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**University of Liverpool**

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

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**Reflection Asymmetric Shapes**

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

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**Regions of Enhanced Octupole Correlations**

134 220Rn 224,226Ra 88 148Nd 56 34 long range multipole-multipole force 3 3

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**Octupole Collectivity**

Soft Static Rigid Octupole Deformation Deformation 4 4

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**Rotating octupole shapes**

3ħ 3ħ 0ħ 0ħ Octupole deformed Octupole vibrational

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**Actual Behaviour (near the ground state)**

Octupole vibrational 3ħ 0ħ 3ħ 0ħ Octupole deformed 3ħ 0ħ JFC Cocks et al PRL 78 (1997) 2920, Nucl. Phys. A645 (1999) 61

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**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

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**Electric dipole transitions**

Macroscopic contribution to E1 moment = a A.Z (charge) – b (N-Z) (neutron skin) = 0.1 efm for 224Ra Microscopic contribution to E1 moment = -0.1 efm for 224Ra

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**Experimental E1 moments in octupole nuclei**

Q1 (efm) ARa

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

B(E3) transitions B(E3; 0+ → 3-) ~ 30 – 50 single 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

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**Coulomb excitation and g-ray decay**

REX-ISOLDE 60Ni target 120Sn target Spectrum taken with MINIBALL 224Ra

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**E2 and E3 moments in “octupole” mass region**

radioactive beams radioactive targets (1993) LP Gaffney et al Nature 497 (2013) 199 octupole vibrational (2013)

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**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]

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**Comparison with theory**

E2 moments E3 moments 1 2 3 4 5 1. Shneidman et al PRC 67 (2003) 2. Robledo & Bertsch PRC 84 (2011) 3. Rutz et al. NP A590 (1995) 680 4. Engel et al. PRC 68 (2003) 5. Nazarewicz et al NP A429 (1984) 269

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**The largest B(E3)s B(E3:0+ 0-) (Wu) 228U Robledo & Bertsch**

PRC 84, (2011) B(E3:0+ 0-) (Wu)

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**Prospects for measuring 226,228U**

oct. vibrational N=134 oct. deformed PT Greenlees et al J. Phys. G: Nucl. Part. Phys. 24 (1998) L63

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**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 17

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**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

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**J Dobaczewski (Trento, 2010)**

Octupole enhanced atomic EDM moment See Next Talk!! related to Q3 V Spevak, N Auerbach, and VV Flambaum PR C 56 (1997) 1357 P,T-violating n-n interaction 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)

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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 Technische Universität Darmstadt University of Edinburgh GANIL University of Jyväskylä Universität zu Köln KU Leuven Laboratory Lawrence Livermore NL University of Liverpool University of Lund Universidad Autónoma de Madrid University of Michigan Ludwig-Maximilians-Universität and Technische Universität München SCK CEN University of Rochester University of Warsaw, Heavy Ion Lab University of York

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