Unveiling nuclear structure with spectroscopic methods Beihang University, Beijing, Sep. 18, 2014

 Atomic spectroscopy (Hydrogen spectrum)  Infrared/Raman spectroscopy of molecules ( Vibration-Rotation Spectrum of HCl ) Spectroscopy provides a unique way to explore micro. world Bohr model

What do we study in nuclear physics? Jochen Erler et al., Nature 486, 509 (2012) Excitations (angular momentum, Temperature, …) Ground state neutron proton Exciting the atomic nuclei and then observing the gamma-ray e.g. Coulomb excitation, inelastic scattering, etc. Producing nucleus at excited states and then observing the gamma-ray e.g. Fusion/fragmentation, etc

Physics of low-spin states Connection between low-lying states and underlying shell-structure Magic numbers: 8, 20, 28, 50, 82, 126 Closed-shell Open-shell Excitation energy of the first 2+ state keV 3.89E E E E E E E E E E E E E E E E E E E E E E+1

Magic number and nuclear shell structure Where are the magic numbers from? Large separation energy

Magic number and nuclear shell structure

leading to the simultaneous publication of the papers (1949) by Mayer and the German group on the shell model with a strong spin-orbit coupling. Maria Mayer in 1948 published evidence for the particular stability for the numbers 20, 50, 82 and 126. it sparked a lot of interest in the USA and with Haxel, Jensen and Suess in Germany.

Magic number and nuclear shell structure leading to the K. L. Jones et al., Nature 465, 454 (2010) (d,p) reaction s.p. energy structure can be probed with (d,p) reaction.

Excitation of nuclei with magic number Lowest excitation

Excitation of nuclei with magic number leading to the E ( MeV ) E2 High excitation energy 16 O

Excitation of nuclei with magic number leading to the simultaneous publication of the papers by Mayer and the German group on the shell model with a strong spin-orbit coupling. leading to the E2 Maria Mayer in 1948 published evidence for the particular stability for the numbers 20, 50, 82 and 126. it sparked a lot of interest in the USA and with Haxel, Jensen and Suess in Germany. E2 16 O from NNDC Many non-collective excitations

Deformation and Nilsson diagram Ring & Schuck (1980) β Nilsson model: deformed HO+LS+L^2 Deformed the shell structure

Deformation and Nilsson diagram Nilsson diagram Jahn-Teller effect: geometrical distortion (deformation) that removes degeneracy can lower the energy of system. shell structure is changed by deformation.

Q. S. Zhang, Z. M. Niu, Z. P. Li, JMY, J. Meng, Frontiers of Physics (2014) Deformation and nuclear shapes Systematic calculation of nuclear ground state with CDFT PC-PK1

Shape transition and coexistence Excitation energy of the first 2+ state N=60

Rotation of quadrupole deformed nuclei Nuclear quadrupole deformed shapes: prolate oblate

Quadrupole vibration of atomic nuclei Imposed by invariance of exchange two phonons

Quadrupole vibration of atomic nuclei 114 Cd Strong anharmonic effect

The rotation-vibration model (1952) 5DCH

Evolution of nuclear shape and spectrum W. Greiner & J. Maruhn (1995)

Evolution of nuclear shape From NNDC A microscopic theory to describe the shape evolution and change in low-energy nuclear structure with respect to nucleon number unkno wn

5 Construct 5-dimensional Hamiltonian (vib + rot) E(J π ), BE2 … Cal. Exp. 3D covariant Density Functional ph + pp Coll. Potential Moments of inertia Mass parameters Diagonalize: Nuclear spectroscopy Niksic, Li, Vretenar, Prochniak, Meng & Ring, PRC79, (09) Libert, Girod & Delaroche, PRC60, (99) Prochniak & Rohozinski, JPG36, (09) Courtesy of Z.P. Li 5DCH based on EDF calculation

 Spectrum  Characteristic features: Sharp increase of R 42 =E(4 1 )/E(2 1 ) and B(E2; 2 1 →0 1 ) in the yrast band X(5) Courtesy of Z.P. Li Shape transition in atomic nuclei/5DCH

Microscopic description of nuclear collective excitations α distinguishes the states with the same angular momentum J |q> is a set of Slater determinants from the constrained CDFT calc. P J and P N are projection operators onto J and N. K=0 if axial symm. is assumed. Projections and GCM on top of CDFT: JMY, J. Meng, P. Ring, and D. Vretenar, PRC 81 (2010) ; JMY, K. Hagino, Z. P. Li, J. Meng, and P. Ring, PRC 89 (2014) Variation of energy with respect to the weight function f(q) leads to the Hill- Wheeler-Griffin (HWG) integral equation: Definition of kernels: q‘ rotation & vibration/shape mixing

Q. S. Zhang, Z. M. Niu, Z. P. Li, JMY, J. Meng, Frontiers of Physics (2014) cranking approximation Significant improv. on BE: 2.6 -> 1.3 MeV 575 e-e nuclei unbound Corrected by the DCE Rotational energy Not good if deformation collapse Correlation energy beyond MF approximation N. Chamel et al., NPA 812, 72 (2008)

SLy4(TopGOA): M. Bender, G. F. Bertsch, and P.-H. Heenen, PRC73, (2006). SLy4 Correlation energy beyond MF approximation

Symmetry conservation and configuration mixing effect on nuclear density profile

bubble best candidate Reduced s. o. splitting of (2p3/2; 2p1/2) true bubble Semi-bubble G. Burgunder (2011)

JMY, S. Baroni, M. Bender, P.-H. Heenen, PRC 86, (2012) GCM+1DAMP+PNP (HFB-SLy4): bubble structure is quenched by configuration mixing effect.

M. Grasso et al., PRC79, (2009) SLy4 (HF) JMY et al., PRC86, (2012) JMY et al., PLB 723, 459 (2013) The central depletion in the proton density of 34 Si is shown in both RMF and SHF calculations. Both central bump in 36 S and central depletion in 34 Si are quenched by dynamical correlations. The charge density in 36 S has been reproduced excellently by the MR- CDFT calculation with PC- PK1 force. 2s1/2 orbital unoccupied

 Deformation has significant influence on the central depletion.  The 34 Si has the largest central depletion in Si isotopes. Central depletion factor:g.s. wave function:

Spherical state: bubble structure in 46Ar Dynamical deformation: No bubble structure Inverse of 2s1/2 and 1d3/2 around 46Ar leads to bubble structure in spherical state. X. Y. Wu, JMY, Z. P. Li, PRC89, (2014)

Benchmark for Bohr Hamiltonian in five dimensions

Triaxiality in nuclear low-lying states

Existence of shape isomer state (E0) Evidence of the oblate deformed g.s. (Coulex) Lifetime measurements of 2+ and 4+ states (RDM) prolate shape? H. Iwasaki et al., PRL 112, (2014) Evidence for rapid oblate- prolate shape transition Large collectivity of 4+ state suggests a prolate character of the excited states. = Shape transition in a single-nucleus

Direct measurement on the shape of 2+ state GOSIA GCM+PN1DAMP (axi.) Preliminary results Reorientation effect Nara Singh et al., in preparation (2014) 5DCH ??? In collaboration with experimental group

Nara Singh et al., in preparation (2014) Preliminary results GOSIA 5DCH (Triaxial) 5DCH Reorientation effect Direct measurement on the shape of 2+ state ???

Nara Singh et al., in preparation (2014) Preliminary results GOSIA 5DCH (Triaxial) 5DCH Reorientation effect Direct measurement on the shape of 2+ state ??? Sato & Hinohara, (NPA2011)

Nara Singh et al., in preparation (2014) Preliminary results GOSIA 5DCH Reorientation effect Direct measurement on the shape of 2+ state ??? ♦ T. Rodriguez, private communication (2014) GCM+PN3DAMP M 22 =0.87 eb M 02 =0.82 eb GCM (D1S)

Nara Singh et al., in preparation (2014) Preliminary results GOSIA 5DCH Reorientation effect Direct measurement on the shape of 2+ state ??? ♦ GCM (D1S) GCM+PN3DAMP (PC-PK1) ♦ GCM (PCPK1) M 22 =0.14 eb M 02 =0.77 eb Preliminary results

Hypernucleus in excited state H. Tamura et al., Phys. Rev. Lett. 84 (2000) 5963 K. Tanida et al., Phys. Rev. Lett. 86 (2001) 1982 J. Sasao et al., Phys. Lett. B 579 (2004) 258 O. Hashimoto and H. Tamura, PPNP 57, 564 (2006)  The facilities built at J-PARC enable the study of hypernuclear γ- ray spectroscopy.

Description of hypernuclear low-lying states based on EDF

 Low-energy excitation spectra β = 1.2 Application to 9 Λ Be

 Low-energy excitation spectra [1] R.H. Dalitz, A. Gal, PRL 36 (1976) 362.[2] H. Bando, et al., PTP 66 (1981) 2118.; [3] T. Motoba, H. Bandō, and K. Ikeda, Prog. Theor. Phys.70, 189 (1983).[4]H. Bando, et al., IJMP 21 (1990) Be analog band 8 Be analog band genuinely hypernuclear genuinely hypernuclear 9 Be analog band 9 Be analog band Application to 9 Λ Be Cluster model Motoba, et al.

 Low-energy excitation spectra [1] T. Motoba, H. Bandō, and K. Ikeda, Prog. Theor. Phys.70, 189 (1983). 92.8(s 1/2 ⊗ 0 + ) (s 1/2 ⊗ 2 + ) (p 1/2 ⊗ 0 + )+44.5(p 3/2 ⊗ 2 + )+… 52.4(p 3/2 ⊗ 0 + )+22.0(p 3/2 ⊗ 2 + ) +21.7(p 1/2 ⊗ 2 + )+… ( l j ⊗ I c ) Application to 9 Λ Be Motoba, et al.

 Low-energy excitation spectra Application to 9 Λ Be

Jie Meng (PKU) Zhongming Niu (Anhui U.) Peter Ring (TUM&PKU) Dario Vretenar (Zagreb U.) Kouichi Hagino (Tohoku U.) Hua Mei (Tohoku U. & SWU) T. Motoba (Osaka Electro- Communications U.) Michael Bender (U. Bordeaux) Paul-Henri Heenen (ULB) Simone Baroni (ULB) Acknowledge to all collaborators evolved in this talk Zhipan Li, Xian-ye Wu, Qian-shun Zhang (SWU)

Physics of high-spin states

In case of 9 Be (  +  + n) n n Allowed Forbidden by Pauli principle For p state, l = 1, m l = 0, ±1 m l = 0 Parallel to axial m l = ±1 Perpendicular to axial 1s 1/2 1p 3/2 1p 1/2 1/2[110] 3/2[101] 1/2[101] 8 Asymptotic quantum numbers Projection of the single-particle angular momentum, j, onto the symmetry axis ( m j ); The principal quantum number of the major shell; The number of nodes in the wave function along the z axis; The projection of the orbital angular momentum l on the symmetry axis ( m l );