1.  Standard Model goes pear-shaped in CERN experiment The Register  Physicists get a good look at pear-shaped atomic nuclei The Los Angeles Times  Exotic atoms could explain why Big Bang created more matter Newstrack India The lopsided nuclei, described today (May 8) in the journal Nature, could be good candidates for researchers looking for new types of physics beyond the reigning explanation for the bits of matter that make up the universe (called the Standard Model), said study author Peter Butler, a physicist at the University of Liverpool in the United Kingdom. The findings could help scientists search for physics beyond the Standard model, said Witold Nazarewicz. An electric dipole moment would provide a way to test extension theories to the Standard Model, such as supersymmetry, which could help explain why there is more matter than antimatter in the universe. Until now, only one pear-shaped nucleus had been found experimentally: radium 226, whose shape was sketched out back in 1993. H.J. Wollersheim, H. Emling, H. Grein, R. Kulessa, R.S. Simon, C. Fleischmann, J. de Boer, E. Hauber, C. Lauterbach, C. Schandera, P.A. Butler, T. Czosnyka; Nucl. Phys. A 556, 261 (1993).

2. „If equal amounts of matter and antimatter were created at the Big Bang, everything would have been annihilated, and there would be no galaxies, stars, planets or people“ (Tim Chupp Univ. Michigan) The Standard Model describes four fundamental forces or interactions

3. Quarks Leptons Force Carriers I II III Three Generations of Matter Gauge bosons Elementary Particles

4. Shape parameterization axially symmetric quadrupoleaxially symmetric octupole =2  20 ≠0,  2±1 =  2±2 = 0 =3  30 ≠0,  3±1,2,3 = 0  20 ≠0,  2±1,2 = 0

5. Octupole collectivity R.H. Spear At. Data and Nucl. Data Tables 42 (1989), 55 Y 30 coupling Δℓ=3 Δj=3 some subshells interact via the r 3 Y 30 operator e.g. in light actinide nuclei one has an interaction between j 15/2 and g 9/2 neutron orbitals i 13/2 and f 7/2 proton orbitals (W.u.)

6. Octupole collectivity Octupole correlations enhanced at the magic numbers: 34, 56, 88, 134 Microscopically … Intruder orbitals of opposite parity and ΔJ, ΔL = 3 close to Fermi level 226 Ra close to Z=88 N=134

7. 226 Ra + + + + + - - - - - In an octupole deformed nucleus the center of mass and center of charge tend to separate, creating a non-zero electric dipole moment. Octupole collectivity

8. The double oscillator -a a V V0V0 Merzbacher ‘Quantum Mechanics’ octupole deformed β3β3 β3β3 octupole vibrational

9. Coulomb excitation scattering angle impact parameter

10. 3-3- 4+4+ 2+2+ 0+0+ channel number counts Scattered α-spectrum of 226 Ra (t 1/2 = 1600 yr) 4 He → 226 Ra E α = 16 MeV θ lab = 145 0 λβ λ (exp)β λ (theo) 22.27 (3)0.165 (2)0.164 31.05 (5)0.104 (5)0.112 41.04 (7)0.123 (8)0.096 beam direction 226 Ra-target  Si-detector 226 Ra: t 1/2 = 1600 yr

11. 3-3- 4+4+ 2+2+ 0+0+ channel number counts Scattered α-spectrum of 226 Ra 4 He → 226 Ra E α = 16 MeV θ lab = 145 0 beam direction 226 Ra-target  Si-detector InIn IiIi IfIf 0+0+ 4+4+ 2+2+ E2 E4 λβ λ (exp)β λ (theo) 22.27 (3)0.165 (2)0.164 31.05 (5)0.104 (5)0.112 41.04 (7)0.123 (8)0.096

12. 226 Ra PPAC ring counter 15 0 ≤Θ L ≤45 0, 0 0 ≤φ L ≤360 0 4 PPAC counter 53 0 ≤Θ L ≤90 0, 0 0 ≤φ L ≤84 0 208 Pb beam Ge 1 Ge 2 Ge 3 Ge 4 Ge 7 Ge 6 Ge 5 Ge8 Experimental set-up 226 RaBr 2 (400 μg/cm 2 ) on C-backing (50 μg/cm 2 ) and covered by Be (40 μg/cm 2 )

13. Coulomb excitation of 226 Ra

14. γ-ray spectrum of 226 Ra energy [keV] counts 208 Pb → 226 Ra E lab = 4.7 AMeV 15 0 ≤ θ lab ≤ 45 0 0 0 ≤ φ lab ≤ 360 0

15. γ-ray spectrum of 224 Ra 224 Ra → 60 Ni / 120 Sn E lab = 2.83 AMeV

16. Signature of an octupole deformed nucleus β 2 = 0.16 β 3 =-0.11 β 4 = 0.10 E2E1 Single rotational band with spin sequence: I = 0 +, 1 -, 2 +, 3 -, … excitation energy E ~ I·(I+1) competition between intraband E2 and interband E1 transitions E1 transition strength 10 -2 W.u. π: + π: -

17. Signature of an octupole deformed nucleus E2E1 π: + π: - 224 Ra Observation of unexpectedly small E1 moments in 224 Ra, R.J. Poynter, P.A. Butler et al., Phys. Lett. B232 (1989), 447

18. Signature of an octupole deformed nucleus Energy displacement δE between the positive- and negative-parity states if they form a single rotational band W. Nazarewicz et al.; Nucl. Phys. A441 (1985) 420

19. Electric transition quadrupole moments in 226 Ra negative parity states positive parity states W. Nazarewicz et al.; Nucl. Phys. A467 (1987) 437 rigid rotor model: liquid drop: Q 2 (exp) = 750 fm 2 Q 2 (theo) = 680 fm 2 β 2 = 0.21 H.J. Wollersheim et al.; Nucl. Phys. A556 (1993) 261

20. Static quadrupole moments in 226 Ra H.J. Wollersheim et al.; Nucl. Phys. A556 (1993) 261 negative parity states positive parity states rigid rotor model: rigid triaxial rotor model: Davydov and Filippov, Nucl. Phys. 8, 237 (1958)

21. Electric transition octupole moments in 226 Ra β 3 0.18 0.12 0.06 W. Nazarewicz et al.; Nucl. Phys. A467 (1987) 437 - 0.1 0.1 - 0.1 0 0 0.16 β3β3 β2β2 β3β3 H.J. Wollersheim et al.; Nucl. Phys. A556 (1993) 261 liquid drop:

22. Electric transition octupole moments in 224 Ra

23. Intrinsic electric dipole moments in 226 Ra liquid-drop contribution: rigid rotor model: G. Leander et al.; Nucl. Phys. A453 (1986) 58H.J. Wollersheim et al.; Nucl. Phys. A556 (1993) 261

24. Intrinsic electric dipole moments in 226 Ra liquid-drop contribution: G. Leander et al.; Nucl. Phys. A453 (1986) 58 224 Ra: Q 1 (e fm) IπIπ 19892013 3-3- 0.027(3)0.031(6) 5-5- 0.040(10)0.028(9) 7-7- < 0.05< 0.08

25. Collective parameters In general, forbidden – density change! forbidden – CM moves! OK... λ=0 λ=1 λ=2 λ=3 time

26. Center of mass conservation The coordinates (x, y, z) can be expressed by The dipole coordinate is not an independent quantity. It is non-zero for nuclear shapes with both quadrupole and octupole degrees of freedom.

27. Intrinsic electric dipole moment The local volume polarization of electric charge can be derived from the requirement of a minimum in the energy functional. (Myers Ann. of Phys. (1971)) where ρ p and ρ n are the proton and neutron densities, C LD is the volume symmetry energy coefficient of the liquid drop model and V C is the Coulomb potential generated by ρ p inside the nucleus (r < R 0 ) Keeping the center of gravity fixed, the integral

28. Intrinsic electric dipole moment

29. C LD ≈ 20 MeV

30. Summary  single rotational band for  no backbending observed  β 2, β 3, β 4 deformation parameters are in excellent agreement with calculated values  octupole deformation is three times larger than in octupole- vibrational nuclei  equal transition quadrupole moments for positive- and negative- parity states  static quadrupole moments are in excellent agreement with an axially symmetric shape  electric dipole moments are close to liquid-drop value ( )  octupole deformation seems to be stabilized with increasing rotational frequency

31. Coulomb excitation of 226 Ra 226 Ra target broken after 8 hours Christoph Fleischmann