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Majorana Neutrino: Invention and True Nature

Explore the invention of the Majorana Neutrino by Ettore Majorana and uncover its true nature. Discover the experimental evidence for distinguishing between Dirac and Majorana Neutrinos, as well as the concept of Neutrinoless Double Beta-Decay and its implications. Learn about Majorana Fermions in solid-state physics and their potential applications in quantum computing.

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Majorana Neutrino: Invention and True Nature

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  1. Whydid Ettore Majorana inventthe „Majorana Neutrino“ andisthe Neutrino really „Majorana“? Amand Faessler University of Tuebingen, GERMANY Messina 3 -6 October 2018

  2. 1930 Beta-Decay 1930 Beta-Spectrum : Z Z+1 + e- Z Z+1 Wolfgang Pauli: On December 4th. 1930: Letter fromZuerichto Tuebingen: Sehr geehrte radioaktiven Damen und Herren, Dearradioactive Ladies andGentelmen, Z (,N)  Z+1 (,N-1) + e- + nc ElectronEnergy Pauli: „The Neutrino can not bemeasured.“ Amand Faessler, Messina

  3. Detectionofthe Neutrinos: • 1956 Reines andCowan : Electron-Neutrinos • 1962 Steinberger : Myon-Neutrinos • 2000 DONAT Collaboration : Tau-Neutrinos • 1995 on: Neutrino Oscillations Neutrinos have a mass • Helicity not goodfor massive Neutrinos. HELICITY≠CHIRALITY vneutrinolefthanded Vanti-nrighthanded Spin Spin Amand Faessler, Messina

  4. Whydid Ettore Majorana inventthe „Majorana Neutrino“? 1933 -1937: Ettore Majorana livessecluded in Rome (See talkof E. Recami) 1933 – 1937 livedpracticallyalone in an appartmentofthe Majorana family in Rome, curtainsclosedand onlyhisphysicsfriends send himsomtimes a haircutter. He publishesnopaper. 1937 competitionforthreetheoreticalchairs (Chairman ofcommittee: EnriquoFermi *1901, +1954 ) shortlist: 1. Gian Carlo Wick (Palermo => Turino, *1909 +1992) 2. Giulio Racah (Pisa => Israel. *1909, +1965) 3. Giovanni Gentile (junior,*1906 +1942; Cagliari/Sardinia) Father Minister of Mussolini (Castelveterano) Amand Faessler, Messina

  5. Ettore Majorana (See talkof Erasmo Recami) Surprisingapplicationfor a chairsby Ettore Majorana: „Chiara fama“ (due totheundoubtablegoodreputation) → Naples Forthecompetitionhashastowrite an scientificarticle: „La Teoricasimmetricadell‘ electrone e del positrone“ NuovoCimento , Vol. 14, 1937, pp. 171 – 184. Electron different from Positron (Dirac Particle), but Ettore Majorana: Neutrino canbeidenticalwithantineutrino:Majorana Neutrino Amand Faessler, Messina

  6. Ettore Majoranain NaplesOct. 1937 Script of the Lecture 25.1.XVI Copy from Aldo Covello 25. Januar 1938 in Napels 26. March 1938 disappearedwithout a trace Ship: Napels→ Palermo → Napels ?? Amand Faessler, Messina

  7. Can onedistinguishexperimentallybetween Dirac and Majorana Neutrinos? Nucleus: Z+1, A Proton P P Electron Antineutrino Spin parallel n n neutron Thesis: Maria Goeppert- Mayer1935 Goettingen: Two-Neutrino Double-Beta Decay. Nucleus: Z, A Howcanweproof, thattheNeutrino is „Majorana“?

  8. Neutrinoless Double Beta-Decay (LeptonNumberandHelicity ) forbiddenin theStandard Model. Se P P Left Phase Space 106x2νββ Energydifference 76Ge  76Se: Q = 2038 keV ν Left n n Onlypossibleformassive Majorana Neutrinos. Amand Faessler, Messina

  9. GERDA 76Ge  76Se (Heidelb.+Muenchen+Tueb.) in Gran Sasso, Jan. 2018; Qbb = 2038 keV 2038 keV SumofEnergyofthetwoElectrons [keV] 90 % Confidence Limit: T0n½ > 8x1025 [years]; Background: 10-3counts/(keV*kg*year) GERDA Collaboration: Agostini et al. Phys. Rev. Lett. 120 (2018) 132503 Amand Faessler, Messina

  10. CUORE 130Te  130Xe (Status 2018, Milano, Roma Sapienza, Zaragoza) in Gran Sasso; Qbb= 2528 keV 60Co 2528 keV SumofEnergiesofthetwoelectrons [keV] 90 % Confidence Limit : T0n1/2 > 2.7x1024 [years]

  11. Majorana Fermions in Solid State PhysicsS. R. Elliott and M. Franz: Rev. Mod. Phys. 87 (2015) 137 Fermi Surface Fermi-Energy vk2 = u-k2 = 1/2 Supra- conductor: (vk)2 Sharp „Fermi Surface“ Diffuse „Fermi Surface„ u2 + v2 = 1 1 Electron Occupation (vk)2 =1-(u-k)2 ElectronEnergy Quasi-Particle: a+k = ukc+k + vk c-k ; ak= uk c-k + vkc+k Quasi-Particle = Quasi-Hole near/at the Fermi Surface Amand Faessler, Messina

  12. New Commutative Properties: Winding Number A Novel Quantum-MechanicalBehavior Bosons - Fermions Majorana (topologic, chiral) Fermions Non-AbelianAnyions Amand Faessler, Messina

  13. Quantum Computer morestablequbits due totopological (chiral) winding number. • q-bits = q; Binary code. • |0> [= q = 0] winding numberzero ; • |1> [= q = 1] winding number 1 q = a |0> + b |1>; a2 + b2 = 1 Quanten–Computer: |q6 q5 q4 q3 q2 q1> all numbersfrom 0 to 63 Amand Faessler, Messina

  14. Summary ofthe „Majorana Neutrinos“ • Dirac-Neutrinos: Neutrino different from Antineutrino • Majorana-Neutrino: Neutrino = Antineutrino • Neutrino Oscillations Neutrinos have a mass (helicity ???) (Grand Unified Theories) requireas a rule Majorana Neutrinos. • Neutrinoless Double Beta Decayonlypossiblefor massive Majorana Neutrinos. Not yetfound. • Neutrinoless Double Beta Decayallowstodeterminethemassofthe Majorana Neutrino withthematrixelement. • Majorana Fermions in supraconductingsolids. Hope: TopolocicalWinding Number  morestable q-bits? The END Amand Faessler, Messina

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