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Study of mixed-symmetric excitations via inelastic proton-scattering

Study of mixed-symmetric excitations via inelastic proton-scattering. A. Hennig 1 , M. Spieker 1 , V. Werner 2,3 , V. Derya 1 , M. Elvers 1,2 , J. Endres 1 , A. Heinz 2,4 , S. G. Pickstone 1 , P. Petkov 1,5 , D. Radeck 1,2 , D. Savran 6,7 , and A. Zilges 1.

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Study of mixed-symmetric excitations via inelastic proton-scattering

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  1. Study of mixed-symmetric excitations via inelastic proton-scattering

    A. Hennig1, M. Spieker1, V. Werner2,3, V. Derya1, M. Elvers1,2, J. Endres1, A. Heinz2,4, S. G. Pickstone1, P. Petkov1,5, D. Radeck1,2, D. Savran6,7, and A. Zilges1 1Institute for Nuclear Physics, University of Cologne 2Wright Nuclear Structure Laboratory, Yale University 3Institute for Nuclear Physics, Technical University of Darmstadt 4Department of Fundamental Physics, Chalmers University of Technology, Göteborg 5Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia 6Extreme Matter Institute EMMI and Research Division, GSI Darmstadt 7Frankfurt Institute for Advanced Studies FIAS, Frankfurt 11th International Spring Seminar on Nuclear Physics May 2014, Ischia Supported by the DFG under contract ZI 510/4-2 and US DOE Grant No. DE-FG02-01ER40609
  2. Outline Introduction Mixed-symmetry states in the N=52 isotones Octupole and hexadecapole mixed-symmetry states Experiments at WNSL, Yale and IKP, Cologne Octupole mixed-symmetry states Hexadecapole excitations sdg-IBM-2 calculations Shell-model calculations
  3. MS quadrupole excitations F = Fmax -1 Ex F = Fmax 3e 2e l+e 1e 0 IBM-2: Characterization of mixed symmetry states by F-spin: FMSS < Fmax N. Pietralla et al., Prog. Part. Nucl. Phys. 60 (2008) 225.
  4. MS quadrupole excitations M1 F = Fmax -1 Ex E2 F = Fmax E2 3e M1 2e l+e 1e E2 0 IBM-2: Characterization of mixed symmetry states by F-spin: FMSS < Fmax Strong M1 transitions between MSS and FSS M1 transitions between Fmax states forbidden with basic M1 operator N. Pietralla et al., Prog. Part. Nucl. Phys. 60 (2008) 225.
  5. MSS in the N=52 isotones 50 52 54 MS quadrupole excitations found in all stable N=52 isotones Pd 96 Pd 97 Pd 98 Pd 99 Pd 100 46 Rh 95 Rh 96 Rh 97 Rh 98 Rh 99 Interplay of single-particle effects and collective phenomena Ru 94 Ru 95 Ru 96 Ru 97 Ru 98 44 Higher-order multipolarity MSS observed for 92Zr and 94Mo MS octupole excitations Hexadecapole excitations Tc 93 Tc 94 Tc 95 Tc 96 Tc 97 p: g9/2 Mo 92 Mo 93 Mo 94 Mo 95 Mo 96 42 Nb 91 Nb 92 Nb 93 Nb 94 Nb 95 p: p1/2 Zr 90 Zr 91 Zr 92 Zr 93 Zr 94 40 n: d5/2
  6. MS octupole excitations 92Zr and 94Mo: M1 transition between lowest 3- states observed [1,2] M1 M1 E1 E1 E1 E1 M1 M1 E2 E2 Evidence for mixed-symmetry octupole excitations [3] Strong E1 transitions to to 2+1,s and 2+1,ms predicted from sdf-IBM-2 [4] ~ 0.1∙10-3 e2fm2 (94Mo) [1] C. Fransen et al., PRC 71 (2005) 054304. [3] M. Scheck et al., PRC 81 (2010) 064305. [2] C. Fransen et al., PRC 67 (2003) 024307. [4] N. A. Smirnova et al., NPA 678 (2000) 235.
  7. Hexadecapole excitations 92Zr and 94Mo: Strong M1 transition between lowest 4+ states observed [1,2] 92Zr: B(M1;4+2→ 4+1) = 0.26(3) mN2 94Mo: B(M1;4+2→ 4+1) = 1.23(20) mN2 Evidence for symmetric/mixed-symmetric hexadecapole excitations? Shell-model calculations (MSDI) for 94Mo[3]: Dominant s=2, j=4 configurations of 4+1,2 states sdg-IBM-2 calculations for 94Mo [4] : M1 transition is reproduced g-boson contents in the 4+1,2 states [1] C. Fransen et al., PRC 71 (2005) 054304. [3] A.F. Lisetskiy et al., NPA 677 (2000) 100. [2] C. Fransen et al., PRC 67 (2003) 024307. [4] R. Casperson et al., PLB 721 (2013) 51.
  8. Experiments Experiments on 96Ru
  9. 96Ru(p,p‘g) experiments YRAST-ball @ WNSL, Yale g-decay branching ratios Ep= 8.4 MeV 9 Clover detectors 5 silicon particle detectors Multipole mixing ratios
  10. 96Ru(p,p‘g) experiments YRAST-ball @ WNSL, Yale g-decay branching ratios HORUS/SONIC @ IKP, Cologne Ep= 7.0 MeV 12 single HPGe-detectors 2 Clover detectors 6 silicon particle detectors Ep= 8.4 MeV 9 Clover detectors 5 silicon particle detectors Lifetime measurement via DSAM from pg-coincidences Multipole mixing ratios
  11. Octupole excitations in 96Ru Octupole excitations
  12. Octupole excitations in 96Ru M1 transitions between low-lying 3--states E [MeV] 96Ru 92Zr 3-2 3 M1 3-1 94Mo 96Ru 0.14(2) mN2 2+3 2 2+2 E1 M1 0.69(9) mN2 1 2+1 E2 0 0+1 Factor of three weaker compared to 94Mo Only weak E1 transition to 2+1 observed: B(E1) = 0.002∙10-3 e2fm2 But: Strong E1 transition to 2+2observed: B(E1) = 0.25 ∙10-3 e2fm2
  13. Hexadecapole excitations in 96Ru Hexadecapole excitations
  14. Hexadecapole excitations in 96Ru M1 transitions between low-lying 4+-states E [MeV] 96Ru 3 4+2 2+3 0.90(7) mN2 M1 2 2+2 4+1 E2 M1 0.69(9) mN2 1 2+1 E2 4-2 → 4-2: t = 72(5) fs 0 0+1
  15. Hexadecapole excitations in 96Ru M1 transitions between low-lying 4+-states E [MeV] 96Ru 3 4+2 2+3 0.90(7) mN2 M1 2 2+2 4+1 E2 M1 0.69(9) mN2 1 2+1 E2 0 0+1 Comparable to 4+2 → 4+1 transition in 94Mo M1 strength comparable to the 2+ms → 2+1 M1 transition strength 96Ru 94Mo 92Zr
  16. sdg-IBM-2 calculations Motivated by successful reproduction of 4+2→ 4+1 M1 strength in 94Mo [1] Quadrupole Operator: [1] R. Casperson et al., PLB 721 (2013) 51.
  17. sdg-IBM-2 calculations Motivated by successful reproduction of 4+2→ 4+1 M1 strength in 94Mo [1] Quadrupole Operator: Limited toχd = χg = 0 No SU(3) contributions (only U(5) and O(6)) Conservation of F-spin quantum number Calculations with the program ArbModel[2] [1] R. Casperson et al., PLB 721 (2013) 51. [2] S. Heinze, ArbModel code, University of Cologne
  18. sdg-IBM-2 calculations Motivated by successful reproduction of 4+2→ 4+1 M1 strength in 94Mo [1] Five free parameters fitted to describe key features of 96Ru: R4/2 ratio and E(2+1,ms) B(E2;4+1→2+1)/B(E2;2+1→0+1), B(M1;4+2→4+1)/B(M1;2+1,ms→2+1,s) M1 and E2 transition operators: Effective charges and g-factors fixed to reproduce B(E2;2+1→0+1) and B(M1;2+1,ms→2+1,s) [1] R. Casperson et al., PLB 721 (2013) 51.
  19. sdg-IBM-2 calculations F = Fmax theory: sdg-IBM-2 Comparison to experimental data F = Fmax - 1 E [MeV] E2 transitions M1 transitions experiment 3 2 M1 M1 1 E2 E2 0+ 3+ 4+ 2+ 1+ 0 3+ 4+ 0+ 2+ 1+
  20. sdg-IBM-2 calculations Comparison to experimental data F = Fmax F = Fmax - 1 M1 transitions E [MeV] sdg-IBM-2 Experiment 3 0.563 mN2 0.17(5) mN2 0.08(1) mN2 0.13 mN2 2 0.69 mN2 0.69(9) mN2 0.90(7) mN2 1.13 mN2 1 0 3+ 4+ 0+ 0+ 3+ 4+ 2+ 2+ 1+ 1+
  21. sdg-IBM-2 calculations Structure of 4+1 and 4+2 states? s-, d-, and g-boson contents in the IBM wave functions:
  22. sdg-IBM-2 calculations Structure of 4+1 and 4+2 states? s-, d-, and g-boson contents in the IBM wave functions: Enhanced g-bosoncontri- bution MS-characterof 4+2state
  23. sdg-IBM-2 calculations Structure of 4+1 and 4+2 states? s-, d-, and g-boson contents in the IBM wave functions: Enhanced g-bosoncontri- bution MS-characterof 4+2state Enhanced E4 strengths predicted by sdg-IBM-2: B(E4; 4+1→ 0+1) = 1.1 W.u. and B(E4; 4+2→ 0+1) = 0.6 W.u. B(E4; 4+3→ 0+1) = 0.0 W.u. No experimental values for B(E4) so far for 96Ru
  24. sdg-IBM-2 calculations Structure of 4+1 and 4+2states – sdg-IBM-2 results Strong 4+2→ 4+1 M1 transition strength Enhanced g-boson contributions for 4+2 and 4+1 states Mixed-symmetry character for 4+2 state Enhanced E4 strengths for 4+2 and 4+1 states Strong evidence for one-phonon FS/MS hexadecapole contributions
  25. Conclusions Study of MSS of higher order multipolarity in the N=52 isotones Investigated in two proton-scattering experiments g-decay branching ratios Spins and multipole mixing ratios Level lifetimes Absolute transitionstrengths Identification of mixed-symmetry octupole excitation Observation of strong 4+2→ 4+1 M1 transition sdg-IBM-2 calculations Level scheme and transition strengths are reproduced Evidence for FS and MS hexadecapole content in 4+1,2 states
  26. Outlook Shell-model calculations for 96Ru using modified surface delta interaction (MSDI) Also: Reproduction of M1 strength Dominant hexadecapole structure of 4+1 state But: More complex structure of 4+2 state predicted in contrast to IBM-2 Different structure or inadequate description by SM?
  27. Outlook Shell-model calculations for 96Ru using modified surface delta interaction (MSDI) Also: Reproduction of M1 strength Dominant hexadecapole structure of 4+1 state But: More complex structure of 4+2 state predicted in contrast to IBM-2 Different structure or inadequate description by SM? Other mechanisms contribute to formation of M1 strength? Magnetic moments of individual microscopic configurations Need for more sophisticated calculations Shell-model calculations with more realistic interactions QRPA/QPM calculations
  28. Collaborators V. Derya, M. Elvers, J. Endres, J. Mayer, L. Netterdon, S. G. Pickstone, D. Radeck, P. Scholz, M. Spieker, M. Weinert, J. Wilhelmy, A. Zilges D. Savran V. Werner A. Heinz Thank you! Grazie! P. Petkov H. W. Becker, D. Rogalla
  29. Backup Backup
  30. Isovector-octupole excitations in 96Ru MS octupole excitations
  31. Isovector-octupole excitations in 96Ru Comparison to sdf-IBM-2 calculations Calculation within the dynamical symmetry limit [1] 3-ms→ 3-s matrix element scales with 2+ms→ 2+s matrix element: This work: R = 0.533 96Ru of more O(6) like character than e.g. 94Mo and 92Zr N = 52 [1] N. A. Smirnova et al., NPA 678 (2000) 235. Data from M. Scheck et al., PRC 81 (2010) 064305.
  32. Backup Shell model calculations
  33. Shell model calculations for 96Ru Existing shell model calculations: MSDI interaction (H. Klein et al., PRC 65 (2002), 044315) Vlow-k interaction (J.D. Holt et al., PRC 76 (2007), 034325) New calculations in view of the new experimental data: MSDI interaction RITSSCHIL code Model space: p: g9/2, p1/2 n: d5/2, s1/2, g7/2 , d3/2 , h11/2 SPE’s and TBME’s adop-ted from [1] [1] A.F. Lisetskiy et al., NPA 677(2000), 100
  34. Shell-model calculations Comparison to experimental data F = Fmax E2 transitions M1 transitions E [MeV] 96Ru - Experiment 96Ru - shell model 3 2 1 0 0+ 3+ 4+ 2+ 1+ 0+ 3+ 4+ 2+ 1+ Experimental level energies and transition strengths are well reproduced
  35. Shell-model calculations Comparison to experimental data F = Fmax M1 transitions E [MeV] 96Ru - Experiment 96Ru - shell model 3 2 1 0 0+ 3+ 4+ 2+ 1+ 0+ 3+ 4+ 2+ 1+
  36. Shell-model calculations Comparison to experimental data F = Fmax E2 transitions E [MeV] 96Ru - Experiment 96Ru - shell model 3 2 1 0 0+ 3+ 4+ 2+ 1+ 0+ 3+ 4+ 2+ 1+
  37. Shell-model calculations Comparison to experimental data Shell model configurations of lowest lying 4+ states (> 5%): pn-symmetric dominant p-conf. dominant n-conf. dominant p-conf.
  38. Hexadecapole excitations in the N=52 isotones 92Zr and 94Mo: Strong M1 transition between lowest 4+ states observed [1,2] 92Zr: B(M1;4+2→ 4+1) = 0.26(3) mN2 94Mo: B(M1;4+2→ 4+1) = 1.23(20) mN2 Evidence for isoscalar/isovector hexadecapole excitations? Shell-model calculations (MSDI) for 94Mo[3]: Dominant n=2, j=4 configurations of 4+1,2 states [1] C. Fransen et al., PRC 71 (2005) 054304. [3] A.F. Lisetskiy et al., NPA 677 (2000) 100. [2] C. Fransen et al., PRC 67 (2003) 024307.
  39. Shell-model calculations Evolution of 4+ energies in the N=52 isotones 92Zr Jπ = 3+,4+ 94Mo 96Ru 98Pd Good description for 94Mo Downsloping of 4+2,3 not confirmed experimentally
  40. sdg-IBM-2 calculations sdg-IBM-2 calculations
  41. Hexadecapole excitations in 96Ru M1 transitions between low-lying 4+-states E [MeV] 96Ru 3 4+2 2+3 0.90(7) mN2 M1 2 2+2 4+1 E2 M1 0.69(9) mN2 4-2 → 4-2: t = 72(5) fs 1 2+1 E2 0 0+1 Strong M1 transition for 4+2 → 4+1 also observed in 96Ru Comparable to 4+2 → 4+1 transition in 94Mo M1 strength comparable to 2+ms → 2+1 transition 96Ru 94Mo 92Zr
  42. sdg-IBM-2 calculations Hamiltonian and transition operators adopted from [1] Quadrupole Operator: Five free parameters for the parameter scan: ζ = 0.78, α = 1.1, λsd = 0.026, λsg = 0.018, β = 1.5 χd = 0, χg = 0 [1] R. Casperson et al., PLB 721 (2013) 51.
  43. sdg-IBM-2 calculations Hamiltonian and transition operators adopted from [1] Parameters for the transition operators: eBπ= 2.26, gd π = gg π = 1.34 eBν= gd ν = gg ν = 0 [1] R. Casperson et al., PLB 721 (2013) 51.
  44. sdg-IBM-2 calculations F = Fmax sdg-IBM-2 Comparison to experimental data F = Fmax - 1 E [MeV] E2 transitions M1 transitions Experiment 3 2 1 0+ 3+ 4+ 2+ 1+ 0 3+ 4+ 0+ 2+ 1+ Experimental level energies and transition strengths are well reproduced
  45. sdg-IBM-2 calculations Comparison to experimental data F = Fmax F = Fmax - 1 M1 transitions E [MeV] sdg-IBM-2 Experiment 3 0.563 mN2 0.17(5) mN2 0.08(1) mN2 0.13 mN2 2 0.69 mN2 0.69(9) mN2 0.90(7) mN2 1.13 mN2 1 0 3+ 4+ 0+ 0+ 3+ 4+ 2+ 2+ 1+ 1+
  46. sdg-IBM-2 calculations sdg-IBM-2 Comparison to experimental data F = Fmax F = Fmax - 1 E [MeV] E2 transitions Experiment 3 2 1 0+ 3+ 4+ 2+ 1+ 0 3+ 4+ 0+ 2+ 1+ Experimental level energies and transition strengths are well reproduced
  47. Backup Mixed symmetry quadrupole excitations
  48. Mixed-symmetry quadupole states Fingerprints for 2+ms excitation: M1 transition between MS and FS with abs. matrix elements of ~1mN E2 transition between MS and g.s. with a few W.u. 2+ms identified via Coulex in inverse kinematics 12C(96Ru,96Ru*) [1] B(M1;2+3→2+1) = 0.78 (23) mN2 B(E2; 2+3→0+1) = 1.6 (3) W.u. Picture courtesy: K. Heyde et al., Rev. Mod. Phys. 82 (2010) 2365 [1] N. Pietralla et al., PRC 64, (2001) 031301(R)
  49. Mixed-symmetry quadupole states Fingerprints for 2+ms excitation: M1 transition between MS and FS with abs. matrix elements of ~1mN E2 transition between MS and g.s. with a few W.u. 2+ms identified via Coulex in inverse kinematics 12C(96Ru,96Ru*) [1] This work: complete M1- and E2- strength distribution to 2+1 and g.s.: B(M1;2+3→2+1) = 0.69 (9) mN2 B(E2; 2+3→0+1) = 1.4 (2) W.u. 96Ru - Experiment Confirmation of 2+ms [1] N. Pietralla et al., PRC 64, (2001) 031301(R)
  50. One-phonon 2+ms state – Exp. vs. SM 2+ms state identified in 12C(96Ru, 96Ru*) experiment Comparison to shell-model calculations 96Ru - Experiment 96Ru – Shell model
  51. (2+1,s x 2+1,ms) quintuplet Candidates for 2+ and 3+ members proposed, based on comparison of g-decay branching ratios to 94Mo Now: Identification based on absolute transitions strength 3+2, t = 432 fs 2+5 , t = 440 fs 0.10 mN2 0.08 mN2 0.34 W.u. 0.28 W.u. 2+1,ms 2+1,ms 2+2 2+2 0.69 (9) mN2 0.69 (9) mN2 2+1 2+1 1.4 (2) W.u. 1.4 (2) W.u. 0+1 0+1 and are a factor of 3 weaker compared to 94Mo
  52. Mixed-symmetry excitations in N=52 isotones MS quadrupole, octupole and hexadecapole excitations observed in all stable even-even N=52 isotones 94Mo 96Ru 92Zr 2+ms: Maximum in M1 strength for 96Ru predicted 3-ms and 4+ms: Maximum in M1 strength for 94Mo observed 4+ms: Maximum reproduced in simple MSDI SM-calculations J.D. Holt et al., PRC 76 (2007) 034325.
  53. Backup (p,p‘g) Experiments on 96Ru
  54. Experiments on 96Ru 96Ru(p,p’g) @ WNSL, Yale g-decay branching ratios Proton energy Ep = 8.4 MeV 9 BGO shielded Clover detectors 5 silicon particle detectors Multipole mixing ratios Particle-detector array Mounted at predominantly backward angles Energy resolution: DE ≈ 120 keV
  55. Experiments on 96Ru 96Ru(p,p’g) @ IKP, Cologne Proton energy Ep = 7.0 MeV 12 single HPGe-detectors 2 BGO shielded Clover detectors 6 silicon particle detectors p Lifetime measurement Si 5 Si 6 Si 1 Si 2 Particle-detector array SONIC Mounted at 131°, 122° and 61° 90° positions used for HPGe Energy resolution: DE ≈ 70 keV Si 4 Si 3 Beam direction
  56. Proton-g coincidence matrix 96Ru – Cologne experiment
  57. Proton-g coincidence matrix p g x-axis projection: Excitation spectrum y-axis projection: g-ray spectrum
  58. Proton-g coincidence matrix p g x-axis projection: Excitation spectrum y-axis projection: g-ray spectrum Gating on excitation energy: Almost background-free spectra
  59. Backup pg coincidence DSAM
  60. Dopplershift Attenuation Method (DSAM) HPGe Short-lived state: Recoil nucleus decays in flight Observed Dopplershift is related to the nuclear level-lifetime t: g-ray beam Recoil Modeling of slowing-down process necessary for lifetime extraction Target Stopper Measurement of sub-picosecond lifetimes possible DE(qg) cnts Eg E0
  61. Dopplershift Attenuation Method (DSAM) Advantages of using pg-coincidence data for DSAM Fixed reaction kinematics Knowledge of and No averaging procedure necessary for F(t) determination Si p' (Ep',Qp,fp) p beam axis vrec qg (Eg,Qg,fg) HPGe
  62. Dopplershift Attenuation Method (DSAM) Advantages of using pg-coincidence data for DSAM Fixed reaction kinematics Knowledge of and No averaging procedure necessary for F(t) determination Extraction of centroid shift from gated spectra Even weak transitions can be analysed Feeding from higher lying states is eliminated Extraction of „real“ lifetimes instead of effective ones Particle detectors at backward angles Larger momentum transfer → Larger shift Higher sensitivity
  63. Dopplershift Attenuation Method (DSAM) DSAM using proton-g coincidence data Sorting of all 84 (Sili,HPGe)-pairs into 11 groups that share similar qgvalues Extraction of experimental attenuation factor F(t): p' p vrec qg HPGe F(t) = 0.78(4)
  64. Dopplershift Attenuation Method (DSAM) Simulation of the slowing-down process Monte-Carlo simulation program dstop96 [1] Applying Lindhard, Scharff and Schiøtt (LSS) theory: Electronic stopping: Stopping power tables from Northcliffe and Schilling[2] Nuclear stopping: fn = 0.7 [1] P. Petkov et al., NPA 640 (1998) 293. [2] L.C. Northcliffe and R.F. Schilling, Nucl. Data Tables A 7 (1970) 233.
  65. Dopplershift Attenuation Method (DSAM) Comparison with previously measured lifetimes: Excellent agreement with (g,g’) and Coulomb-excitation data
  66. Dopplershift Attenuation Method (DSAM) Comparison with previously measured lifetimes: Excellent agreement with (g,g’) and Coulomb-excitation data In total, the lifetime of 30 excited states extracted, 22 for the first time
  67. Dopplershift Attenuation Method (DSAM) Detailed knowledge of target and stopper composition and thicknesses crucial for simulation of stopping process RBS analysis at RUBION Bochum 96Ru Si particle detector at 160° Peak-width corresponds to thickness Position corresponds to atomic number and layer structure SiO2 56Fe 12C
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