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

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

Outline

Nuclear Rotations and Vibrations

• What are the signatures (in even-even nuclei) ?– (extreme) theoretical limits

2 (4 ) 4(5) 20

( 1), 3.332 (2 ) 2(

(4 ) 2 = 2.00

3)

( 1

6

2 )N

J

EE N

EE J J

E

E

2

V

2

En

n=0

n=1

n=2

n=3

http://npl.kyy.nitech.ac.jp/~arita/vib

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) g9/2 protons and g7/2 neutrons.

(see Federman and Pittel, Phys. Rev. C20 (1979) p820)

Alignments and rotational motion in ‘vibrational’ 106Cd (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.

2( 1)X

x X ref

ref X ref

I I I K

i I I

I I

ix=5h

CSM ref. Bengtsson Frauendorf and May, At. Data. Nuc. Data. Tab. 35 (1986) p15

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

Alignment (rotational picture at least) driven by Coriolis interaction on high-j, low- orbitals (ie. ones with large jx on collective rotation axis.

Vcor = -jx.

eg.

h11/2 [550]1/2 ‘intruder’

FS for N~57, 2~0.15->0.2

jx

50

82

[550]1/2-

1h11/2

1g9/2

[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 100Ru and neighbours....butmid-shell (Z=40-50) natureis consistent with largest collectivity in the region.

Q.Are these nuclei deformed or vibrational ?

RuMoZr Pd Cd Sn

Experimental Details

96Zr (9Be,3n)102Ru, pace~100mb

Enriched (85%) 670g/cm2 96Zr foil on 5mg/cm2 natPb 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

24

24

2 :Rotor

0 : Vibrator

)2(

242

),1(2

:Rotor

,2

:Vibrator

22

22

J

J

J

n

JR

JR

J

JJER

JEJJE

EJ

nE

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

If we parameterize with (E / J) vs. JCan 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’ h11/2

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 101Ru.

see A.D.Yamamoto et al. Phys. Rev. C66 (2002) 024302

Decay scheme for 101Ru

Band-like sequences observed on ‘intrinsic’ 11/2-, 5/2+ and 7/2+ states.

Backbending observed in positiveparity bands (1 and 2), but not innegative parity band (band 3).

Pauli blocking argumentssuggest aligning particles are therefore of h11/2 neutron nature.

Quasi-particle alignments and kinematic moments of inertia

ix=10 h11/2

band

h11/2

band

TRS calculations for 101Ru by Furong Xu (Bejing) for differentparity (and signature) configs.

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)

equn. GOS-E orginal toreduces this0for note

)2()2(

)2(

24

24

2][4

2)(

i.e., ,normalised be should energies

, spin, bandhead with case rotationalfor

24

2)(

2

2

2

2

2

2

KKI

KRER

RKIRKI

KIE

KI

KE

KI

KIKIR

K

KI

I

KI

EKIR

Krotor

K

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

Ebeam ~15-20% above Coulomb barrier

beam

target

(i) (ii) (iii)

max

3

1blfmax

3

1tlf

max

3/13/1

0

221

max

1

1

7

2

1

1

7

2

fragments. twoebetween th mom. ang. relative the

and , intosplit is limit, mode rolling In the

25.12

cosec1.4

where, approach,closest of distance by thegiven is

max. issection -cross DIC the whereangle The

. and 219.0

is mom. ang. peripheral max. y theclassicall-Semi

l

AA

ll

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l

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grazing

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AAVERl

B

T

T

B

blftlf

TBgraz

k

TB

TBCMCM

0

10

20

30

40

50

620

677

733

790

%>Ecoul

Ltlf (roll)

v/c (tlf)

Linear(%>Ecoul)

0

10

20

30

40

50

60

620 648 677 705 733 761 790Beam Energy (MeV)

blf_ang

tlf_ang

lmax/10

Kinematics and angular mom. input calcs (assumes ‘rolling mode’) for 136Xe beam on 100Mo target.

Estimate ~ 25hbar in TLFfor ~25% above Coul. barrier. For Eb(136Xe)~750 MeV,blf~30o and tlf~50o.

100Mo +136Xe (beam) DIC calcs.

100Mo + 136Xe @ 750 MeVGAMMASPHERE + CHICO

TLFs

BLFs

elastics

-1

cos-1

by calculated then is correctionDoppler The

coscoscoscossinsinsinsin)cos(

where

)cos(r.r

by given is angleray -fragment/ the

k )cos( , j )sin()sin( ,i )cos()sin(

k, and j i, rsunit vectoCartesian For

2

2,1'

2121212112

122121

1,2

1,2

EE

rr

rzryrx

z

x

y

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

Use known delayed lines in 101Mo (182 and 57 keV) to identify previously unknown h11/2 band (+ 34 keV E1 decay).

112Cd

Vib.

rotor

(h11/2)2 alignment in A~130 region appears tohave analogous behaviourto (h11/2)2 alignment in A~100 region.

Conclusion?

In many cases, ‘rotational alignment’ is actually acrossing between a quasi-vibrational groundstate configuration and a deformed rotational sequencecaused by stiffening of potential by population of high-j, equatorial (h11/2) orbitals

Summary and Future Look• 101,102Ru (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).

• 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)

NUSTAR’05International Conference on

NUclear STructure, Astrophysics and Reactions

The University of Surrey, Guildford, UK

9-12 January 2005