuclei structure calculations Hypernuclear Phenomena Feedback from hypernuclei to interaction models complementing the lack of YN scattering data

5. Development of Nijmegen interaction models NHC-D 1977 NHC-F 1979 NHC= Nijmegen Hard Core NSC = Nijmegen Soft Core ESC = Extended Soft Core NSC89 Rijken & Yamamoto NSC97 ESC04 ESC08

6. YN c = ( B1B2, T, L, S, J ) Coordinate representation G-matrix interaction depends on kF (orρ)

7. Intermediate–state (off-shell) spectra Continuous Choice (CON) : off-shell potential taken continuously from on-shell potential Gap Choice (GAP) : no off-shell potential our calculations ω rearrangement effect working repulsively

8. Most important quantities obtained from YN G-matrices Single particle potential of hyperon in nuclear matter UΛ, UΣ, UΞand their partial-wave contributions Basic features of YN interactions are reflected qualitatively

9. For structure calculations Fitted in a Gaussian form

11. G-matrix folding model G-matrix interactions G(r;kF) Averaged-kF Approximation A simple treatmentkF is an adjustable parameter Mixed density obtained from core w.f. H.O.w.f SkHF w.f. etc.

12. Yamamoto-Bando(1990) Λt folding model with various G-matrix interactions Jeulich-A/B NHC-D/F NSC89 Spin-Spin parts of all available interactions are inadequate for spin-doublet states in A=4 hypernuclei A motivation to develop NSC97 models Rijken, Stoks, Yamamoto (1999)

13. NSC97a-f versions good correspondence G-matrix result Uσσ= -0.24 0.77 3.10 reasonable Hypertriton Λ3H (by Miyagawa) JA/JBunbound 97a-dunbound 97every weakly bound 97f reasonably bound Faddeev Calculations Reasonable 0+-1+ splitting in Λ4H is given by NSC97e/f

14. by Hiyama et al. (1997) Spin-Orbit splitting in cluster models Λ9Be(ααΛ) and Λ13C(αααΛ) In this treatments, interactions among subunits(αα, ααα, Λα) are adjusted so as to reproduce experimental values ΛN G-matrix interaction GΛN(r; kF) :central+SLS+ALS folded into Λα interaction kF is treated as a parameter to adjust Λα subsystem(Λ5He)

15. LS splitting in9Be Λ ND/NF NSC97 (Large) (Small) SLS SLS +ALS 5/2+ 5/2+ 80～200 keV 140～250 keV 3/2+ 3/2+ 5/2+ 3/2+ Exp. 43±5 keV (Large) - (Large) SLS + ALS 5/2+ Λ 35～40keV 3/2+ α α Quark-based 9Be Similar result in Λ13C Λ

16. Problems in NSC97 models • ΛN spin-orbit interaction is too large compared with EXP data • Potential depths of Σ and Ξ in nuclear matter NSC97 experimentally UΣattractiverepulsive UΞrepulsive weakly attractive Motivation to develop new interaction model (ESC)

17. Th.A. Rijken, M.M.Nagels, Y.Yamamoto : P.T.P. Suppl. No.185(2010) 14 Extended Soft-Core Model (ESC) ●Two-meson exchange processes are treated explicitly ● Meson-Baryon coupling constants are taken consistently with Quark-Pair Creation model PS, S, V, AV nonets PS-PS exchange (ππ),(πρ),(πω),(πη),(σσ),(πK) Parameter fitting consistent with G-matrix analyses for hypernuclear data

18. Important step to ESC08 (latest version) Serious problem in Nijmegen soft-core models NSC89/97 and ESC04 Attractive UΣ It is difficult to make UΣ repulsive consistently with properties in other channels Experimentally UΣ is repulsive

19. Why is UΣ attractive for Nijmegen soft-core models ? Origin of cores in NSC89/97 ESC04 pomeron ω meson Repulsive cores are similar to each other in all channels Repulsive ∑-potentials cannot be obtained from these models ! In Quark-based models Pauli-forbidden states play an essential role for repulsive UΣ

20. Quark-Pauli effect in ESC08 models Repulsive cores are similar to each other in all channels ESC core = pomeron + ω Assuming “equal parts” of ESC and QM are similar to each other Almost Pauli-forbidden states in [51] are taken into account by changing the pomeron strengths for the corresponding channels phenomenologically gP factor *gP Important also in ΞN channels

21. by Oka-Shimizu-Yazaki Pauli-forbidden state in V[51] strengthen pomeron coupling ESC08a/b

22. ESC08c VBB=αVpomeron BB (S,I) α NN (0,1)(1,0) 1.0 ΛN (0,1/2)(1,1/2) 1.02 ΣN(0,1/2) 1.17 (1,1/2) 1.02 (0,3/2) 1.0 (1,3/2) 1.15 ΞN (0,0) 0.96 (0,1) 1.12 (1,0) 1.04 (1,1) 1.06 QM result is taken into account more faithfully α

23. UΣ(ρ0) and partial wave contributions (Continuous Choice) no Pauli-forbidden state Pauli-forbidden state in QCM  strong repulsion in T=3/2 3S1 state taken into account by adapting Pomeron exchange in ESC approach

24. Λ hypernuclei and ΛN interactions based on ESC08 model

25. UΛ(ρ0) and partial-wave contributions CONr = continuous choice & ω-rearrangement spin-spin interactions in ESC08a/b/c between NSC97e and NSC97f

26. Spin-Orbit splitting in Scheerbaum approximation kF=1.0 fm-1 S.O. splitting for ESC08a/b/c are smaller than that for NSC97f

27. Hotchi et al. 2001 Most important data for UΛ double-peak structures left-side peaks are Λ+ground-state core

28. 89ΛY f d p s by G-matrix folding potential (ESC08a with CONr) SkHF wave function for core nucleus

29. Overall agreement to exp. data ESC08a “no free parameter”

30. ΛΛ interactions

31. with G-matrix interaction GΛΛ(r; kF) with Averaged-kF Approximation

32. ΛΛ binding energies BΛΛ Uniquely determined E373: Nagara Danysz (1963) E373: Hida E176 with G-matrix interaction GΛΛ(r; <kF>)

33. Experimental data suggesting attractive Ξ-nucleus interactions BNL-E885 12C(K-,K+)X KEK-E176 Twin Λ hypernuclei WS14 UΞ~ -14 MeV UΞ~ -16 MeV represented by Woods-Saxon potential

34. UΞ(ρ0) and partial wave contributions Shallow Ξ-nucleus potentials Ξ hypernuclei ?

35. Ξ- -11C binding energy G-matrix folding potential derived from ESC08c is attractive comparably to WS14

36. Energy spectra of Ξ hypernuclei with G-matrix folding potentials E(Ξ0) E(Ξ-) Remarkable Coulomb-force contribution !

37. (K-,K+) production spectra of Ξ-hypernuclei by Green’s function method in DWIA Ξ-nucleus G-matrix folding model ESC08c pK+=1.65 GeV/c θK+=0° spreading width of hole-states experimental resolution ΔE=2 MeV are taken into account

38. s Peak structures of bound states can be seen even for shallow Ξ-nucleus potentials derived from ESC08c

39. Conclusion G-matrix interactions derived from ESC08 models explain all basic features of hypernuclei consistently UΛ and ΛN spin-dependent parts quantitatively Repulsive nature of UΣ Reasonable strength of VΛΛ Predictions of Ξ- hypernuclei