Neutron Halo in Deformed Nuclei

Transcription

1 Advances in Nuclear Many-Body Theory June 7-1, 211, Primosten, Croatia Neutron Halo in Deformed Nuclei Ó Li, Lulu Ò School of Physics, Peking University June 8, 211 Collaborators: Jie Meng (PKU) Peter Ring (TUM) En-guang Zhao (ITP, CAS) Shan-gui Zhou (ITP, CAS)

2 Content 1 Introduction 2 Theoretical framework 3 Results and discussion Bulk properties of Mg isotopes Halo in 42 Mg 4 Summary

3 Introduction Properties of halo nuclei: Large spatial distribution. Like 11 Li. Tanihata PRL1985 Halo nucleons may polarize the core. Charge radius of 9 Li is fm, and fm for 11 Li. Sanchez et al. PRL26 Charge radius of 4 He is fm, 2.68 fm for 6 He, and fm for 8 He. Mueller et al. PRL21 Oscillation of the weakly bound halo nucleons against the core pygmy dipole resonance Adrich et al. PRL25 Non-linear and cluster effects. Borromean nuclei 11 Li 6 He. Zhukov et al. PRep1993 What about the shape of halo nuclei?

4 Halo in deformed nuclei? 11 Be The spin-parity of the ground state and first exciting state are and 1 2. The parity-inversion phenomenon may caused by deformation. Li et al. PRC1996, Misu et al. NPA1997, Pei et al. NPA26 14 Be Halo structure is obtained with spherical RMF model. Ren, et al. PLB1995 A kinematical complete measurement of the fragments suggests a large (2s1) 2 admixture and (1d5) 2 in 14 Be. 2 2 Deformation. Labiche et al. PRL21 31 Ne The major components of wave function might be 3 Ne( + 1 ) 2p 3/2(C 2 S =.12), 3 Ne(2 + 1 ) 2p 3/2(C 2 S =.27), 3 Ne(2 + 1 ) 2f 7/2(C 2 S =.25)....as such, suggests that it will be strongly deformed. Nakamura et al. PRL29 Three body model: Our results suggest that it is unlikely to find (two neutron) halo nuclei on the dripline of deformed nuclei Nunes NPA25

5 Halo in deformed nuclei? Deformed halo? With energy density functional theory, Halo structure is obtained for 11 Li, by taking into account the continuum. Meng and Ring PRL1996 Giant neutron halo was predicted. Meng and Ring PRL1998 Halo in deformed nuclei? Deformed halo? Deformed energy density functional theory needed. Pairing effect and the contribution of continuum Bogouliubov transformation used. Traditional Harmonic Oscillator basis is not suitable for halo nuclei. RHB equation should be solved in coordinate space or equivalent basis, like Woods-Saxon basis. A self consistent deformed Relativistic Hartree-Bogoliubov theory in WS basis is established. S.G. Zhou, J. Meng, P. Ring, E.G. Zhao, Phys. Rev. C 82, 1131R (21) Present work: the halo phenomena in Mg isotopes is studied with developed theory.

6 Deformed relativistic hartree-bogoliubov theory RHB Equation ( d 3 r (hd (rσp,rσ p ) λ) (rσp,r σ p ) (rσp,r σ p ) ( h D (rσp,rσ p )+λ) σ p Dirac hamiltonian Scalar and vector density read h D = α p+v(r)+β(m +S(r)) S(r) = g σσ(r) V(r) = g ωω (r)+g ρτ 3 ρ (r)+e 1 τ 3 A (r) 2 Equations of corresponding meson and photon feilds ( +m 2 σ)σ(r) = g σρ s(r) ( +m 2 ω)ω (r) = g ωρ v(r) ( +m 2 ρ)ρ (r) = g ρρ 3 (r) ρ s(r) = ψψ ρ v(r) = ψ ψ ρ 3 (r) = ψ τ 3 ψ )( Uk (r σ p ) ) V k (r σ p ) ) = E k ( Uk (rσp) V k (rσp) A (r) = eρ p(r) ρ c(r) = ψ 1 τ 3 ψ 2

7 Deformed relativistic hartree-bogoliubov theory Coefficients of RHB equation are expanded with Dirac Woods-Saxon basis iκ ( ) u(m) k,(iκ) ϕ iκm(rσp) Uk (rσp) iκ u( m) = ϕ iκm(rσp) k,(ĩκ) V k (rσp) iκ v(m) k,(iκ) ϕ iκm(rσp) iκ v( m) ϕ iκm(rσp) k,(ĩκ) Spherical Dirac spinor {ϕ iκm (rσp); i =, 1, 2,,κ = ±1, ±2,, m = ± 1 2, ±3 2,,±( κ 1 )} 2 ϕ iκm (rσp) = 1 ( ) igiκ (r)φ κm(ωσ), r F iκ (r)φ κm (Ωσ) where φ κm(ωσ) = m l m s lm l sm s jm Y lml (Ω)χ ms (σ), and Ω = (θ,φ) φ κm (Ωσ) = m l m s lm l sm s jm Y lm l (Ω)χ ms (σ), κ = ±(j +1/2) for j = l 1/2, j = κ 1 2, l = j +sign(κ)/2, l = j sign(κ)/2

8 Numerical details Box size R = 2 fm and step size dr =.1 fm are used for solving DWS basis. Energy cut off is chosen to be E cut = 1 MeV. Density dependent delta force is used for pairing, and smooth cut off is used. ( ) s(e k ) = 1 E k E q.p. cut 1 2 (Ek E q.p. cut ) 2 +(Γ q.p. cut ) 2 Parameters of pairing interaction is chosen by fitting the proton pairing energy of spherical 2 Mg given by Gogny D1S. Model Pairing force Parameters E p pair (MeV) SRHBHO Gogny D1S RCHB Surface δ V = 374 MeV fm with ρ sat =.152 fm 3 sharp cutoff E q.p. cut = 6 MeV DRHBWS Surface δ V = 38 MeV fm with ρ =.152 fm 3 smooth cutoff E q.p. cut = 6 MeV Γ q.p. cut = 5.65 MeV

9 Bulk properties of Mg isotopes Mg isotopes λ n (MeV) Mg -2 PK1 NL A β Mg -.2 Exp. -.4 PK1 NL A 42 Mg is the drip line nucleus (PK1). 32 Mg is spherical for both parameter sets. S. Raman, et al., Atom. Data Nucl. Data Tab. 78, 1 (21)

10 Bulk properties of Mg isotopes Mg isotopes E B (MeV) Mg A Exp. PK1 NL3 S 2n (MeV) Mg A Exp. PK1 NL3 Reasonable two neutron separation energy obtained. Strong shell effect of N = 2 is observed with mean field theory. G. Audi, et al., Nucl. Phys. A 729 (23) L.S. Geng, Ph.D Thesis (25)

11 Bulk properties of Mg isotopes Mg isotopes (radii) PK1, R n PK1, R p PK1, R t NL3, R n NL3, R p NL3, R t R (fm) Mg Slope of neutron radii changes slightly at 32 Mg Shell effect with mean field theory. Slope of neutron radii changes slightly at 4 Mg ö A

12 Bulk properties of Mg isotopes Mg isotopes (neutron density profiles) ρ n [fm -3 ] Mg 3 Mg 32 Mg 34 Mg 36 Mg 38 Mg 4 Mg 42 Mg 44 Mg ρ n [fm -3 ] Mg 3 Mg 32 Mg 34 Mg 36 Mg 38 Mg 4 Mg 42 Mg 44 Mg 1-5 NL3 θ = r [fm] 1-5 NL3 θ = r [fm] In the direction of z axis, neutron density profile of Mg isotopes changes smoothly. In the direction of x axis, neutron density of 42 Mg extend far away from the center. Oblate halo

13 Bulk properties of Mg isotopes Mg isotopes (neutron density profiles) ρ n [fm -3 ] Mg 3 Mg 32 Mg 34 Mg 36 Mg 38 Mg 4 Mg 42 Mg ρ n [fm -3 ] Mg 3 Mg 32 Mg 34 Mg 36 Mg 38 Mg 4 Mg 42 Mg 1-5 PK1 θ = r [fm] 1-5 PK1 θ = r [fm] In the direction of z axis, neutron density profile of Mg isotopes changes smoothly. In the direction of x axis, neutron density of 42 Mg extend far away from the center. Oblate halo

14 Halo in 42 Mg 42 Mg: single particle levels E can (MeV) Mg PK1 Neutron 7 1/2 - [1f 5/2 + 2p 1/2 ] 6 7/2 - [1f 7/2 ] 5 3/2 - [2p 3/2 + 1f 7/2 ] 4 1/2 - [2p 3/2 + 1f 5/2 + 2p 1/2 ] 3 5/2 - [1f 7/2 ] 2 1/2 - [2p 1/2 + 1f 7/2 ] 1 3/2 - [1f 7/2 + 2p 3/2 ] 3/2 + 1/2-1/2 + E can (MeV) Mg NL3 Neutron 7 1/2 - [1f 5/2 + 2p 1/2 ] 6 7/2 - [1f 7/2 ] 5 3/2 - [2p 3/2 + 1f 7/2 ] 4 1/2 - [1f 5/2 + 2p 3/2 + 2p 1/2 ] 3 5/2 - [1f 7/2 + 1f 5/2 ] 2 1/2 - [2p 1/2 + 1f 7/2 ] 1 3/2 - [1f 7/2 + 2p 3/2 ] 3/2 + 1/2-1/ v 2 v 2 Weakly bound and continuum orbitals Halo Deeply bound orbitals Core

15 Halo in 42 Mg 42 Mg: density profile ρ(r) = λ ρ λ (r)p λ (cosθ), λ =,2, Halo λ = λ = 2 λ = λ = λ = 2 λ = 4 ρ n (fm -3 ).1 ρ n (fm -3 ) Mg PK Mg PK r (fm) Shape decoupling between core and halo. Oblate halo Prolate core r (fm)

16 Halo in 42 Mg 42 Mgñdensity profile of halo and core z (fm) E-1 1.E-2 1.E-3 1.E-4 1.E-5 1.E-6 z (fm) E-1 1.E-2 1.E-3 1.E-4 1.E-5 1.E x (fm) 42 Mg Shape decoupling between core and halo. Oblate halo Prolate core x (fm) 42 Mg

17 Halo in 42 Mg 42 Mg: single particle levels E can (MeV) Mg PK1 Neutron v 2 7 1/2 - [1f 5/2 + 2p 1/2 ] 6 7/2 - [1f 7/2 ] 5 3/2 - [2p 3/2 + 1f 7/2 ] 4 1/2 - [2p 3/2 + 1f 5/2 + 2p 1/2 ] 3 5/2 - [1f 7/2 ] 2 1/2 - [2p 1/2 + 1f 7/2 ] 1 3/2 - [1f 7/2 + 2p 3/2 ] 3/2 + 1/2-1/2 + Level 4, 5 give most contributions of the halo. ρ n (fm-3 ) ρ n (Ωπ ) / ρ n Mg PK1 Total Core Halo 1 3/2-2 1/2-3 5/2-4 1/2-5 3/2-6 7/2-7 1/ /2-4 1/2-5 3/2-6 7/2-7 1/2 - r (fm) 42 Mg PK r (fm)

18 Halo in 42 Mg 42 Mg: shape of the halo E can (MeV) Mg PK1 Neutron 7 1/2 - [1f 5/2 + 2p 1/2 ] 6 7/2 - [1f 7/2 ] 5 3/2 - [2p 3/2 + 1f 7/2 ] 4 1/2 - [2p 3/2 + 1f 5/2 + 2p 1/2 ] 3 5/2 - [1f 7/2 ] 2 1/2 - [2p 1/2 + 1f 7/2 ] 1 3/2 - [1f 7/2 + 2p 3/2 ] 3/2 + 1/2-1/ v 2 Level 4 2p 3/2 : gives 37% of the contribution, in which Λ = component domains; 1f 5/2 : gives 32% of the contribution, in which Λ = 1 component domains; 2p 1/2 : gives 21% of the contribution, in which Λ = 1 component domains. Level 5 2p 3/2 : gives 79% of the contribution, only has the component of Λ = 1.

19 Summary Summary It is focused on halo phenomena in deformed nuclei (Mg isotopes). Halo may occur, depending on intrinsic properties of orbitals around the Fermi level. There might be shape decoupling between core and halo ( 42,44 Mg). Perspective How about the halo in odd-a nuclei? What about the contribution of Fock term to halo phenomena? The effect of π meson, The effect of tensor force,...