2 decay study of 150 nd : ssd hypothesis and bosonic neutrinos

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