2 decay study of 150 Nd : SSD hypothesis and bosonic neutrinos

1. 2 decay study of150Nd :SSD hypothesis and bosonic neutrinos Rastislav Dvornický Comenius University

2. Double beta decay 2Maria Goepert Mayer – 1935 Observedon isotopes : 48Ca, 76Ge, 82Se,100Mo, 116Cd, 128Te, 150Nd

3. Double beta decay where and matrix elements are defined as

4. Single state dominance hypothesis aproximation of energetic denominators

5. SSD  decay electron capture

6. The operators O(J) are defined as follows Fermi and Gamow Teller transitions forbiden transitions  decay Supressed by factor coming from the p1/2 wave of the emited e-

7. EC The case is experimentally not observed yet Let’s made assumption NME (  )  NME ( EC ) for 150Pm T1/2EC  6.1016 years SSD for 100 Mo-1+ state of theintermediate nucleus HSD for 150Nd ? - 1- state forthe intermediatenucleus ( p1/2wave of the emited e- ) ====================================== Nucleus Ei-Ef [MeV] T1/2SSD [y] T1/2exp[y] ––––––––––––––––––––––––––––––––––––––––––- 100Mo 4.057 6.8 1018 7.1 1018 150Nd 4.389 4.0 1024 9.7 1018 ======================================

8. Single electrons energydistributionfor 0+ 0+, 2+ 2 of 100Mo and 150Nd here the factor DNKL is defined as and the energetic denominators are

9. Single electrons energydistributionfor 0+ 0+, 2+ 2 of 100Mo and 150Nd These normalized energy distribution is free of NME, gA and G

10. Single electrons energydistributionfor 0+ 0+, 2+ 2 of 100Mo and 150Nd By precise measurements of the electron energy distribution we can decide whether the SSD and HSD is realised or not

11. Bosonic neutrino Neutrino was suggested iny. 1930 by Pauli toexplainthe continuity ofspectrum as a half spin particle obeying Fermi-Dirac statistics Barabash, Dolgov, Dvornicky, Šimkovic, Smirnov : arXiv: 0704.2944v1 [hep-ph] 23 Apr 2007 - to be published in Nucl. Phys. B

12. Can we imagine that half spin praticles can obey Bose–Einstein statistics ? Bosonic n introduced: Ignatiev, Kuzmin, Yad. Fiz 46 (1987) 786 Bosonic n in 2nbb-decay: Dolgov, Smirnov, PLB 621 (2005) 1 instead of

13. 2 2 is a unique process. Two neutrinos in the final state

14. SSD 100Mo Ratio is different for the bosonic case as for the fermionic one

15. 150Nd We have also possibility to look at the energy distribution of the emited electrons Energy distribution is free of log ft value unlike the half live

16. HSD These NME give contribution to the decay rate Therefore such combinations of energetic denominators occur For transition both K+L and K-L denominators enter decay rate For to the excited state only K – L combination contributes

17. 0+ 0+ Here E denotes the single electron energy and E the sum of the kinetic energy of the emited electrons

18. 0+ 2+ 2 decay half-lives ( 0+ 0+ , 0+ 2+ ) : HSD – NME necessary SSD – log ft values needed Normalized differential characteristics : free of NME and log ft - the single electron energy distribution - The distribution of the total energy of two electrons

19. Mixed statistics Definition of mixed state with commutation relations Amplitude for 2 Decay rate Partly bosonic neutrino requires knowing NME or log ft values for HSD or SSD ( calculations are in progres )

20. Conclusions • The estimation of the 2 half-live of 150Nd shows that the SSD is not realized unlike the case of 100Mo. From the differential characteristics one should decide whether HSD is realized in this nuclear system or not. • The analysis of 2 of 100Mo to the ground state and excited state of the final nucleus excludes the possibility of pure bosonic neutrino • Measurements of the differential characteristics in 2 can give us interesting information not only about the nuclear systems but also about the properties of neutrino