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2 decay study of 150 Nd : SSD hypothesis and bosonic neutrinos. Rastislav Dvornický Comenius U niversity. D ouble beta decay 2 Maria Goepert Mayer – 1935 Observed on i s otop es : 48 Ca, 76 Ge, 82 Se, 100 Mo, 116 Cd, 128 Te, 150 Nd. D ouble beta decay - PowerPoint PPT Presentation
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2 decay study of 150Nd :SSD hypothesis and bosonic neutrinos
Rastislav Dvornický
Comenius University
Double beta decay
2 Maria Goepert Mayer – 1935
Observed on isotopes : 48Ca, 76Ge, 82Se,100Mo, 116Cd, 128Te, 150Nd
eeAZAZ ~22),(),2(
Double beta decay
where
and matrix elements are defined as
Single state dominance hypothesis
aproximation of energetic denominators
SSD
decay
electron capture
)0()1()0( 150150150 SmPmNd
)0()1()0( 100100100 RuTcMo
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-
2
2
Z
EC The case is experimentally not observed yet
Let’s made assumption NME ( ) NME ( EC ) for 150Pm T1/2
EC 6.1016 years
SSD for 100 Mo - 1+ state of the intermediate nucleusHSD for 150Nd ? - 1- state for the intermediate nucleus
( p1/2 wave of the emited e- )
)0()1( 150150 NdPm
======================================Nucleus Ei-Ef [MeV] T1/2
SSD [y] T1/2exp[y]
––––––––––––––––––––––––––––––––––––––––––-100Mo 4.057 6.8 1018 7.1 1018
150Nd 4.389 4.0 1024 9.7 1018
======================================
Single electrons energy distribution for 0+ 0+, 2+ 2 of 100Mo and 150Nd
here the factor DNKL is defined as
and the energetic denominators are
Single electrons energy distribution for 0+ 0+, 2+ 2 of 100Mo and 150Nd
These normalized energy distribution is free of NME, gA and G
Single electrons energy distribution for 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
Bosonic neutrino
Neutrino was suggested in y. 1930 by Pauli to explain the 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
eZAZA )1,(),(
Can we imagine that half spin praticles can obey Bose–Einstein statistics ?
Bosonic introduced: Ignatiev, Kuzmin, Yad. Fiz 46 (1987) 786
Bosonic in 2-decay: Dolgov, Smirnov, PLB 621 (2005) 1
instead of 0)}(),({ 11 kdkd
0)](),([ 11 kdkd
2
2 is a unique process. Two neutrinos in the final state
eeAZAZ ~22),(),2(
SSD100Mo
Ratio is different for the bosonic case as for the fermionic one
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
HSDThese 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
00
20
Here E denotes the single electron energy and E the sum of the kinetic energy of the emited electrons
0+ 0+
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
0+ 2+
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 )
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