1. 0νββ nuclear matrix elements within QRPA and its variants W. A. Kamiński 1, A. Bobyk 1 A. Faessler 2 F. Šimkovic 2,3, P. Bene š 4 1 Dept. of Theor. Phys., Maria Curie-Skłodowska University, Lublin, Poland 2 Inst. of Theor. Phys., University of Tuebingen, Germany 3 Dept. of Nucl. Phys., Comenius University, Bratislava, Slovakia 4 IEAP, Czech Technical University, Prague, Czech Republic

2. Motivation Upper bound on the neutrino mass: Experiment gives upper bound on must come from the theory

3. QRPA drawbacks BCS state is not a QRPA ground state: do not fulfil the bosonic commutation relations The operators:

4. QRPA drawbacks (cont.) QRPA ground state has a non-vanishing quasiparticle content: The QRPA built naively on the BCS would be a pure TDA:

5. What should we learn? The description of the ground state should be made consistent with that of the excited states One should go beyond QBA and not neglect the scattering terms

6. Formalism – RQRPA The mapping: The renormalized operators and amplitudes:

7. Formalism – RQRPA (cont.) The linear equations for q.p. densities: with Solve the RQRPA iteratively, i.e. n a (out)=n a (in).

8. Formalism – SQRRPA The modified BCS tensors: Computational procedure: iterate between BCS and RQRPA untill the convergence is achieved, i.e. n a (out)=n a (in).

9. 76 Ge → 76 Se: dependence on the s.p. basis SRQRPA RQRPA QRPA number of levels no core 16 O core

10. 100 Mo → 100 Ru: dependence on the s.p. basis no core 16 O core

11. 116 Cd → 116 Sn 0.00.20.40.60.81.01.21.41.61.82.0 g pp -0.1 0.0 0.1 0.2 M 2 GT [MeV ] gph=1.0 QRPA gph=1.0 RQRPA gph=1.0 SRQRPA gph=0.8 QRPA gph=0.8 RQRPA gph=0.8 SRQRPA

12. 128 Te → 128 Xe g ph =1.0 QRPA g ph =1.0 RQRPA g ph =1.0 SRQRPA g ph =0.8 QRPA g ph =0.8 RQRPA g ph =0.8 SRQRPA

13. 130 Te → 130 Xe 0.4 0.5 M 2 GT [MeV ] g ph =1.0 QRPA g ph =1.0 RQRPA g ph =1.0 SRQRPA g ph =0.8 QRPA g ph =0.8 RQRPA g ph =0.8 SRQRPA

14. 136 Xe → 136 Ba -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 M 2 GT [MeV ] g ph =1.0 QRPA g ph =1.0 RQRPA g ph =1.0 SRQRPA g ph =0.8 QRPA g ph =0.8 RQRPA g ph =0.8 SRQRPA

15. 146 Nd → 146 Sm 0.00.20.40.60.81.01.21.4 g pp -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 M 2 GT [MeV ] g ph =1.0 QRPA g ph =1.0 RQRPA g ph =1.0 SRQRPA g ph =0.8 QRPA g ph =0.8 RQRPA g ph =0.8 SRQRPA

16. 150 Nd → 150 Sm GT [MeV ] g ph =1.0 QRPA g ph =1.0 RQRPA g ph =1.0 SRQRPA g ph =0.8 QRPA g ph =0.8 RQRPA g ph =0.8 SRQRPA

17. Summary

18. Conclusions The RQRPA and the SRQRPA are more stable with growing dimension of the single-particle model space The RQRPA reproduces the experimental data for higher values of the particle-particle force The SRQRPA behaves like QRPA, but the collapse is pushed forward towards higher g pp values

19. Conclusions (cont.) 0νββ nuclear matrix elements can be accurately reproduced within QRPA, RQRPA and SQRPA by fixing the g pp value using 2νββ experimental data For the closed and partially closed shell nuclei ( 48 Ca, 116 Sn, 136 Xe) a further improvement in the description of pairing interaction is necessary

20. References S. M. Bilenky, A. Faessler, F. Šimkovic, Phys. Rev. D 70, 033003 (2004) V. A. Rodin, A. Faessler, F. Šimkovic, P. Vogel, Phys. Rev. C 68, 044302 (2003) A. Bobyk, W. A. Kamiński, F. Šimkovic, Phys. Rev. C 63, 051301(R) (2001)

21. Thank you for attention! W. A. Kamiński, A. Bobyk A. Faessler F. Šimkovic, P. Bene š