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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, 1p1/2, 0g9/2 4levels: Ikeda Sum rule 50 % 6levels: 0f7/2, 1p3/2, 0f5/2, 1p1/2, 0g9/2, 0g7/2 9levels:0f7/2, 1p3/2, 0f5/2, 1p1/2, 0g9/2, 0g7/2, 1d5/2, 2s1/2, 1d3/2 Amand Faessler, Tuebingen

  13. 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 (0f7/2;1p3/2;0f5/2;1p1/2;0g9/2) 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 (g9/2;d5/2;s1/2;g7/2;d3/2;h11/2) 2.7 128Te 7lev QRPA 13.7 -10.3 3.4 100 128Te 13lev QRPA 16.8 -13.0 3.8 100

  14. 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

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

  16. 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

  17. 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

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