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From Vibrations to Rotations as a Function of Spin

From Vibrations to Rotations as a Function of Spin. Paddy Regan Dept. of Physics, University of Surrey, Guildford, GU2 7XH, UK e-mail: p.regan@surrey.ac.uk. Outline. Main physics question, Are nuclei (with Z=40-50) Rotators or Vibrators ?

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From Vibrations to Rotations as a Function of Spin

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  1. From Vibrations to Rotations as a Function of Spin Paddy Regan Dept. of Physics, University of Surrey, Guildford, GU2 7XH, UK e-mail: p.regan@surrey.ac.uk

  2. Outline Main physics question, Are nuclei (with Z=40-50) Rotators or Vibrators ? * Signatures of vibrator-rotor structural evolution. * 102Ru from WNSL-Yale * 99-102Mo alignments/phase changes (using DICs). * 112,114Cd medium spins from WNSL-Yale * Odd-A cases, 101Ru

  3. Nuclear Rotations and Vibrations • What are the signatures (in even-even nuclei) ? • (extreme) theoretical limits

  4. En n=3 n=2 n=1 n=0 b2 V http://npl.kyy.nitech.ac.jp/~arita/vib b2

  5. Signatures of (perfect) vibrators and rotors State lifetimes, i.e., B(E2) values and selection rules (eg. Dn=1).

  6. Nuclei in the Sr-Sn region show dramatic change in structure around N~60. Sudden explosion of b2 deformation in Sr-Ru isotopes at N=60 has been explained by strong spatial overlap of Spin-Orbit Partners (SOPs) g9/2 protons and g7/2 neutrons. (see Federman and Pittel, Phys. Rev. C20 (1979) p820)

  7. Alignments and rotational motion in ‘vibrational’ 106Cd (Z=48, N=58), PHR et al. Nucl. Phys. A586 (1995) p351

  8. Can subtract off a reference (core) aligned angular momentum to see effect of quasi-particle alignments as a function of frequency. Dix=5h CSM ref. Bengtsson Frauendorf and May, At. Data. Nuc. Data. Tab. 35 (1986) p15

  9. h11/2 neutron orbital responsible for 1st crossing in even-even systems. Energy appears to correlate with transition to deformed ground states at N~60

  10. 82 1h11/2 50 [550]1/2- 1g9/2 Alignment (rotational picture at least) driven by Coriolis interaction on high-j, low-W orbitals (ie. ones with large jx on collective rotation axis. Vcor = -jx.w eg. nh11/2 [550]1/2 ‘intruder’ FS for N~57, b2~0.15->0.2 jx [541]3/2-

  11. Ru (Z=44) in the centre of the ‘deformed’ region for N=56-58 Anharmonic vibrator for the ground state ‘band’ is the usual explanation for 100Ru and neighbours....but mid-shell (Z=40-50) nature is consistent with largest collectivity in the region. Q.Are these nuclei deformed or vibrational ? Zr Mo Ru Pd Cd Sn

  12. Experimental Details 96Zr (9Be,3n)102Ru, space~100mb 96Zr(9Be,4n)101Ru, space~800mb Enriched (85%) 670mg/cm296Zr foil on 5mg/cm2natPb support. Ebeam=44 MeV, lmax~25 h YRASTBALL array at WNSL 6 clover germaniums @ 90o 5 co-axial detectors @ 50o + 126o 3 co-axial detectors @ 160o see Yamamoto, PHR, Beausang et al., Phys. Rev. C66 (2002) 024302

  13. PHR, Beasang, Zamfir, Casten et al., Phys. Rev. Lett. 90 (2002) 152502

  14. PHR, Beausang, Zamfir, Casten, Zhang et al., Phys. Rev. Lett. 90 (2003) 152502

  15. If we parameterize with (Eg / J) vs. J Can see if rotor or vibrator by inspection

  16. Structural change from vibrator to rotator appears to be a regular feature of this region. Rotation stabilized by core stiffening due to population of ‘rotation-aligned’ h11/2 neutrons. Special type of crossing, Vibrator to Rotor !!!

  17. Q. Are backbends necessarily due to rotational alignment ? A. NO ! Can be vibrational – rotational structure change!!

  18. Detailed spectroscopy allowed by investigating gamma-decay sequences from high-spin states. YRASTBALL allows triples to show band-like structures in 101Ru. see A.D.Yamamoto et al., Phys. Rev. C66 (2002) 024302

  19. Quasi-particle alignments and kinematic moments of inertia nh11/2 band Dix=10 nh11/2 band

  20. TRS calculations for 101Ru by Furong Xu (Bejing) for different parity (and signature) configs. g b2 w=0.2MeV w=0.3MeV w=0.4MeV w=0.6MeV

  21. See PHR, Yamamoto, Beausang, Zamfir, Casten, Zhang et al., AIP Conf. Proc. 656 (2002) p422

  22. z x q1 q2 f1 f2 y

  23. For Odd-A (Carl Wheldon’s idea)

  24. (iii) (ii) (i) Ebeam ~15-20% above Coulomb barrier beam target Z N Can not use fusion-evaporation reactions to study high-spin states (and thus vibrational-rotational transitions, alignments etc.) in beta-stable and neutron-rich systems. Use deep-inelastic reactions.

  25. Kinematics and angular mom. input calcs (assumes ‘rolling mode’) for 136Xe beam on 100Mo target. Estimate ~ 25hbar in TLF for ~25% above Coul. barrier. For Eb(136Xe)~750 MeV, qblf~30o and qtlf~50o. 100Mo +136Xe (beam) DIC calcs.

  26. 100Mo + 136Xe @ 750 MeV GAMMASPHERE + CHICO BLFs TLFs elastics

  27. Isomer gating very useful in DIC experiments. Test with known case…..

  28. Use known delayed lines in 101Mo (182 and 57 keV) to identify previously unknown nh11/2 band (+ 34 keV E1 decay).

  29. E-GOS for other regions ? Z ~90 ? rotor vibrator

  30. Vib. rotor

  31. (ph11/2)2 alignment in A~130 region appears to have analogous behaviour to (nh11/2)2 alignment in A~100 region. Conclusion? In many cases, ‘rotational alignment’ is actually a crossing between a quasi-vibrational ground state configuration and a deformed rotational sequence caused by stiffening of potential by population of high-j, equatorial (h11/2) orbitals

  32. 112Cd

  33. Summary and Future Look • 101,102Ru (and neighbours) look like g-soft, anharmonic vib. nuclei at low-spins (eg. E(4+)/E(2+)~2.3)..... BUT also have apparent rotational-like behaviour eg. band-crossing, alignments etc. • Paradoxically, Coriolis (rotational) effects are largest in nuclei which have SMALL deformations (ie. require large energies/frequencies to rotate). ‘Vibrational’ A=100 may be the best tests of nuclear Coriolis effects. • Vibrational – Rotational ‘phase’ change around spin 10? Smooth evolution with crossing of anharmonic vibrational states and rotation-aligned configurations. • ‘E-GOS’ Plot of Eg /J vs. J gives model independent information on vibrational-rotational crossing.

  34. many thanks to...... • Arata Yamamoto (Surrey/Yale student). • 101-102Ru Expt. Con Beausang (+ Yalies) • 100Mo+136Xe CHICO, Rochester (Chin-Yen Wu et al.,), Manc. (John Smith et al,) + LBNL • 7Li+110Pd, Scott Langdown (+Yalies + Paisley) • Vibrator-Rotator (E-GOS) plots, Con B., Rick Casten, Victor Zamfir, Jing-Ye Zhang et al., • Odd-A, Carl Wheldon (now at GSI)

  35. NUSTAR’05International Conference onNUclear STructure, Astrophysics and Reactions The University of Surrey, Guildford, UK5-8 January 2005

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