1. Search for the Cosmic Neutrino Background and the Nuclear Beta Decay.
Amand Faessler
University of Tuebingen
Germany
Publication: Amand Faessler, Rastislav Hodak,
Sergey Kovalenko, Fedor Simkovic:
arXiv: [nucl-th] 20. April 2013.

2. Cosmic Microwave Background Radiation
(Photons in the Maximum 2 mm)
Decoupling of the photons from matter about
years after the Big Bang, when the electrons are captured by the protons and He4 nuclei and the universe gets neutral. Photons move freely.
Today: ~550 Photons /cm3 (~340 Neutrinos/cm3)

3. Planck Satellite Temperature Fluctuations Comic Microwave Background (Release March 21. 2013)
e(f) = (8ph/c3) f3df/[exp(hf/kBT)-1][Energy/Volume]

4. Neutrino Decoupling and Cosmic Neutrino Background
For massless-massive Neutrinos:

6. Estimate of Neutrino Decoupling
Universe Expansion rate: H=(da/dt)/a;
a ~ 1/T; (today, Planck)  H = 67km/(sec*Mpc)
~ n Interaction rate: G= ne-e+<svrelative>

7. Neutrino Decoupling G/H = ( kB T/ 1MeV)3 ~ 1
T(Neutrinos)decoupl ~ 1MeV ~ 1010 Kelvin;
today: Tn = 1.95 K
Time after Big Bang: 1 Second

9. (Energy=Mass)-Density of the Universe
Radiation dominated: r ~ 1/a4 ~ 𝑇4=Stefan-Boltzmann
log r
Matter dominated: r ~ 1/a3 ~ T3
Dark Energy
a(t)~1/T
1/Temp
1 MeV
1sec
n dec.
1 eV
3x104y
3000 K y
g dec.
8x109 y
g K
n 1.95 K
today

10. Mass of the Electron Neutrino? Tritium decay (Mainz + Troisk)
With:
Hamburg, March

11. Measurement of the upper Limit of the Neutrino Mass in Mainz: mn < 2.2 eV 95% C.L.
Kurie-Plot
Eur. Phys. J.
C40 (2005) 447
mn2 <0
mn 2>0
Electron Energy
Q = keV

12. Search for Cosmic Neutrino Background CnB by Beta decay: Tritium
Kurie-Plot of Beta and induced Beta Decay: n(CB) + 3H(1/2+)  3He (1/2+) + e-
Infinite good resolution
Q = keV
Resolution Mainz: 4 eV
 mn < 2.3 eV
Emitted electron
Resolution KATRIN: eV
 mn < 0.2 eV 90% C. L.
Electron Energy
Fit parameters:
mn2 and Q value meV
2xNeutrino Masses
Additional fit: only intensity of CnB

13. Solution of the Nuclear Structure Problem:
Pairing
Quasi-Boson Approximation

14. Neutrino Capture: n(relic) + 3H 3He + e-
20 mg(eff) of Tritium  2x1018 T2-Molecules: Nncapture(KATRIN) = 1.7x10-6 nn/<nn> [year-1]
Every years a count!! for <nn> = 56 cm-3

15. Additional fit: only intensity of CnB
Two Problems
Number of Events with average Neutrino Density of nne = 56 [ Electron-Neutrinos/cm-3]
Katrin: 1 Count in Years
Gravitational Clustering of Neutrinos!!!???
2. Energy Resolution (KATRIN) DE ~ 0.93 eV
Kurie-Plot
Emitted electron
Resolution KATRIN: eV
 mn < 0.2 eV 90% C.L.
Electron Energy
Fit parameters:
mn2 and Q value meV
2xNeutrino Masses
Additional fit: only intensity of CnB

16. Gravitational Clustering of Neutrinos
R.Lazauskas,P. Vogel and C.Volpe, J. Phys.g. 35 (2008) ;
Light neutrinos: Gravitate only on 50 Mpc (Galaxy Cluster) scale: nn/<nn> ~ nb/<nb> ~ 103 – 104; <nb>= cm-3
A. Ringwald and Y. Wong: Vlasov trajectory simulations. Clustering on Galactic Scale possible (30 kpc to 1 Mpc) nn/<nn> = nb/<nb> ~ 106 ; (R = 30 kpc)
Nncapture(KATRIN) = 1.7x10-6 nn/<nn> (year-1)= 1.7 [counts per year]
Effective Tritium Source: 20 microgram  2 milligram
Nncapture(KATRIN*) = 1.7x10-4 nn/<nn> (year-1)= 170 [counts peryear];
See also: B. Monreal, J. A. Formaggio, Phys. Rev. D80 (2009) „Relativistic cyclotron radiation detection of tritium decay electrons“

17. Summary 1 The Cosmic Microwave Background allows to study the Universe
year after the BB.
The Cosmic Neutrino Background
1 sec after the Big Bang (BB):
Tn(today) = 1.95 Kelvin

18. THE END Summary 2 2. Measure only an upper limit of nn
Average Density: nne = 56 [ Electron-Neutrinos/cm-3]
Katrin: 1 Count in Years
Gravitational Clustering of Neutrinos nn/<nn> < 106
 1.7 counts per year (2 milligram 3H 170 per year)
2. Measure only an upper limit of nn
Kurie-Plot
Electron Energy
Emitted electron
THE END
2xNeutrino Masses