2. Search for the Cosmic Neutrino Background and the Nuclear Beta Decay (KATRIN). Amand Faessler University of Tuebingen Germany Publication: Amand Faessler, Rastislav Hodak, Sergey Kovalenko, Fedor Simkovic: arXiv: 1304.5632 [nucl-th] 20. April 2013 and J. Phys. G38 (2011) 075202

3. Cosmic Microwave Background Radiation (Photons in the Maximum 2 mm) Decoupling of the photons from matter about 300 000 years after the Big Bang, when the electrons are captured by the protons and He4 nuclei and the universe gets neutral. Photons move freely.

4. Penzias and Wilson; BellTelephon Nobel Price 1978 Radiation follows exactly the Planck Black Body formula with T = 2.7255(6) Kelvin in all directions. Microwave Background Radiation

5. 4 (2002) Temperature-Fluctuations of the Cosmic Microw.-Background: 1/100 000 COBE  WMAP COBE = Cosmic Background Explorer 1989-90 WMAP = Wilkinson Microwave Anisotropy Probe 2001

6. Planck Satellite Temperature Fluctuations Comic Microwave Background (Release March 21. 2013)

7. 6 Curvature of the Univers flat xxx We know the size of the hot spots.

8. The Universe is flat. The density has the critical value:  = 1.00+-0.02 We can only see till the sphere of the the last photon- electron scattering: ~14 x10 12 light years

9. Black body radiation. Temperature adjusted (pdg 2012): T=2.7255(6) K Experiment Microwave Background Radiation T = 2.7255(6) Kelvin

10. The relative number abundance of the light nuclei formed in the big bang allows to determine the absolute baryon density and relative to the critical density (flat universe).  Baryon =  Baryon /  critical = 0.02h -2 = 0.04 n B = 0.22 m -3 e B = 210 MeV/m -3 h = 0.71 h 2 = 0.5 Hubble-Konstant= H = 100 h [km/(sec Mpc)]  B h 2 = 0.02 h = 0.71

11. Planck‘s Black Body Radiation

13. Photons and Neutrinos   e,  W

14. Decoupling of Photons and Neutrinos from Matter „Re“-combination of Electrons with Protons and  -Particles (1  out of 1.7x10 9 from upper tail)  3000 Kelvin; 300 000 years after Big Bang; e- + p  neutral Hydrogen-Atom 2e- +   neutral Helium-Atom Photons move freely since 14x10  years. Last sphere of scattering: Radius = 14x10 12 light years. Today T  = 2.7255(6) Kelvin independent of the direction.

15. Neutrino Decoupling and Cosmic Neutrino Background For massless  massive Neutrinos:

16. Temperatures of Photons and Neutrinos Phase Transition: e + + e -   Neutrinos decouple 1 second after Big Bang; T decoupling (Neutrinos) = 1 MeV = 10 10 Kelvin Photons decouple 300 000 years after Big Bang; T decoupling (Photons) = 0.3 eV = 3000 Kelvin Entropy ~ g i x T i 3 = g f x T f 3 = const

17. Neutrino Decoupling and Cosmic Neutrino Background For massless  massive Neutrinos:

18. Estimate of Neutrino Decoupling Universe Expansion rate: H=(da/dt)/a  Interaction rate:  n e-e+

19. Neutrino Decoupling   /H = ( k B T/ 1MeV) 3 ~ 1 T(Neutrinos) decoupl ~ 1MeV ~ 10 10 Kelvin; today: 1.95 K Time after Big Bang: 1 Second T(Photons) decoupling = 3000 Kelvin; today: 2.7255 K Time(Photons) decoupling = 300 000 years Below T = 1 MeV:

20. (Energy=Mass)-Density of the Universe log  a(t)~1/T Matter dominated:  ~ 1/a 3 ~ T 3 Dark Energy 1/Temp 1 MeV 1sec  dec. 1 eV 3x10 4 y today 3000 K 300 000 y  dec. 8x10 9 y  2.7255 K 1.95 K

21. Hamburg, March 3. 2008. (Bild) Results from Oscillations: No Hierarchy, no absolute Mass Scale Fogli, Lisi, Marrone, Palazzo: Phys. Rev. D86 (2012) 013012

22. 1. The Neutrino Mass from  -Decay: Tranformation from Mass to Flavor Eigenstates

23. Mass of the Electron Neutrino? Tritium decay (Mainz + Troitsk) With:

24. Measurement of the upper Limit of the Neutrino Mass in Mainz: m < 2.2 eV 95% C.L. Kurie-Plot Q = 18.562 keV m 2 >0 m 2 <0 Electron Energy Eur. Phys. J. C40 (2005) 447

25. Negatives Squares of the Measured Neutrino Masses Ch. Kraus, B. Bornschein, L. Bornschein, J. Bonn, B. Flatt, A. Kovalik, B. Ostrick, E. W. Otten, J. P. Schall, Th. Thümmler, Ch Weinheimer: Eur. Phys. J. C40 (2005) 447-468.

26. 2. Neutrino Mass from Astrophysics: Density Distribution of Matter in the Universe (Power Spectrum of Matter Distribution) h= 0.68 Planck-Satelite2013; H= 100 h [km/(sec*Mpc)]

27. Fourier Transform of Distance Distribution of Galaxies

28.  0 = 1.0   = 0.66  b = 0.04 H 0 = 72 n s = 0.94  = 0 0.01 Cosmic Background Radiation n S = power index for fluctuations k**n S after inflationary expansion.

29.  0 = 1.0   = 0.66  b = 0.04 H 0 = 72 n s = 0.94  = 0.05 0.01

30. Matter Power Spectrum for  = 0.25

32. How can one detect the Cosmic Neutrino Background? 1.Anihilation of extreme high energy neutrino with low energy relic neutrino into Z 0 burst. 2. Free floating divided cylinder with neutrino absorber and neutrino non-absorbing material. 3. Electron-Neutrino capture on Tritium.

33. relic D GZK =50Mpc Neutrino E = 4x(10 21 to 10 22 ) eV 1. Anihilation of Relic Neutrinos with extreme High Energy Neutrinos > 10 22 eV Z0Z0 Above GZK Anihilation below Greisen-Zatsepin-Kuzmin Radius of 50 Mpc m  = 1.0 and 0.1 eV

34. Cosmic Radiation from Z-Burst expected at 10 21 -10 22 eV

35. 2. Free magnetic floating cylinder with half  absorbing material Permanent Magnet Superconducting Magnet Cylinder shaped One half  absorbing, the other sterile. Balanced. The system rotates into the neutrino wind. Thomas Müller pointed this out to me. A. Ringwald: arXiv:hep- ph/031157v1; 2003.

36. 3. Search for Cosmic Neutrino Background C B by Beta decay: Tritium Kurie-Plot of Beta and induced Beta Decay: (CB ) + 3 H(1/2 + )  3 He (1/2 + ) + e - Electron Energy 2xNeutrino Masses Emitted electron Q = 18.562 keV Infinite good resolution Resolution Mainz: 4 eV  m < 2.3 eV Resolution KATRIN: 0.93 eV  m < 0.2 eV 90% C. L. Fit parameters: m 2 and Q value meV Additional fit: only intensity of C B

37. Search for Cosmic Neutrino Background C B by Beta decay: 187 Re Kurie-Plot of beta and induced beta Decay: (CB ) + 187 75 Re 112 (5/2 + )  187 76 Os 111 (1/2 - ) + e - Electron Energy 2xNeutrino Masses Emitted electron Q = 2.460 keV Infinite good resolution MARE-Genova:  E ~ 11 eV  m ~ 2 eV Milano-Bicocca:  E ~24 eV  m ~ 3-4 eV Fit parameters: m 2 and Q value meV Additional fit: only intensity of C B

38. 37 Solution of the Nuclear Structure Problem: Pairing Quasi-Boson Approximation

39. Tritium Beta Decay: 3 H  3 He+e - + c e

41. Neutrino Capture: (relic) + 3 H  3 He + e - 20  g(eff) of Tritium  2x10 18 T 2 -Molecules: N capture(KATRIN) = 1.7x10 -6 n / [year -1 ] Every 590 000 years a count!! for = 56 cm -3

44. Beta-Decay 187 75 Re 112  187 76 Os 111 +e - + c e

45. Capture: e (relic) + 187 75 Re(5/2) +  187 76 Os(1/2) - + e - 760 grams of AgReO 4  N capture(MARE) = 6.7x10 -8 n / [year -1 ] Every 15 Million years a count!!! Main Contribution:  s(1/2); e -  p(3/2)

46. Kurie-Plot Electron Energy 2xNeutrino Masses Emitted electron Resolution KATRIN: 0.93 eV  m < 0.2 eV 90% C.L. Fit parameters: m 2 and Q value meV Additional fit: only intensity of C B Problems 1.Number of Events with average Neutrino Density of n e = 56 [ Electron-Neutrinos/cm -3 ] Katrin: 1 Count in 590 000 Years Gravitational Clustering of Neutrinos!!!??? 2. Energy Resolution (KATRIN)  E ~ 0.93 eV

47. Gravitational Clustering of Dark Matter and Neutrinos in Galaxies Was kompensiert die Zentrifugalkraft? Dunkle Materie ? Faktum erwartet

48. Gravitational Clustering of Neutrinos A. Ringwald, Y. Wong: arXiv:hep-ph/0408241; solved Vlasov eq. for ; Dark Matter from Navarro et al. Ap J490 (1997) 493 Circles: 1h -1 kpc; Pentagons: 10h -1 kpc; Squares: 100h -1 kpc; Triangles 1000h -1 kpc. h -1 = 2 The solar system is 8 kpc = 24 000 ly from the galactic center. Virial Mass: M vir = 5v2R/G; v = velocity in sight

49. Gravitational Clustering of Neutrinos R. Lazauskas, P. Vogel and C. Volpe, J. Phys.g. 35 (2008) 025001; Light neutrinos: Gravitate only on 50 Mpc (Galaxy Cluster) scale: n / ~ n b / ~ 10 3 – 10 4 ; = 0.22 10 -6 cm -3 A.Ringwald and Y. Wong: Vlasov trajectory simulations. Clustering on Galactic Scale possible (30 kpc ) n / = n b / ~ 10 6 ; (R = 30 kpc) N capture(KATRIN) = 1.7x10 -6 n / (year -1 )= 1.7 [counts per year] Effective Tritium Source: 20 microgram  2 milligram N capture(KATRIN*) = 1.7x10 -4 n / (year -1 )= 170 [counts peryear];

50. How many electrons come out without scattering from a gaseous Tritium source?

51. (  *d) free = 1/  (e  tritium) Mean free path of e:  = 1/(  *  ) = d free KATRIN Design Report

52. Gravitational Clustering of Neutrinos R.Lazauskas,P. Vogel and C.Volpe, J. Phys.g. 35 (2008) 025001; Light neutrinos: Gravitate only on 50 Mpc (Galaxy Cluster) scale: n / ~ n b / ~ 10 3 – 10 4 ; = 0.22 10 -6 cm -3 A.Ringwald and Y. Wong: Vlasov trajectory simulations. Clustering on Galactic Scale possible (30 kpc) B.n / = n b / ~ 10 6 ; (R = 30 kpc) N capture(KATRIN) = 1.7x10 -6 n / (year -1 )= 1.7 [counts per year] Effective Tritium Source (~50 cm 2 ): 20 microgram  2 milligram N capture(KATRIN*) = 1.7x10 -4 n / (year -1 )= 170 [counts peryear]; Source Area larger  Magnetic Flux-conservation: Area(Source ~50 cm 2 )*B(Source) = Area(Spectro, 63.6 m 2 ) *B(Spectro, 3 Gauss) B(source) = 3.6*10 4 Gauss; B(Spectro) = 3 Gauss; Area (Spectro)/Area(Source) = B(Source)/B(Spectro) = 12 000

53. 3 H-Source, Spectrometer and Detector Magnetic Flux Conservation: Area*Magnetic Field; Electron Momentum p e B(Source) = 3.6*10 4 Gauss Area(Source)~ 50 cm 2 B(Spectro) = 3 Gauss Area(Spectro) = 63.6 m 2 KATRIN Design Report

54. Gravitational Clustering of Neutrinos R.Lazauskas,P. Vogel and C.Volpe, J. Phys.g. 35 (2008) 025001; Light neutrinos: Gravitate only on 50 Mpc (Galaxy Cluster) scale: n / ~ n b / ~ 10 3 – 10 4 ; = 0.22 10 -6 cm -3 A.Ringwald and Y. Wong: Vlasov trajectory simulations. Clustering on Galactic Scale possible (30 kpc to 1 Mpc) B.n / = n b / ~ 10 6 ; (R = 30 kpc) N capture(KATRIN) = 1.7x10 -6 n / (year -1 )= 1.7 [counts per year] Effective Tritium Source (~50 cm 2 ): 20 microgram  2 milligram N capture(KATRIN*) = 1.7x10 -4 n / (year -1 )= 170 [counts peryear]; Flux-conservation: Area(Source ~50 cm 2 )*B(Source) = Area(Spectro, 63.6 m 2 ) *B(Spectro, 3 Gauss) B(source) = 3.6*10 4 Gauss; B(Spectro) = 3 Gauss; Area (Spectro)/Area(Source) = B(Source)/B(Spectro) = 12 000

55. KATRIN Spectrometer tank on the way from the Rhine to the FZ Karslsruhe A giant on trip Hamburg, March 3. 2008.

56. How to increase the counts in the Spectro ? Effective Tritium Source (~50 cm 2 ): 20 microgram  2 milligram N capture(KATRIN*) = 1.7x10 -4 n / (year -1 )= 170 [counts peryear]; Flux-conservation: Area(Source ~50 cm 2 )*B(Source) = Area(Spectro, 63.6 m 2 ) *B(Spectro, 3 Gauss) B(source) = 3.6*10 4 Gauss; B(Spectro) = 3 Gauss; Area (Spectro)/Area(Source) = B(Source)/B(Spectro) = 12 000 Modify Parameters so to increase the intensity by factor 100: Area(Source ~5000 cm 2 ; d = 80 cm); B(Source 360 Gauss) Condense beam to 8 cm by magnetic field of 36 000 Gauss. Beat magnetic mirror by accelerating electrons. Area(Spectro, 63.6 m 2 ); B(Spectro 3 Gauss);  E = 0.93 eV Area (Spectro)/Area(Source) = B(Source)/B(Spectro) = 120

57. Gravitational Clustering of Neutrinos R.Lazauskas,P. Vogel and C.Volpe, J. Phys.g. 35 (2008) 025001; Light neutrinos: Gravitate only on 50 Mpc (Galaxy Cluster) scale: n / ~ n b / ~ 10 3 – 10 4 ; = 0.22 10 -6 cm -3 A. Ringwald and Y. Wong: Vlasov trajectory simulations. Clustering on Galactic Scale possible (30 kpc to 1 Mpc) n / = n b / ~ 10 6 ; (R = 30 kpc) N capture(KATRIN) = 1.7x10 -6 n / (year -1 )= 1.7 [counts per year] Effective Tritium Source: 20 microgram  2 milligram N capture(KATRIN*) = 1.7x10 -4 n / (year -1 )= 170 [counts peryear]; See also: B. Monreal, J. A. Formaggio, Phys. Rev. D80 (2009) 051301 „Relativistic cyclotron radiation detection of tritium decay electrons“

58. Summary 1 The Cosmic Microwave Background allows to study the Universe 300 000 years after the BB. The Cosmic Neutrino Background 1 sec after the Big Bang (BB).

59. 2xNeutrino Masses Emitted electron Kurie-Plot Electron Energy Summary 2 1.Average Density: n e = 56 [ Electron-Neutrinos/cm -3 ] Katrin: 1 Count in 590 000 Years Gravitational Clustering of Neutrinos n / < 10 6  1.7 counts per year (2 milligram 3 H  170 per year) 2. Measure only an upper limit of n ENDE