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

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

3. Introduction  Two succesive  decays through intermediate virtual states.  Second order process in weak interaction  energy denominator.  One of the most rare events in nature, T 1/2 ~ 10 19 – 10 21 s.  Observed in 48 Ca 76 Ge 82 Se 96 Zr 100 Mo 116 Cd 128 Te 130 Te 150 Nd.  Strong dependence on nuclear structure, in particular nuclear deformation. AXAX AYAY AZAZ 2 2  decay

4. Introduction 0 2  decay  Virtual emitted in the first  decay is absorbed in the second  decay.  For virtual neutrinos, (Majorana particles)  Also a very rare event, observation not yet confirmed.  Also s trong dependence on nuclear structure  comparison with 2 2  nuclear matrix elements needed. AXAX AYAY AZAZ

5. Mean field + pairing + proton-neutron correlations Theoretical formalism  def. HF (Skyrme)  BCS (  exp  G)  pnQRPA .  (  ph +  pp )

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

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

8. Theoretical formalism 136 Xe 136 Cs 136 Ba 

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

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

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

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

13. 1)Improvement of overlap between RPA intermediate virtual states. 2)Introduction of a realistic residual interaction giving rise to spin-isospin transitions (to be treated within RPA). 3)Closure approximation. Current calculations

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

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

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

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

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

20. 3) Closure approximation

21. BCS overlap for parent and daughter nuclei with different deformation: with

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

23. Theoretical 2 2  decay nuclear matrix elements are essential information to study 0 2  decays, which give new information on 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. Conclusions

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

25. Atomic nucleus Detector of NEMO3 0 2  experiment 3 m 10 -14 m The best laboratory to measure neutrino properties is not necessarily very big!

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

27. APPENDIX

28. Deformed Hartree-Fock with Skyrme forces Single particle states (axially symmetric even-even nuclei)  Expansion into eigenfunctions of deformed h.o.   (R,  ) with  Pairing correlations in BCS approximation and Residual interactions consistent with the HF mean field  ph,  pp A simplified scheme pnQRPA phonon operator for GT excitations QRPA equations     X  K , Y  K   Transition amplitudes in the intrinsic frame Average over nuclear volume

29. Xe isotopes in 2  processes

30. GT +   GT – Gamow-Teller strength distributions  J = 0, 1 (no 0+  0+)  T z = 1  T = 0,1 HF + BCS(G) + QRPA Results single  Xe isotopes