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Pear-shaped nuclei. Peter Butler University of Liverpool . Generalised octupole shapes Rotating even-even nuclei Odd electric moments Odd-mass nuclei & EDMs. Reflection Asymmetric Shapes.

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Peter Butler University of Liverpool

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Peter butler university of liverpool

Pear-shapednuclei

Peter Butler

University of Liverpool

Generalised octupole shapes

Rotating even-even nuclei

Odd electric moments

Odd-mass nuclei & EDMs


Peter butler university of liverpool

Reflection Asymmetric Shapes

If alm is non-zero for odd l then the nuclear shape becomes reflection-asymmetric, or pear-shaped.

or


Regions of enhanced octupole correlations

Regions of Enhanced Octupole Correlations

134

220Rn

224,226Ra

88

148Nd

56

34

long range multipole-multipole force


Peter butler university of liverpool

Octupole Collectivity

Soft Static Rigid

OctupoleDeformation Deformation


Peter butler university of liverpool

Rotating octupole shapes

Octupole deformed

Octupole vibrational


Peter butler university of liverpool

Actual Behaviour (near the ground state)

Octupole vibrational

Octupole deformed

JFC Cocks et al PRL 78 (1997) 2920, Nucl. Phys. A645 (1999) 61


Peter butler university of liverpool

Electric moments

El moment

Since the El operator is an odd function of r if l is odd,

the moment is:

Zero for diagonal matrix elements (unless P, T are violated, see later)

Non-zero for transition matrix elements if yn has opposite parity to ym


Peter butler university of liverpool

Electric dipole transitions

Macroscopic contribution to E1 moment

= aA.Z(charge) – b (N-Z) (neutron skin)

= 0.1 efm for 224Ra

Microscopic contribution to E1 moment

= -0.1 efm for 224Ra


Peter butler university of liverpool

Experimental E1 moments in octupole nuclei

Q1(efm)

ARa


Peter butler university of liverpool

B(E3) transitions

B(E3; 0+ → 3-) ~ 30 – 50single particle units for b3 ~ 0.1

To study the “best” candidates for octupole shapes, we excite either radioactive targets

(e.g. 226Ra, 1600y) or use radioactive beams


Peter butler university of liverpool

Coulomb excitation and g-ray decay

REX-ISOLDE

60Ni target

120Sn target

Spectrum taken

with MINIBALL

224Ra


Peter butler university of liverpool

E2 and E3 moments in “octupole” mass region

radioactive

beams

radioactive

targets

(1993)

LP Gaffney et al

Nature 497 (2013) 199

octupole

vibrational

(2013)


Peter butler university of liverpool

Rotating charged pear-shape

220Rn

224Ra

226Ra

LP Gaffney et al

Nature 497 (2013) 199

HJ Wollersheim et al.,

NP A556 (1993) 261

E2 matrix elements [e·fm2]

E3 matrix elements [e·fm3]


Peter butler university of liverpool

Comparison with theory

E2 moments

E3 moments

1

2

2

3

4

5

1. Shneidman et al PRC 67 (2003) 014313

2. Robledo & Bertsch PRC 84 (2011) 054302

3. Rutz et al. NP A590 (1995) 680

4. Engel et al. PRC 68 (2003) 025501

5. Nazarewicz et al NP A429 (1984) 269


Peter butler university of liverpool

The largest B(E3)s

228U

Robledo & Bertsch

PRC 84, 054302 (2011)

B(E3:0+ 0-) (Wu)


Peter butler university of liverpool

Prospects for measuring 226,228U

226U

oct. vibrational

N=134

oct. deformed

PT Greenlees et al J. Phys. G: Nucl. Part. Phys. 24 (1998) L63


Peter butler university of liverpool

Octupole collectivity in odd-mass nuclei

17/2-

17/2+

15/2+

15/2-

13/2-

13/2+

11/2-

11/2+

9/2-

9/2+

7/2+

5/2+

Smaller octupole correlations

Large parity splitting

Large octupole correlations

Small parity splitting ~ 50 keV

M Dahlinger et al Nucl. Phys. A484 (1988) 337


Peter butler university of liverpool

Neutron and Atomic EDM moment

Static Electric Dipole Moment implies CP-violation

Schiff Theorem: neutral atomic system of point particles in electric field readjusts itself to give zero E field at all charges.

BUT: finite size and shape of nucleus breaks the symmetry


Peter butler university of liverpool

Octupole enhanced atomic EDM moment

See Next Talk!!

related to Q3

P,T-violating n-n interaction

V Spevak, N Auerbach, and VV Flambaum

PR C 56 (1997) 1357

Schiff moment:

energy splitting of parity doublet

Schiff moment enhanced by ~ 3 orders of magnitude in pear-shaped nuclei

SKOL

219,221Rn inferior to 223,225Ra

224Ra

J Dobaczewski (Trento, 2010)


Peter butler university of liverpool

Summary

Strong circumstantial evidence that some nuclei are pear-shaped

Best evidence comes from behaviour of energy levels and B(E3)s. Wide discrepancy of theories for this quantity.

Odd mass octupole-deformed nuclei offer greatly increased sensitivity for EDM searches

“Last year’s discovery has left the scientists there a little deflated because the Higgs has turned out to be a boring, just-as-they-predicted kind of particle. The nucleus of the radium atom, on the other hand, is much more interesting.”

CERN-ISOLDE

TechnischeUniversitätDarmstadt University of Edinburgh

GANIL

University of Jyväskylä

UniversitätzuKöln

KU Leuven

Laboratory Lawrence Livermore NL

University of Liverpool

University of Lund

Universidad Autónoma de Madrid

University of Michigan

Ludwig-Maximilians-Universität and TechnischeUniversitätMünchen

SCK CEN

University of Rochester

University of Warsaw, Heavy Ion Lab

University of York


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