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Advances and Challenges in Double Beta Decay Matrix Elements in Deformed Nuclei

This study explores the theoretical framework and calculations related to double beta decay (2n2b) nuclear matrix elements within the Tübingen-Madrid collaboration. It highlights the significance of nuclear deformation in the decay process, which significantly affects the transition probabilities. The paper discusses improvements in overlap between RPA intermediate virtual states and introduces realistic residual interactions. The findings indicate a good agreement with experimental data while providing insights into future research directions related to neutrino properties and decay processes.

nigel-austin
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Advances and Challenges in Double Beta Decay 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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