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Nuclear Structure , the Double Beta Decay and the Neutrino Mass

Nuclear Structure , the Double Beta Decay and the Neutrino Mass. Occupation probabilities for 76 Ge  76 Se. F. Simkovic, A. Faessler, P. Vogel: Phys.Rev C 79 (2009) 015502; O. Moreno, E. Moya de Guerra, P. Sarriguren, A. Faessler: Phys. Rev. C81(2010) 041303

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Nuclear Structure , the Double Beta Decay and the Neutrino Mass

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  1. NuclearStructure, the Double Beta Decayandthe Neutrino Mass • Occupation probabilities for 76Ge  76Se. • F. Simkovic, A. Faessler, P. Vogel: Phys.Rev C 79 (2009) 015502; O. Moreno, E. Moya de Guerra, P. Sarriguren, A. Faessler: Phys. Rev. C81(2010) 041303 • 2. Which neutron pairs contribute to the Double Beta Decay ? A. Escuderos, A. Faessler, V. Rodin, F. Simkovic arXiv: 1001.3519 (2010) Amand Faessler University ofTuebingen

  2. Oνββ-Decay (forbidden in Standard Model) e2 P e1 P Left ν Phase Space 106x2νββ Left n n n = nc Majorana Neutrino Neutrino must have a Mass Amand Faessler, Tuebingen

  3. Neutrinoless Double Beta- Decay Probability Amand Faessler, Tuebingen

  4. 1. From which Neutrons come the two Protons? J. Schiffer et al. Phys. Rev. Lett. 100 (2008)112501Double Beta Decay: 7632Ge44 7634Se42 7632Ge44(d,p) or (a,3He) 7634Se42(p,d) or (3He,a) Saxon-Woods + BCS 50 g9/2 Fn 40 p1/2 Saxon-Woods (Bertsch)+ BCS f5/2 Fp p3/2 28 f7/2 Neutron Holes below 50 Amand Faessler, Tuebingen

  5. Selfconsistent Hartree-Fock-Bogoliubov with Skyrme3 (Sk3) Moreno, Moya de Guerra, Sarriguren and Faessler Phys. Rev. C81(2010) 041303 • Neutron Two Body Spin-Orbit Force istosmall : V. O. Nesterenko , J. Kvasil, P. Vesely, W. Kleinig, P. G. Reinhard, V. Yu. Ponomarev: Spin-flip M1 giantresonacesas a challengefortheSkyrmeforces: J. Phys. G37(2010)064034 • Skyrme3n: W0 = 120  200 [MeV fm5] NeutronSk3 Sk3n 1g7/2 1g 1g9/2 Amand Faessler, Tuebingen

  6. Protons and Neutrons above the 28 Shell 7632Ge44 7634Se42 Amand Faessler, Tuebingen

  7. 2nbb and Running Sum of Double Gamow-Teller Distributions for 76Ge 76Se From experimental Charge Exchange Reactions (Madey et al (p,n) and Frekers et al. (d,2He)) 1+ (p,n) (d,2He) 76As 0+ 76Ge 0+ 76Se Amand Faessler, Tuebingen

  8. 0.0 Amand Faessler, Tuebingen

  9. New points in this work:  • The neutron occupation probabilities (Schiffer et al.) are reproduced by Sk3n. • Sk3nreproduces 2nbb. Old Sk3 by a factor 1/8 to small.   • Sk3n  running sum = Gamow-Teller strength distribution (R. Madey et al. and E. W. Grewe et al. ).  • Root mean square radii of 76Ge and 76Se with Sk3n:76Ge Sk3n: 4.09 (SK3: 4.12)theor 4.08 fm exp ;76Se Sk3n: 4.14 (Sk3: 4.17)theor 4.14 fmexp; • The total binding energy for 76Ge with Sk3n: Theor.: 662.0 MeVtheor Exp.: 661.6 MeVexp.  Amand Faessler, Tuebingen

  10. 2. Which Angular Momentum Jp Neutron Pairs contribute to the Neutrinoless Double Beta decay? • Quasi-Particle Random Phase Approach (QRPA; Tübingen). • Shell Model (Poves et al. : Nucl. Phys. A818 (2009) 139). • Angular Momentum Projected Hartee-Fock-Bogoliubov (Tübingen; P. K. Rath et al.). • Interacting Boson Model (Barea and Iachello). Amand Faessler, Tuebingen

  11. QRPA all the Ring digrams: • Ground State: 0, 4, 8, 12 , … quasi- particles (seniority) b) The Shell Model Ground state: 0, 4, 6, 8, …. Problem for SM: Size of the Single Particle Basis. Amand Faessler, Tuebingen

  12. Basis Size Effect for 82Se on the Neutrinoless Double Beta Decay. 4levels (Shell Model): 1p3/2, 0f5/2, 1p3/2, 0g9/2 4levels: Ikeda Sum rule 50 % 6levels: 0f7/2, 1p3/2, 0f5/2, 1p3/2, 0g9/2, 0g7/2 9levels:0f7/2, 1p3/2, 0f5/2, 1p3/2, 0g9/2, 0g7/2, 1d5/2, 2s1/2, 1d3/2 Amand Faessler, Tuebingen

  13. Contribution of Higher Angular Momentum Pairs in Projected HFB. HFB 0bbn Only even Angular Momentum Pairs with Positive Parity can contribute. IBM: = 0+ and 2+ Pairs Amand Faessler, Tuebingen

  14. QRPA (TUE), Shell Model (Madrid-Strassburg), IBM2, PHFB Amand Faessler, Tuebingen

  15. Neutrino Mass from 0nbb • Experiment Klapdor et al. 76Ge • Mod. Phys. Lett. A21,1547(2006) ; • T(1/2; 0nbb) = (2.23 +0.44 -0.31) x 1025 years; 6s Matrix Elements: QRPA Tuebingen • <m(n)> = 0.24 [eV] (exp+-0.02; theor+-0.01) [eV] Amand Faessler, Tuebingen

  16. Summary • Increased neutron two-body Spin-Orbit Force Skyrme3 plus Deformation reproduces Schiffer occupation probabilities, 2nbb, the running sum of 2nbb, root mean square radii and total binding energies. • Different approaches give different contributions for the different angular momentum neutron pairs (QRPA ~ Shell model). THE END Amand Faessler, Tuebingen

  17. Ikeda Sumrule • Single nucleonbasis (SM): p3/2, f5/2, p1/2, g9/2; Fit to 2nbb gpp = 2.3; Only 50% 0f Ikeda sumrule; Nocollective GTR; Main M1-strength: 7 MeVtolow; • f7/2, p3/2, f5/2, p1/2, g9/2, g7/2; fit 2nbb  gpp = 0.9; 100% of Ikeda sumrule; GTR correct; • f7/2  500 MeV, p3/2, f5/2, p1/2, g9/2, g7/2  500MeV Fit 2nbb 2.3; Sumto 600 MeV: 100% Ikeda SR; Sumto 10 MeV: 50% Ikeda SR; Nocollective GTR; Low energiesasforfourlevels. Amand Faessler, Tuebingen

  18. Different Seniority Contributions s for 82Se and 128Te in QRPA and the Shell Model M0n   s=0     s= 4, (6), 8,… total ISR% 82Se 4lev QRPA  6.7         -5.6           1.1 50 82Se 4lev SM 7.8 -5.8 2.0 82Se 5lev SM 2.5 82Se 6lev   QRPA 10.7          -6.6            4.1 100 82Se 9lev   QRPA 11.9           -7.6            4.3 100 128Te 5lev QRPA 9.7 -8.3 1.4 60 128Te 5lev SM 10.6 -8.4 2.2 128Te 6lev SM 2.7 128Te 7lev QRPA 13.7 -10.3 3.4 100 128Te 13lev QRPA 16.8 -13.0 3.8 100 Amand Faessler, Tuebingen

  19. Additive Contributions of 0, 4, 6, … Quasi-Particle States in the SM (Poves et al.). 128Te Not in QRPA 82Se Increasing Admixtures in the Ground State Amand Faessler, Tuebingen

  20. Contributions to the neutrinoless matrix elements for different nuclei, basis sets and seniorities and the exhaustion of the Ikeda Sum Rule.

  21. Amand Faessler, Tuebingen

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