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Double beta decay nuclear matrix elements in deformed nuclei

Double beta decay nuclear matrix elements in deformed nuclei. Past, present and future calculations within Tübingen-Madrid collaboration. O. Moreno , R. Álvarez-Rodríguez, P. Sarriguren, E. Moya de Guerra. F. Š imkovic, A. Faessler H. Müther. Summary. Introduction Theoretical formalism

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Double beta decay nuclear matrix elements in deformed nuclei

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  1. Double beta decay nuclear matrix elements in deformed nuclei Past, present and future calculations within Tübingen-Madrid collaboration O. Moreno, R. Álvarez-Rodríguez, P. Sarriguren, E. Moya de Guerra F. Šimkovic, A. Faessler H. Müther

  2. Summary Introduction Theoretical formalism Results Current work Conclusions & outlook

  3. Introduction AY AX AZ 2n 2b decay Two succesive b decays through intermediate virtual states. Second order process in weak interaction  energy denominator. One of the most rare events in nature, T1/2~ 1019 – 1021 s. Observed in 48Ca 76Ge 82Se 96Zr 100Mo 116Cd 128Te 130Te 150Nd. Strong dependence on nuclear structure, in particular nuclear deformation.

  4. Introduction AY AX • Virtual n emitted in the first b decay is absorbed in the second b decay. •  For virtual neutrinos, (Majorana particles) •  Also a very rare event, observation not yet confirmed. • Also strong dependence on nuclear structure  comparison with 2n2b nuclear matrix elements needed. AZ 0n 2b decay

  5. Theoretical formalism  def. HF (Skyrme)  BCS (DexpG)  pnQRPAs.t (cph+kpp) Mean field + pairing + proton-neutron correlations

  6. Theoretical formalism Nuclear wavefunction: adiabatic + harmonic collective motion Dynamics: Classical variational principle

  7. Theoretical formalism (Skyrme interactions) (Pairing BCS) + HF & RPA equations:

  8. Theoretical formalism  136Cs 136Xe 136Ba

  9. Results Parent Daughter bexp Qexp Qexp HF (Sk3) + BCS Alvarez-Rodriguez et al. PRC 70 (2004) 064309

  10. Results Alvarez-Rodriguez et al. PRC 70 (2004) 064309

  11. Results Alvarez-Rodriguez et al. PRC 70 (2004) 064309

  12. Results Alvarez-Rodriguez et al. PRC 70 (2004) 064309 Alvarez-Rodriguez et al. PRC 70 (2004) 064309

  13. Current calculations • Improvement of overlap between RPA intermediate virtual states. • Introduction of a realistic residual interaction giving rise to spin-isospin transitions (to be treated within RPA). • Closure approximation.

  14. Current calculations I  136Cs 136Xe 136Ba • Improvement of overlap between RPA intermediate virtual states.

  15. NEW RPA phonon operators on initial (i) and final (f) nuclei  where • Improvement of overlap between RPA intermediate virtual states.

  16. Improvement of overlap between RPA intermediate virtual states. Unitarity test F. Šimkovic, DBD06-ILIAS/N6 Collaboration meeting Valencia 2006

  17. Current calculations II Two-body matrix element of a realistic interaction V (CD Bonn, Vlow k ,…): Introducing JT coupling: Gamow-Teller transitions 2) Introduction of a realistic residual interaction giving rise to spin-isospin transitions

  18. 2) Introduction of a realistic residual interaction giving rise to spin-isospin transitions Change of basis: from original spherical harmonic oscillator w.f. to deformed HF w.f.: Ready to be introduced in the RPA equations:

  19. Current calculations III  136Cs 136Xe 136Ba 3) Closure approximation

  20. 3) Closure approximation

  21. BCS overlap for parent and daughter nuclei with different deformation: with 3) Closure approximation

  22. M = 2v GT closure E 3) Closure approximation Comparison 1+RPA – Closure to get energy denominator:

  23. Conclusions • Theoretical 2n2b decay nuclear matrix elements are essential information to study 0n2b decays, which give new information on n character. • Our calculations through deformed RPA intermediate virtual states show: - a reduction effect due to deformation differences between parent and daughter nuclei. - a good agreement with single and double beta experimental data.

  24. Conclusions • Current work includes: - Improvement of RPA overlaps. - Use of realistic spin-isospin residual interactions. - Closure approximation. • Get more accurate results on 2n2b and go to 0n2b.

  25. Conclusions 3 m Detector of NEMO3 0n2b experiment The best laboratory to measure neutrino properties is not necessarily very big! 10-14 m Atomic nucleus

  26. Double beta decay nuclear matrix elements in deformed nuclei Past, present and future calculations within Tübingen-Madrid collaboration O. Moreno, R. Álvarez-Rodríguez, P. Sarriguren, E. Moya de Guerra F. Šimkovic, A. Faessler H. Müther

  27. APPENDIX

  28. Deformed Hartree-Fock with Skyrme forces • Single particle states (axially symmetric even-even nuclei) • Expansion into eigenfunctions of deformed h.o. fa (R,s) • with • Pairing correlations in BCS approximation • and • Residual interactions consistent with the HF mean field • cph, kpp A simplified scheme pnQRPA phonon operator for GT excitations QRPA equationsg (wK, XwKpn , YwKpn ) Transition amplitudes in the intrinsic frame Average over nuclear volume

  29. Xe isotopes in 2b processes

  30. Results single b Xe isotopes Gamow-Teller strength distributions DJ = 0, 1 (no 0+  0+) DTz = 1 DT = 0,1 HF + BCS(G) + QRPA GT +   GT –

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