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Theoretical Status of the Double Beta Decay

This article discusses the uncertainty in the calculated nuclear matrix elements for neutrinoless double beta decay and the obstacles it poses in understanding neutrinos. It explores various theoretical models and their predictions for the decay probability.

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Theoretical Status of the Double Beta Decay

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  1. Theoretical Status of the Double Beta Decay „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 Amand Faessler, Tuebingen TAUP2009, Wednesday, July first 2009

  2. Oνββ-Decay (forbidden in Standard Model) only formassive MajoranaNeutrinos ν = νc P P Left ν Phase Space 106x2νββ Left n n TAUP2009, Wednesday, July first 2009

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

  4. QRPA and RQRPA (Tuebingen) with errors from Basis Size, exp. 2-Neutrino Decay, axial Coupling Constant gA = 1.25 and 1.00 and Short Range Correlations ( UCOM + Jastrow) QRPA Tuebingen 2008 TAUP2009, Wednesday, July first 2009

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

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

  7. Gutsche Rodin Saleh Kovalenko Faessler Simkovic Petr Vogel TAUP2009, Wednesday, July first 2009

  8. Tuebingen  Jyväskylä TAUP2009, Wednesday, July first 2009

  9. Angular Momentum for the Pair : Neutron x Neutron  Proton x Proton Shell Model basis: 1f5/2, 2p3/2, 2p1/2, 1g9/2 SM+Spin-Orbit: 1f5/2, 2p3/2, 2p1/2, 1g9/2, 1f7/2, 1g7/2 1f5/2, 2p3/2, 2p1/2, 1g9/2, 1f7/2, 1g7/2, 1d5/2, 1d3/2, 2s1/2 Neutron-Neutron -> Proton-Proton relative TAUP2009, Wednesday, July first 2009

  10. IBM Angular Momentum for the Pair : Neutron x Neutron  Proton x Proton 0+ 2+ TAUP2009, Wednesday, July first 2009

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

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

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

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

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

  16. Overconstraining the 2nbb by adjusting gpp und gA to b-, EC and 2nbb for116Cd and 100Mo (Bari+Tuebingen) 1+ 1+ EC 1+ b- 0+ 2nbb 0+ 116Cd 100Mo TAUP2009, Wednesday, July first 2009

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

  18. Renormalized QRPA 0nbb Half Lives calculated in TUE with the Bonn CD force and Jastrow correlations for quenched gA = 1.00; errors from 2nbb experiments for <mn> = 50 meV 76Ge  76Se T(1/2) [years] = (1.10+-0.13)* 1027 82Se  82Kr T(1/2) [years] = (3.50+-0.42)* 1026 100Mo  100Ru T(1/2) [years] = (3.33+-0.45)* 1026 128Te  128Xe T(1/2) [years] = (7.35+-1.00)* 1027 150Nd  150Sm T(1/2) [years] = (3.55+-0.50)* 1025 But 150Nd + 150Sm is deformed! TAUP2009, Wednesday, July first 2009

  19. Double Beta Decay System 76Ge 76Se. Kay, Schiffer et al. Phys. Rev. C79 (2009) 021301 Proton occupancy v2 Proton removal reactions: v2 76Ge(d,3He)75Ga; 76Se(d,3He) Se – Ge experiment Proton additon reactions: u2 76Ge(3He,d)77As; 76Se(3He,d) Fn 50 Ge – Se experiment g9/2 7632Ge44 bp = 0.10 40 p1/2 Fp f5/2 7634Se42 bp= 0.16 p3/2 28 Neutron vacancy u2 f7/2 TAUP2009, Wednesday, July first 2009

  20. 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 TAUP2009, Wednesday, July first 2009

  21. Omega W Single neutron energies for N = 42 9/2 g 9/2 7/2 5/2 3/2 1/2 p 1/2 5/2 1/2 f 5/2 3/2 3/2 p3/2 1/2 j 1/2 N = 28 W Deformation b2 TAUP2009, Wednesday, July first 2009

  22. Parity p < 0; deformed mixed: p1/2, p3/2 ,f5/2 Deformation affects the occupation Probabilities of neutrons mainly. p > 0: g9/2 b2 = 0.23 b2 = 0.26 b2 = 0.16 b2 = 0.1 TAUP2009, Wednesday, July first 2009 exp exp

  23. Summary: Neutrino Mass from 0nbb • Exp. Klapdor et al. Mod. Phys. Lett. A21,1547(2006) ; 76Ge • T(1/2; 0nbb) = (2.23 +0.44 -0.31) x 1025 years; 6s Theory with R-QRPA and gA = 1.25 (Tuebingen) • <m(n)> = 0.22 [eV] (exp+-0.02;theor+-0.01) Bonn CD, Consistent Brückner Correlations • <m(n)> = 0.24 [eV] (exp+-0.02; theor+-0.01) Argonne, Consistent Brückner Correlations THE END • Shell Model 4 to 5 levels (Strassburg + Madrid): • <m(n)> ~ 0.45 [eV] Jastrow Correlations TAUP2009, Wednesday, July first 2009

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