Nuclear structure of lowest 229Th states and time-dependent fundamental constants 1Elena Litvinova, 2Hans Feldmeier, 3,4Jacek Dobaczewski, 5Victor Flambaum 1National Superconducting Cyclotron Laboratory & MSU, East Lansing, USA 2GSI Helmholtzzenrum für Schwerionenforschung, Darmstadt, Germany 3Institute of Theoretical Physics, University of Warsaw, Poland 4Department of Physics, University of Jyväskylä, Finland 5School of Physics, University of New South Wales, Sydney, Australia Nuclear isomer clock 2012, EMMI, Sep. 25-27

Outline General properties and microscopic structure of low-lying states in 229Th. Low-lying isomeric state in 229Th: a nuclear physics case for testing variations of fundamental constants. Sensitivity of the 3/2+ -> 5/2+ transition frequency to the potential changes of the fine structure constant α. Skyrme-Hartree-Fock-Bogoliubov calculations for 229Th lowest states and δα/α amplification factor. Conclusions & outlook.

General properties of 229Th 229Th = 228Th + n 228Th is transitional from octupole to quadrupole deformation: 226Th is octupole deformed, 230Th is vibrational-like, 228Th is „octupole soft“ (strong octupole correlations): Bohr & Mottelson, Leander, Otsuka, Nazarewicz, Jolos, Pashkevich, … Octupole vibrational 0- state at 338 keV, β3 ≈ 0 for the ground state (SC mean-field, Macro-Micro models), β3 ≈ 0.12 for 7/2[743] and 1/2[770], no deep minima, E. Ruchowska et al., PRC 73, 044326 (2006), Strutinsky method, β3 ≈ 0.35 at neutron threshold, Effects of parity nonconservation in scattering of polarized neutrons explained by octupole correlations, V.V. Flambaum, V.G. Zelevinsky, PLB 350 , 8 (1995), Clear evidence for parity-partner bands, K. Gulda et al., NPA 703, 45 (2002)

229Th structure from QPM calculations Parity partner bands: 5/2+ 5/2- 3/2+ 3/2- K. Gulda et al., Nuclear Physics A 703, 45 (2002)

Lowest states in 229Th Idea: Enchanced sensitivity of 3/2+ -> 5/2+ transition frequency to possible variations of fundamental constants V.V. Flambaum, PRL 97, 092502 Estimation: Nuclear structure calculations: controversial results for A, Nilsson model, A.C. Hayes, J.L. Friar, PLB 650, 229 (2007), (no self-consistency => no rearrangement): no amplification (A = 0) Self-consistent spherical mean field (relativistic): X.-T. He, Z.-Z. Ren, NPA 806, 117 (2008): large amplification A ~ 105.

Hellmann-Feynman Theorem I. Parametrized Hamiltonian Stationary Schrödinger equation: II. Energy density functional ε(c,x): J. Goodisman, Phys. Rev. A2, 1 (1970) Stationary condition:

A Amplification factor Defined as: Variation of an Energy at stationary points: A Amplification factor m g Defined as:

α – dependence of nucleon masses: Amplification factor α – dependence of nucleon masses: Estimated using: U.-G. Meißner et al., EPJA 31, 357 : Δmnp(EM) = -0.68 MeV

Microscopic calculations with Skyrme density functional: SIII J. Dobaczewski, J. Dudek, CPC 102, 166 (1997), J. Dobaczewski, P. Olbratowski, CPC 158, 158 (2004), J. Dobaczewski, J. Dudek, P. Olbratowski, arXiv:nucl-th/0501008. Deformed mean field + blocking for odd neutron Rearrangement effects & deformation are taken into account self-consistently no pairing pairing

Microscopic calculations with Skyrme density functional: SkM* J. Dobaczewski, J. Dudek, CPC 102, 166 (1997), J. Dobaczewski, P. Olbratowski, CPC 158, 158 (2004), J. Dobaczewski, J. Dudek, P. Olbratowski, arXiv:nucl-th/0501008. Deformed mean field + blocking for odd neutron Rearrangement effects & deformation are taken into account self-consistently no pairing pairing

Microscopic structure: expansion over Nilsson orbits Overlap integrals: <Φν (Ωπ) | Ωπ [N,Nz,Λ]> => Configuration assignment SIII + HFB: „traditional“ assignment SkM* + HFB: competing contributions & changing of nodal structure of the leading components

Energies of 229Th structure from Skyrme-HF & HFB calculations Deformed Skyrme: SkM* & SIII Spherical RMF: NL3 Data [30] G. Audi et al., NPA 729, 337 [9] B.R. Beck et al., PRL 98, 142501 Larger numbers, but less realistic 1-2 orders of magnitude effect from change of nodal structure of the leading components or/and stronger mixing

Conclusions & outlook Magnetic moments-? Data-? 1. 5/2+ and 3/2+ states in 229Th have been studied within self-consistent Skyrme + HFB model – version HFODD of J. Dobaczewski, J. Dudek et al. 2. Upper limit for the amplification factor of fine structure constant is A ≈ (6±3)x104 (SkM*), lower limit – zero (SIII). 3. Accuracy is very important because the calculated amplification is a difference of two big numbers. 4. The source of the amplification is the difference of the nodal structure of the ground state and isomer wave functions and/or comparable contributions of several Nilsson orbits to the total wave functions. 5. Similar effect is obtained for differences of the quadrupole moments: SkM*-HF SkM*-HFB SIII-HF SIII-HFB Magnetic moments-? Data-?

Thank you! Hans Feldmeier Jacek Dobaczewski Victor Flambaum GSI Helmholtzzenrum für Schwerionenforschung, Darmstadt, Germany Jacek Dobaczewski Institute of Theoretical Physics, University of Warsaw, Poland Department of Physics, University of Jyväskylä, Finland Victor Flambaum School of Physics, University of New South Wales, Sydney, Australia Journal reference: E. Litvinova, H. Feldmeier, J. Dobaczewski, V. Flambaum, Phys. Rev. C 79, 064303 (2009). 14