1. „The uncertainty in the calculated nuclear matrix elements for neutrinoless double beta decay will constitute the principle obstacle to answering some basic questions about neutrinos.“ Bahcall et al. Phys. Rev. D70 (2004) 033012 Theoretical Status of the Double Beta Decay Amand Faessler, Tuebingen TAUP2009, Wednesday, July first 2009

2. O νββ -Decay (forbidden in Standard Model) only for massive Majorana Neutrinos ν = ν c P P n n Left ν Phase Space 10 6 x 2 νββ TAUP2009, Wednesday, July first 2009

3. Neutrinoless Double Beta- Decay Probability TAUP2009, Wednesday, July first 2009

4. QRPA Tuebingen 2008 QRPA and RQRPA (Tuebingen) with errors from Basis Size, exp. 2-Neutrino Decay, axial Coupling Constant g A = 1.25 and 1.00 and Short Range Correlations ( UCOM + Jastrow)

5. TAUP2009, Wednesday, July first 2009 QRPA Tuebingen 2008 Blue triangles: Shell model of Strassburg and Madrid group only 4 to 5 single nucleon levels

6. Green Squares IBM2 of Barea and Iachello 2009 TAUP2009, Wednesday, July first 2009 IBM2 Barea, Iachello 2009 QRPA Tuebingen 2008 SM Courier et al.

7. RodinSalehKovalenkoFaessler Petr Vogel Gutsche Simkovic TAUP2009, Wednesday, July first 2009

8. Tuebingen  Jyväskylä

9. Shell Model basis: 1f 5/2, 2p 3/2, 2p 1/2, 1g 9/2 SM+Spin-Orbit: 1f 5/2, 2p 3/2, 2p 1/2, 1g 9/2, 1f 7/2, 1g 7/2 1f 5/2, 2p 3/2, 2p 1/2, 1g 9/2, 1f 7/2, 1g 7/2, 1d 5/2, 1d 3/2, 2s 1/2 Neutron-Neutron -> Proton-Proton relative Angular Momentum for the Pair : Neutron x Neutron  Proton x Proton TAUP2009, Wednesday, July first 2009

10. IBM Angular Momentum for the Pair : Neutron x Neutron  Proton x Proton 0+0+ 2+2+

11. Can one distiguish experimentally betweenQuasi-Particle Random Phase (QRPA) and the Shell Model (SM)? TAUP2009, Wednesday, July first 2009 QRPA GT /2 ~ SM GT QRPA Fermi /5 ~ SM Fermi http://Arxiv.org/abs/0906.1759http://Arxiv.org/abs/0906.1759 Rodin and Faessler: One can measure the Fermi contribution.

12. TAUP2009, Wednesday, July first 2009 Can one distiguish experimentally betweenQuasi-Particle Random Phase (QRPA) and the Shell Model (SM) ? Due to  T Z = 2 only the isotensor part of the „Coulomb interaction“ can contribute. Since the strong Interaction commutes with Isospin, replace „Coulomb“ V C by the total Hamiltonian H total.

13. TAUP2009, Wednesday, July first 2009 Can one distiguish experimentally between QRPA and SM ? Use Closure!

14.  0 + + DIAS 0+ TAUP2009, Wednesday, July first 2009 0+ Isobaric(i) Analog State Can one distiguish experimentally between QRPA and SM ?

15.  0 + + DIAS 0+ TAUP2009, Wednesday, July first 2009 0+ Isobaric Analog State Can one distiguish experimentally between QRPA and SM ? ( p,n); ( 3 He, 3 H) (n,p); (d,2p); ( 3 H, 3 He)

16. Overconstraining the 2  by adjusting g pp und g A to  -, EC and 2  for 116 Cd and 100 Mo (Bari+Tuebingen) -- EC  1+1+ 0+ 116 Cd 100 Mo 0+ TAUP2009, Wednesday, July first 2009 1+1+ 1+1+

17. Solid points: Overconstrained results large and small basis. Open circle QRPA 3 basis sets and g A = 1.00. Only theoretical 1  errors. TAUP2009, Wednesday, July first 2009

18. Renormalized QRPA 0  Half Lives calculated in TUE with the Bonn CD force and Jastrow correlations for quenched g A = 1.00; errors from 2  experiments for = 50 meV 76 Ge  76 Se T(1/2) [years] = (1.10+-0.13)* 10 27 82 Se  82 Kr T(1/2) [years] = (3.50+-0.42)* 10 26 100 Mo  100 Ru T(1/2) [years] = (3.33+-0.45)* 10 26 128 Te  128 Xe T(1/2) [years] = (7.35+-1.00)* 10 27 150 Nd  150 Sm T(1/2) [years] = (3.55+-0.50)* 10 25 TAUP2009, Wednesday, July first 2009 But 150 Nd + 150 Sm is deformed!

19. Kay, Schiffer et al. Phys. Rev. C79 (2009) 021301 Proton removal reactions: v 2 76 Ge(d, 3 He) 75 Ga; 76 Se(d, 3 He) Proton additon reactions: u 2 76 Ge( 3 He,d) 77 As; 76 Se( 3 He,d) f 7/2 p 3/2 p 1/2 f 5/2 g 9/2 28 40 50 76 32 Ge 44  p = 0.10 76 34 Se 42  p  = 0.16 Neutron vacancy u 2 Proton occupancy v 2 Double Beta Decay System 76 Ge  76 Se. TAUP2009, Wednesday, July first 2009 Ge – Se experiment Se – Ge experiment FnFn FpFp

20. TAUP2009, Wednesday, July first 2009 Adjutment of the Neutron Levels to reproduce the Occupation of Schiffer et al. from Simkovic, Faessler and Vogel : Phys. Rev. C79(2009) 015502 and also Suhonen and Civitarese: Phys. Lett. B668 (2008) 277 50 40

21. TAUP2009, Wednesday, July first 2009 Omega  1/2 3/2 5/2 7/2 9/2 g 9/2 p 1/2 f 5/2 1/2 3/2 5/2 1/2 3/2 p 3/2 Deformation  2 Single neutron energies for N = 42  j N = 28

22. Deformation affects the occupation Probabilities of neutrons mainly. Parity  < 0; deformed mixed: p 1/2, p 3/2,f 5/2  > 0: g 9/2 exp  2 = 0.1  2 = 0.16  2 = 0.23  2 = 0.26 TAUP2009, Wednesday, July first 2009

23. Summary: Neutrino Mass from   Exp. Klapdor et al. Mod. Phys. Lett. A21,1547(2006) ; 76 Ge  T(1/2; 0  ) = (2.23 +0.44 -0.31) x 10 25 years; 6  Theory with R-QRPA and g A = 1.25 (Tuebingen)  = 0.22 [eV] (exp+-0.02;theor+-0.01) Bonn CD, Consistent Brückner Correlations  = 0.24 [eV] (exp+-0.02; theor+-0.01) Argonne, Consistent Brückner Correlations Shell Model 4 to 5 levels (Strassburg + Madrid):  ~ 0.45 [eV] Jastrow Correlations THE END TAUP2009, Wednesday, July first 2009