From Vibrations to Rotations as a Function of Spin Paddy Regan Dept. of Physics, University of Surrey, Guildford, GU2 7XH, UK

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

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

22 V 22 EnEn n=0 n=1 n=2 n=3

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

Nuclei in the Sr-Sn region show dramatic change in structure around N~60. Sudden explosion of  2 deformation in Sr-Ru isotopes at N=60 has been explained by strong spatial overlap of Spin- Orbit Partners (SOPs) g 9/2 protons and g 7/2 neutrons. (see Federman and Pittel, Phys. Rev. C20 (1979) p820)

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

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

h 11/2 neutron orbital responsible for 1 st crossing in even-even systems. Energy appears to correlate with transition to deformed ground states at N~60

Alignment (rotational picture at least) driven by Coriolis interaction on high-j, low-  orbitals (ie. ones with large j x on collective rotation axis. V cor = -j x.  eg. h 11/2 [550]1/2 ‘intruder’ FS for N~57,  2 ~0.15->0.2 jxjx [550]1/2 - 1h 11/2 1g 9/2 [541]3/2 -

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 100 Ru and neighbours....but mid-shell (Z=40-50) nature is consistent with largest collectivity in the region. Q.Are these nuclei deformed or vibrational ? RuMoZrPdCdSn

Experimental Details 96 Zr ( 9 Be,3n) 102 Ru,  pace ~100mb Enriched (85%) 670  g/cm 2 96 Zr foil on 5mg/cm 2 nat Pb support. E beam =44 MeV, l max ~25 h YRASTBALL array at WNSL 6 clover 90 o 5 co-axial 50 o o 3 co-axial 160 o

See PHR, Beausang, Zamfir, Casten, Zhang, Yamamoto et al., PRL in press.

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

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’ h 11/2 neutrons. Special type of crossing, Vibrator to Rotor !!!

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

(a) gamma-gamma(b) triple coincidences Detailed spectroscopy allowed by investigating gamma-decay sequences from high-spin states. YRASTBALL allows triple coincidences to be routinely observed. Band-like structures are clearly observed in 101 Ru.

see A.D.Yamamoto et al. Phys. Rev. C66 (2002) Decay scheme for 101 Ru Band-like sequences observed on ‘intrinsic’ 11/2 -, 5/2 + and 7/2 + states. Backbending observed in positive parity bands (1 and 2), but not in negative parity band (band 3). Pauli blocking arguments suggest aligning particles are therefore of h 11/2 neutron nature.

Quasi-particle alignments and kinematic moments of inertia  i x =10 h 11/2 band h 11/2 band

TRS calculations for 101 Ru by Furong Xu (Bejing) for different parity (and signature) configs. 22   =0.2MeV  =0.4MeV  =0.3MeV  =0.6MeV

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

For Odd-A (Carl Wheldon’s idea)

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. Z N E beam ~15-20% above Coulomb barrier beam target (i) (ii) (iii)

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

100 Mo MeV GAMMASPHERE + CHICO TLFs BLFs elastics

z x y    

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

Use known delayed lines in 101 Mo (182 and 57 keV) to identify previously unknown h 11/2 band (+ 34 keV E1 decay).

112 Cd

Vib. rotor

(  h 11/2 ) 2 alignment in A~130 region appears to have analogous behaviour to ( h 11/2 ) 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 (h 11/2 ) orbitals

Summary and Future Look 101,102 Ru (and neighbours) look like  -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. Plot of E  /J verses J gives model independent crossing.

many thanks to Arata Yamamoto (Surrey/Yale student) Ru Expt. Con Beausang (+ Yalies) 100 Mo+ 136 Xe CHICO, Rochester (Chin-Yen Wu et al.,), Manc. (John Smith et al,) + LBNL 7 Li+ 110 Pd, 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)

NUSTAR’05 International Conference on NUclear STructure, Astrophysics and Reactions The University of Surrey, Guildford, UK 9-12 January 2005