Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania Institut für Theoretische Physik, Universität Tübingen, Germany

Characteristics of N~Z nuclei in the region : shape coexistence and mixing competition between T=0 and T=1 pairing correlations, isospin mixing rapid structural changes with particle number, angular momentum and excitation energy Isospin symmetry breaking effects in the A~70 mass region on - Superallowed Fermi beta decay - Mirror Energy Differences Self-consistent description of proton-rich A~70 nuclei based on: - beyond mean field variational VAMPIR approaches - realistic effective interactions in large model spaces

Complex EXCITED VAMPIR approach the model space is defined by a finite dimensional set of spherical single particle states the model space is defined by a finite dimensional set of spherical single particle states the effective many-body Hamiltonian is represented as a sum of one- and two-body terms the effective many-body Hamiltonian is represented as a sum of one- and two-body terms the basic building blocks are Hartree-Fock-Bogoliubov (HFB) vacua the basic building blocks are Hartree-Fock-Bogoliubov (HFB) vacua the HFB transformations are essentially complex and allow for proton-neutron, parity the HFB transformations are essentially complex and allow for proton-neutron, parity and angular momentum mixing being restricted by time-reversal and axial symmetry and angular momentum mixing being restricted by time-reversal and axial symmetry the broken symmetries (s=N, Z, I, p) are restored by projection before variation the broken symmetries (s=N, Z, I, p) are restored by projection before variation

Beyond mean field variational procedure complex VAMPIR complex EXCITED VAMPIR

A ~ 70 mass region renormalized G-matrix (OBEP, Bonn A/Bonn CD) short range Gaussians in pp, np, nn channels monopole shifts: model space for both protons and neutrons: 1p 1/2 1p 3/2 0f 5/2 0f 7/2 1d 5/2 0g 9/2 40 Ca - core (charge-symmetric basis + Coulomb contributions to the π-spe from the core)

Superallowed Fermi β decay between 0 + T=1 analog states δc – isospin-symmetry-breaking correction test of the CVC hypothesis test of the unitarity of CKM matrix

Isospin-symmetry-breaking contributions:  electromagnetic interaction Coulomb contribution to the single particle energies resulting from the Ca core Coulomb two-body matrix elements  charge-dependent strong interaction Bonn CD potential Charge-symmetric effective Hamiltonian: same single particle energies for  and   Bonn A potential Isospin-symmetry-breaking effective Hamiltonians:  Bonn A + Coulomb  Bonn CD + Coulomb Isospin operator     a    b       single particle state of the model space ) M F = Strategy:

 Petrovici et al. Nucl. Phys. A747 (2005) 44

   b     r         ms GANIL, J. Garces Narro et al, PRC63 (2001)

A. Petrovici et al, Phys. Rev. C78 (2008)

A. M. Hurst et al, Phys. Rev. Lett.98 (2007) ( 70 Se: No evidence for oblate shapes) J. Ljungvall et al, Phys. Rev. Lett. 100 (2008) ( 70 Se: Evidence for oblate shapes) G. de Angelis et al, Eur. Phys. J. A12 (2001) 51 ( 70 Br) Complex Excited Vampir predictions: oblate-prolate mixing specific for each nucleus (varying with increasing spin). Mirror Energy Differences A= 70, 82, 86

Strong oblate-prolate mixing up to spin 6 + : oblate components dominate the yrast states of 70 Se, but the yrare states of 70 Br

Precise quadrupole moments for low spin states could clarify the open problem.

     High spin states obtained within the Excited Vampir approach (Bonn A + Coulomb)

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       Analog states obtained within the complex Excited Vampir approach

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A. Petrovici et al, Phys. Rev. C78 (2008)

A. Petrovici, J. Phys.G: Nucl. Part. Phys 37 (2010)

Summary and outlook strategy for calculating the isospin-symmetry-breaking effects on the superallowed Fermi β decay based on a self-consistent description of the analog and non-analog branches (experimental branching ratios are needed) in progress: systematic derivation of improved effective interaction in larger model spaces trends in mirror energy differences correlated with shape mixing in the structure of the analog states ( precise quadrupole moment measurements are required) complex Excited Vampir variational approach to coexistence phenomena

In collaboration with: K. W. Schmid, Amand Faessler Tuebingen University, Germany O. Andrei National Institute for Physics and Nuclear Engineering, Bucharest, Romania