Shape of L hypernuclei in ( b,g ) deformation plane

1. Myaing Thi Win, K.Hagino and T.Koike Tohoku University Shape of L hypernuclei in(b,g) deformation plane University of Aizu-JUSTIPEN-EFES Symposium, “Cutting-Edge Physics of Unstable Nuclei 13th November 2010 s d u  Outline of this talk • Background • Motivation • Formalism and Method • Results • Summary & Conclusion

2. Impurity effect of L particle • No Pauli principle between nucleons • and lambda particle “Glue-Like Role of ” • an impurity to explore the various changes of the nuclear structure L • Shrinkage Effect in 7LLi • Theoreticallyby 3-body cluster model • Hiyama et al. PRC 59 (1999) 2351 • Experimentally by B(E2) value • K.Tanida,H.Tamura, D.Abe et al ucl.PhysA,684,560(2001) s Λ d u Smaller size or smaller deformation

3. Self-consistent Mean Field studies on L hypernuclei the presence of strange L-particle • L makes the nucleus more stable • Lextends the drip lines • Lmakes the nucleus shrink • Core polarization effect ,such as Change of total energy and radius of the core • Non-relativistic HF method c.f , D.E.Lanskoy PRC58,3351(98) c.f, M.Rayet, Annals of Phys102,226(76) • Relativistic Mean Field c.f, J.Mares and J.Zofka, Z.Phys.A333,209(89) c.f Y. Sugahara and H.Toki , Prog.Theo.Phys.92,803(94) • Extension of Neutron drip line • Relativistic HFB c.f, D.Vretenar et al, PRC57,R1060(98) • Non-relativistic MF c.f, X.R.Zhou et al, PRC78, 054306(08)

4. Theoretical and experimental interest Change of properties of nuclei induced by L (size, shape and cluster structure, changes of collective motion, etc...) • My interest • within Mean-field approach s d u Deformation?

5. Nuclear deformation • Triaxial deformation Schematic level schemes of deformed nuclei L.M.Robledo,R.Rodriguez-Guzman and P.Sarriguren J.Phys.G.Nucl.Part.Phys.36(2009) • Shape of nuclei  important role in determining nuclear properties, such as quadrupole moment and radius. • Evidence for nuclear deformation • Rotational Bands

6. Previous Studies of Deformation of L hypernuclei • Deformed Skyrme-Hartree Fock approach • No change in deformation due to addition of lambda • X.R.Zhou et.al, PRC76,034312 • Relativistic Mean Field Theory •  Disappearance of nuclear ｄeformation induced by a L • M.T.Win and K.Hagino, PRC78, 054311(08) 6 • SHF and RMF • H.J.Schulze, M.Thi Win, K.Hagino,H.Sagawa Prog.Theo.Phys123,3(10) • Physical origin of deformation changes in terms of lambda and nucleon mean field potentials • compare the results of SHF and RMF • RMF  stronger interaction of lambda with Nuclear core • Disappearance of deformation only in the case of

7. Motivation • Extend the previous studies by taking into account triaxial degree of freedom • Skyrme Hartree Fock +BCS approach • To study the deformation of L hypernuclei in the full (b,g) plane • arXiv:1010.5561v1 g s b d u Triaxial deformation? • The previous studies of the deformation of Lambda hypernuclei  Axial symmetry Disapperance or change of deformation minimum

8. Skyrme HF Formalism for Hypernuclei • M.Rayet, Nucl.Phys.A367,381(81) Total Hypernuclear energy • Skyrme parameters for L-N interaction HF equations for hypernuclear system

9. HF equations for hypernuclear system arising from LN interaction • Skyrme parameters for L-N interaction

10. Parameter sets of Skyrme type LN Interaction Skyrme typeLN interaction Y.Yamamoto et.al, Prog.Theo.Phys.80,5(88) • five parameters : t0L, x0L, t1L,t2L, t3L, a1L= t1+t2/4 • Fitted to reproduce • Small spin-orbit part is not considered. Similar with nuclear Skyrme force • Using these parameter sets BL and L level spacings （Dsp, Dsd ) as a function of A-2/3 are calculated • the results are within experimental error bar

11. Calculation method • P.Bonche et.al. Comp.Phys.comu.171(05) r0 = 0.16 fm-3 V0 = -1000MeV fm3 • Application to sd-shell hypernuclei • Skyrme Interaction SGII • Extend ‘EV8 Code’ for hypernuclei • HF+BCS equations  solved by discretizing the single-particle wave function on 3-D Cartesian mesh • Imaginary Time step method • Pairing • BCS approximation with Density dependent pairing interaction

12. Deformation energy surface of sd shell hypernuclei in (b,g) plane

13. Results: 28Si , 28Si+L Oblate magic number +L

14. Results: 24Mg, 24Mg+L prolate +L

15. Results: 26Mg, 26Mg+L obate prolate Eprolate – Eoblate = 0.39MeV +L

16. Results: 26Si , 26Si+L oblate prolate Eprolate – Eoblate = 0.12MeV +L

17. Gain in Binding energy of L in spherical configuration • L prefers spherical configuration even if the core is deformed.

18. Discussion on softerenergy surface for 26+LMg and 24+LMg Due to the effect of smaller value of b at oblate side Due to larger overlap between L and nucleon densities at the prolate side

19. Overlap between nucleon and lambda densities • L particle density • Nucleon density Overlapl argest for prolate configuration

20. g vibrational energy 24+L Mg, 26+LMg

21. 24Mg • K=0 g.s rotational band and K=2 rotational band built upon the g-vibrational state 32+ 22+ 4+ w24Mg = 4.23MeV (expt) 2+ 0+ 24Mg +L 22+ 4+ 2+ Calculated value 0+ 24+LMg

22. Similarly, g vibration energy for 26+L Mg

23. Summary • Triaxial calculations by Skyrme Hartree-Fock method • PES in (b,g) deformation plane • sd shell hypernuclei • 28 Si+L (p=14, n=14), 24Mg +L (p=12, n=12) • 26Mg +L (p=12, n=14), 26Si +L (p=14, n=12) - similar between core and hypernuclei - Slightly softer along the triaxial degree of freedom • Qualitatively similar results with SGII and SIII parameter sets • Estimation of g vibration energy • g vibration energy is lowered by about 0.15 MeV with the addition of L hyperon