1 Properties of hypernuclei in the Skyrme Hartree-Fock method Xian-Rong Zhou Department of physics, Xiamen University, Xiamen, China Present Status of the Nuclear Interaction Theory, 08/25 -09/19,2014, Beijing, China

2 Outline  Introduction  Extended Skyrme Hartree-Fock  Properties of hypernuclei shapes of hypernuclei effects of hyperon enegery spetrum  Summary

3 N Z ,  Hypernuclei ,  Hypernuclei Strangeness D nuclear chart

4 Multistrange system: Ne utron star, … Why to study hypernuclei? Nucleon-nucleon interaction Hyperon-nucleon interaction Impurity of nuclear system

5 Theoretical studies about hypernuclei Energy spectrum Decay properties The effect of hyperon(s) Shapes …….

6 Studies based on spherical symmetry: 1. Relativistic mean-field model (RMF) 2. Skyrme Hartree-Fock model (SHF) 3. Woods-Saxon potential + YN interaction 4. Few-body theory Theoretical studies about the shapes of hypernuclei

7 Deformed HF with nonrealistic YN interaction: T. H. Ho and A.Volkov, Phys. Lett. B30, 303, W. H. Bassichis, A. Gal, Phys. Rev. C1, 28, J. Zofka, Czech, J. Phys. B30, 95, Nilsson Model: assume the same deformation for core and hypernuclei: K. Hagino, Phys. Rev. C63, , 2001 Calculations considering deformation:

8 Deformed SHF with Microscopic YN int. X.-R. Zhou, H.-J. Schulze, H. Sagawa,et al., Phys. Rev. C76, (2007) Relativistic mean-field model (RMF): Myaing Thi Win, H. Hagino, et al., Phys. Rev. C 78, (2008) Triaxial SHF with Skyrme-like YN interaction: Myaing Thi Win, H. Hagino, et al., Phys. Rev. C 83, (2011) Antisymmetrized molecular dynamics (AMD): M. Isaka,, et al., Phys. Rev. C 83, (2011) Triaxial RMF: Bing-Nan Lu ( 吕炳楠 ), S.-G.Zhou, Phys. Rev. C 84, (2011) Considering deformation self-consistently:

9 Bing-Nan Lu, E. Hiyama, H. Sagawa, and S.-G. Zhou, Phys. Rev. C 89, (2014) Superdeformation in hypernuclei

10 Why to study deformations of hypernuclei Many p-shell and sd-shell nuclei are deformed. For example, experimentally, 10 B and 11 C have large quadrupole moments. F. Ajzenberg-Selove, Nucl. Phys. A490, 1 (1988); A506, 1(1990). Also, 8 Be is known to be strongly deformed due to its double-α structure.

11 Several models for deformed nuclei Alpha-model Projected shell model (PSM) Deformed Skyrme Hartree-Fock (DSHF) Relativistic mean-field model (RMF) Antisymmetrized molecular dynamics (AMD) ……

12 Microscopic hyperon-nucleon interaction for deformed hypernuclei B Y, Hypernuclear Structure Effective YN interaction BHF cal. for asymmetric matter Free YN interaction MF cal. YN: Nijmegen soft-core hyperon-nucleon potential NSC89,NSC97 a,NSC97f,ESC08 NN: Argonne v18 nucleon-nucleon interaction

Comparison of different hyperon-nucleon potential

14 Extended DSHF including hyperon-nucleon interaction Total energy of a hypernucleus in extended DSHF: where the energy density SHF Due to the YN force, DSHF + YN interaction:

The energy density functional ε NΛ is obtained from a fit to the binding energy per baryon, B/A(ρ n, ρ p, ρ), of asymmetric hypermatter, as generated by BHF calculations. Effective mass of hyperon

16 In practice we use the following parametrizations:

17 Extended SHF equation Minimizing the total energy of the hypernucleus, one arrives with extended SHF equation with the modified mean field by hyperon:

18 For light nuclei, For medium-mass and heavy nuclei, Pairing interaction Nucl. Phys. A722, c183, 2003 Euro. Phys. J. A8, 59, 2000 We take a density-dependent delta pairing Nucl. Phys. A551, 434 (1993)

19 1. Hypernuclei is deformed or not?

X.-R. Zhou, H.-J. Schulze, H. sagawa et.al, PRC76, (2007) Binding energies vs deformations

21 Binding energies vs deformations X.-R. Zhou, H.-J. Schulze, H. sagawa et.al, PRC76, (2007)

22 2. The effect of hyperon on nuclear structure?

23 The effect of hyperon in neutron-rich nuclei X.-R. Zhou,A.Polls,H.-J.Schulze, et al.,PRC78,054306(2008)

24 The Oxygen isotopes exp.

25 3. Energy spectrum of hypernulcei

The SHF models can just give the single-particle energies and ground state of Λ hypernuclei in intrinsic frame of reference. The conservation of particle number is destroyed by BCS method. The study of the gamma spectra and electromagnetic transitions needs symmetry restoration. Limitations of extended SHF+BCS method: Angular momentum and particle-number projection (AMP&PNP) are needed !

Projected SHF+BCS Model The projected mean-field state The projection operator Energies with angular momentum and E2 transitions

Energy potential surface of 12 C and Ji-Wei Cui, X.-R. Zhou, in preparation

Energy potential surface of 20 Ne and

Energy potential surface of 24 Mg and

Energy potential surface of 26 Mg and

Energy potential surface of 26 Si and

Energy potential surface of 28 Si and

Comparison of NSC89(upper) and Skyrme-type(lower) ΛN Interactions

Comparison of different Skyrme parameters

Energy spectrum of 12 C and cal1 and cal2 label energy levels with or without the Λ spin-orbit term.

cal1 and cal2 label energy levels with or without the Λ spin-orbit term. Energy spectrum of 20 Ne and

cal1 and cal2 label energy levels with or without the Λ spin-orbit term. Energy spectrum of 24 Mg and

Energy spectrum of 28 Si and cal1 and cal2 label energy levels with or without the Λ spin-orbit term.

Exp data in W.u. from: The B(E2) transitions of hypernuclei become a little smaller due to the shrinkage of the quadruple shape. B(E2) transition probabilities

41 Summary 1.The DSHF was extended to hypernuclei by including a microscopically derived hyperon- nucleon interaction. 3. Due to the effect of hyperons, the nuclei close to the drip line are stabilized and new isotopes are potentially made available. 2.The calculated core nuclei and the corresponding hypernuclei have similar deformations with the same sign when the core nuclei are well deformed. 4. The projected SHF+BCS model gives reasonable initial results of energy spectra and E2 transition rates for well-deformed sd-shell nuclei and hypernuclei.

42 Cooperators H. Sagawa University of Aizu, Japan H.-J. Schulze, University of Catania, Italy En-Guang Zhao Institute of Theoretical Physics, CAS, China Ji-Wei Cui Xiamen University, China

43 Thank you for your attention! Furong Lake Xiamen Univ.