Transcript ppt
Unveiling nuclear structure with spectroscopic methods Beihang University, Beijing, Sep. 18, 2014 Spectroscopy provides a unique way to explore micro. world Atomic spectroscopy (Hydrogen spectrum) Bohr model Infrared/Raman spectroscopy of molecules (Vibration-Rotation Spectrum of HCl) What do we study in nuclear physics? Excitations (angular momentum, Temperature, …) proton neutron Jochen Erler et al., Nature 486, 509 (2012) • 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 keV 3.89E+4 2.74E+4 1.93E+4 1.35E+4 9.57E+3 6.74E+3 4.74E+3 3.34E+3 2.35E+3 1.65E+3 1.16E+3 1.16E+3 8.22E+2 5.78E+2 4.07E+2 2.87E+2 2.02E+2 1.42E+2 1.00E+2 7.05E+1 4.97E+1 3.50E+1 Excitation energy of the first 2+ state http://www.nndc.bnl.gov/chart Magic number and nuclear shell structure Large separation energy Where are the magic numbers from? Magic number and nuclear shell structure Magic number and nuclear shell structure 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. 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. Magic number and nuclear shell structure s.p. energy structure can be probed with (d,p) reaction. leading to the (d,p) reaction K. L. Jones et al., Nature 465, 454 (2010) Excitation of nuclei with magic number Lowest excitation Excitation of nuclei with magic number 16O 2+ (6.917 E2 0+ leading to the High excitation energy E2 E2 MeV) Excitation of nuclei with magic number 16O 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. from NNDC 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 Many non-collective excitations E2 Deformation and Nilsson diagram β Deformed the shell structure Nilsson model: deformed HO+LS+L^2 Ring & Schuck (1980) Deformation and Nilsson diagram Nilsson diagram shell structure is changed by deformation. Jahn-Teller effect: geometrical distortion (deformation) that removes degeneracy can lower the energy of system. Deformation and nuclear shapes Systematic calculation of nuclear ground state with CDFT Q. S. Zhang, Z. M. Niu, Z. P. Li, JMY, J. Meng, Frontiers of Physics (2014) PC-PK1 Shape transition and coexistence Excitation energy of the first 2+ state N=60 http://www.nndc.bnl.gov/chart Rotation of quadrupole deformed nuclei Nuclear quadrupole deformed shapes: oblate prolate Quadrupole vibration of atomic nuclei Imposed by invariance of exchange two phonons Quadrupole vibration of atomic nuclei 114Cd Strong anharmonic effect The rotation-vibration model (1952) 5DCH Evolution of nuclear shape and spectrum W. Greiner & J. Maruhn (1995) Evolution of nuclear shape 3.88 3.74 3.60 3.46 3.32 3.18 3.03 2.89 2.75 2.61 2.47 unkno wn A microscopic theory to describe the shape evolution and change in low-energy nuclear structure with respect to nucleon number. From NNDC 2.47 2.33 2.18 2.04 1.90 1.76 1.62 1.48 1.34 1.19 1.05 5DCH based on EDF calculation Construct Coll. Potential Moments of inertia Mass parameters 5-dimensional Hamiltonian 3D covariant Density Functional (vib + rot) Diagonalize: Nuclear spectroscopy E(Jπ), BE2 … Cal. Exp. ph + pp Courtesy of Z.P. Li Libert, Girod & Delaroche, PRC60, 054301 (99) Prochniak & Rohozinski, JPG36, 123101 (09) Niksic, Li, Vretenar, Prochniak, Meng & Ring, PRC79, 034303 (09)5 Shape transition in atomic nuclei/5DCH Spectrum Characteristic features: X(5) Sharp increase of R42=E(41)/E(21) and B(E2; 21→01) in the yrast band Courtesy of Z.P. Li Microscopic description of nuclear collective excitations Projections and GCM on top of CDFT: rotation & vibration/shape mixing • • • • α distinguishes the states with the same angular momentum J |q> is a set of Slater determinants from the constrained CDFT calc. PJ and PN are projection operators onto J and N. K=0 if axial symm. is assumed. Variation of energy with respect to the weight function f(q) leads to the HillWheeler-Griffin (HWG) integral equation: q‘ Definition of kernels: JMY, J. Meng, P. Ring, and D. Vretenar, PRC 81 (2010) 044311; JMY, K. Hagino, Z. P. Li, J. Meng, and P. Ring, PRC 89 (2014) 054306. Correlation energy beyond MF approximation N. Chamel et al., NPA 812, 72 (2008) unbound cranking approximation Validity of cranking approximation 575 e-e nuclei Corrected by the DCE Rotational energy Significant improv. on BE: 2.6 -> 1.3 MeV Q. S. Zhang, Z. M. Niu, Z. P. Li, JMY, J. Meng, Frontiers of Physics (2014) Not good if deformation collapse Correlation energy beyond MF approximation SLy4 SLy4(TopGOA): M. Bender, G. F. Bertsch, and P.-H. Heenen, PRC73, 034322 (2006). Symmetry conservation and configuration mixing effect on nuclear density profile bubble best candidate Semi-bubble true bubble Reduced s. o. splitting of (2p3/2; 2p1/2) G. Burgunder (2011) GCM+1DAMP+PNP (HFB-SLy4): bubble structure is quenched by configuration mixing effect. JMY, S. Baroni, M. Bender, P.-H. Heenen, PRC 86, 014310 (2012) SLy4 (HF) 2s1/2 orbital unoccupied The central depletion in the proton density of 34Si is shown in both RMF and SHF calculations. Both central bump in 36S and central depletion in M. Grasso et al., PRC79, 034318 (2009) 34Si are quenched by dynamical correlations. The charge density in 36S has been reproduced excellently by the MRCDFT calculation with PCPK1 force. JMY et al., PLB 723, 459 (2013) JMY et al., PRC86, 014310 (2012) g.s. wave function: Central depletion factor: Deformation has significant influence on the central depletion. The 34Si has the largest central depletion in Si isotopes. 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, 017304 (2014) Benchmark for Bohr Hamiltonian in five dimensions Triaxiality in nuclear low-lying states Shape transition in a single-nucleus Existence of shape isomer state (E0) E. Bouchez et al., PRL 90, 082502 (2003) Evidence of the oblate deformed g.s. (Coulex) A. Gade et al., PRL 95, 022502 (2005) prolate shape? Different model calc. = prolate oblate Lifetime measurements of 2+ and 4+ states (RDM) H. Iwasaki et al., PRL 112, 142502 (2014) Large collectivity of 4+ state suggests a prolate character of the excited states. Evidence for rapid oblateprolate shape transition Direct measurement on the shape of 2+ state In collaboration with experimental group Nara Singh et al., in preparation (2014) GOSIA Reorientation effect ??? GCM+PN1DAMP (axi.) Direct measurement on the shape of 2+ state Nara Singh et al., in preparation (2014) GOSIA Reorientation effect ??? 5DCH (Triaxial) Direct measurement on the shape of 2+ state Nara Singh et al., in preparation (2014) GOSIA Reorientation effect ??? 5DCH (Triaxial) Sato & Hinohara, (NPA2011) Direct measurement on the shape of 2+ state Nara Singh et al., in preparation (2014) GOSIA Reorientation effect ??? GCM (D1S)♦ GCM+PN3DAMP M22=0.87 eb M02=0.82 eb 1613 2909 1336 T. Rodriguez, private communication (2014) Direct measurement on the shape of 2+ state Nara Singh et al., in preparation (2014) GOSIA Reorientation effect ??? GCM (D1S)♦ GCM+PN3DAMP (PC-PK1) ♦ GCM (PCPK1) M22=0.14 eb M02=0.77 eb The facilities built at J-PARC enable the study of hypernuclear γray spectroscopy. O. Hashimoto and H. Tamura, PPNP 57, 564 (2006) 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 Description of hypernuclear low-lying states based on EDF Application to 9ΛBe Low-energy excitation spectra β = 1.2 Application to 9ΛBe Low-energy excitation spectra Cluster model 9Be analog band [ Ic l ] Motoba, et al. genuinely hypernuclear 8Be analog band [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) 4021. Application to 9ΛBe I Ls Low-energy excitation spectra l s I Ic j L s l Ic Ic j 52.4(p3/2⊗0+)+22.0(p3/2⊗2+) +21.7(p1/2⊗2+)+… 51.6(p1/2⊗0+)+44.5(p3/2⊗2+)+… 91.9(s1/2⊗2+)+.. 92.8(s1/2⊗0+)+.. ( I c l ) sL Motoba, et al. [1] T. Motoba, H. Bandō, and K. Ikeda, Prog. Theor. Phys.70, 189 (1983). (lj ⊗Ic) Application to 9ΛBe Low-energy excitation spectra Acknowledge to all collaborators evolved in this talk Peter Ring (TUM&PKU) Dario Vretenar (Zagreb U.) Jie Meng (PKU) Zhongming Niu (Anhui U.) Kouichi Hagino (Tohoku U.) Hua Mei (Tohoku U. & SWU) T. Motoba (Osaka ElectroCommunications U.) Michael Bender (U. Bordeaux) Paul-Henri Heenen (ULB) Simone Baroni (ULB) Zhipan Li, Xian-ye Wu, Qian-shun Zhang (SWU) Physics of high-spin states In case of 9Be (a + a + n) 8 1p1/2 1 2 For p state, l = 1, ml = 0, ±1 ml = 0 Parallel to axial ml = ±1 Perpendicular to axial m j ml ms 1/2[101] 3/2[101] n ms n 1p3/2 1/2[110] 1s1/2 Forbidden by Pauli principle Allowed Asymptotic quantum numbers Nnz :Projection of the single-particle angular momentum, j, onto the symmetry axis (mj); N :The principal quantum number of the major shell; nz :The number of nodes in the wave function along the z axis; : The projection of the orbital angular momentum l on the symmetry axis (ml);