Beta Decay and the Cosmic Neutrino Background

Abstract

Abstract. In 1964 Penzias and Wilson detected the Cosmic Microwave Background (CMB). Its spectrum follows Planck's black body radiation formula and shows a remarkable constant temperature of T 0γ ≈ 2.7 K independent of the direction. The present photon density is about 370 photons per cm 3 . The size of the hot spots, which deviates only in the fifth decimal of the temperature from the average value, tells us, that the universe is flat. About 380 000 years after the Big Bang at a temperature of T 0γ = 3000 K already in the matter dominated era the electrons combine with the protons and the 4 He and the photons move freely in the neutral universe. So the temperature and distribution of the photons give us information of the universe 380 000 years after the Big Bang. Information about earlier times can, in principle, be derived from the Cosmic Neutrino Background (CνB). The neutrinos decouple already 1 second after the Big Bang at a temperature of about 10 10 K. Today their temperature is ∼ 1.95 K and the average density is 56 electron-neutrinos per cm 3 . Registration of these neutrinos is an extremely challenging experimental problem which can hardly be solved with the present technologies. On the other hand it represents a tempting opportunity to check one of the key element of the Big Bang cosmology and to probe the early stages of the universe evolution. The search for the CνB with the induced beta decay ν e + 3 H → 3 He + e − is the topic of this contribution. The signal would show up by a peak in the electron spectrum with an energy of the neutrino mass above the Q value. We discuss the prospects of this approach and argue that it is able to set limits on the CνB density in our vicinity. We also discuss critically ways to increase with modifications of the present KATRIN spectrometer the source intensity by a factor 100, which would yield about 170 counts of relic neutrino captures per year. This would make the detection of the Cosmic Neutrino Background possible. Presently such an increase seems not to be possible. But one should be able to find an upper limit for the local density of the relic neutrinos (Cosmic Neutrino Background) in our galaxy. a

Looking for cosmic neutrino background

“…For m ν = 0.3 (0.15) eV, the rate is 7.5 (7.5), 23 (10), and 23 (12), respectively, with FD, NFWhalo and MWnow distribution [11]. A calculation by Faessler et al [29] finds that the NCB rate per year for the 3 H target (50 μg) to be used for the KATRIN experiment [30] is 4.2×10 −6 n ν / < n ν > which is consistent with the result by Cocco et al above for the FD distribution with n ν / < n ν >= 1. A similar calculation for 760 g of 187 Re to be used for the MARE calorimetric experiment [31] finds the event rate per year 6.7×10 −8 n ν / < n ν >, which is too small for a likely value for n ν / < n ν >.…”

Determination of the neutrino mass in 163 Ho

“…The transformation to an integral over the energy yields the factor in front of the third term, which can be deduced from ref. (10). Different neutrino mass eigenstates |i > are mixed into the electron neutrino flavor states by U 2 e,i .…”

“…E f ′ , E f ′ ,p ′ and E f ′ ,p ′ ;q ′ >0 are the 1-hole, the 2-hole shake-up and the 2-hole shake-off excitation energies in Dysprosium (see refs. [7] and [10]). Γ f ′ , Γ f ′ ,p ′ and Γ f ′ ,p ′ ;q ′ >0 are the widths of the one-and two-hole states and the two-hole states with shake-off in Dysprosium [15,16,18].…”

Big Bang, inflation, standard Physics… and the potentialities of new Physics and alternative cosmologies. Present statuts of observational and experimental Cosmology. Open questions and potentialities of alternative cosmologies

“…The standard cosmology of the CνB has been reminded in [115] having in view the use of the Karlsruhe Tritium Neutrino (KATRIN) spectrometer [116][117][118] devoted to the inelastic reaction between an electron neutrino and a 3 H nucleus: ν + 3 H → 3 He + e − . Another experimental project using a tritium target is PTOLEMY (Princeton Tritium Observatory for Light, Early Universe Massive Neutrino Yield) [119,120].…”