Relic Neutrino Detection Using Neutrino Capture on Beta Decaying Nuclei

Relic Neutrino Detection Using Neutrino Capture on Beta Decaying Nuclei

Nuclear Physics B (Proc. Suppl.) 188 (2009) 34–36 www.elsevierphysics.com Relic Neutrino Detection Using Neutrino Capture on Beta Decaying Nuclei Alf...

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Nuclear Physics B (Proc. Suppl.) 188 (2009) 34–36 www.elsevierphysics.com

Relic Neutrino Detection Using Neutrino Capture on Beta Decaying Nuclei Alfredo G. Cocco Istituto Nazionale di Fisica Nucleare - Sezione di Napoli Complesso Universitario di Monte S.Angelo - I80126 Napoli (Italy) In this paper we present a study of the interaction of low energy electron antineutrino on nuclei that undergo electronic capture. We show that the two crossed reactions that could be obtained have a sizable cross section and are both suitable to detect low energy antineutrino. The presence of an energy threshold in one case and the absence of a suitable final state in the other prevent the detection of Cosmological Relic antineutrino background unless very specific conditions on the -value of the decay are met or significant improvements on the performances of ion storage rings are achieved.

1. INTRODUCTION

first is given by

In a previous paper [1] we have shown that nuclei that decay via electron or positron emission are suitable to detect very low energy neutrino. This indeed appears to be a general property of all nuclear decays in which a neutrino (or antineutrino) is present in the final state: due to particle crossing from the final to the initial state the resulting reaction has no threshold on the energy of the incoming (anti)neutrino. The fact that neutrino has a non zero mass can have important consequences on the kinematics of the capture process: in the case of beta decay treated in [1] this led to the possibility to unambiguously detect neutrino of arbitrarily low energy. The case of nuclei that decay through the electron capture (EC) process appear to be worth to explore as well; in the EC process the nucleus of a neutral atom captures one bound electron to produce a daughter atom and an electron neutrino (1) The atom , initially in an excited state having an electron vacancy in an inner atomic shell, decays electromagnetically releasing a total energy ; by simple considerations it turns out that is the captured electron binding energy in the field of the daughter nucleus. The nucleus of atom can be produced in an excited nuclear state as well. Electron capture transitions are suitable to detect electron antineutrino via two crossed reactions: the 0920-5632/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2009.02.006

(2) and involves a simultaneous exchange of the electron and the neutrino in the initial and final states. The second reaction that can be obtained by crossing from the EC decay is given by (3) which involves the exchange of the electron neutrino in the final state to an electron antineutrino in the initial state. In the following we will show under which circumstances these two process could be used for the detection of very low energy antineutrino. 2. KINEMATICS OF CAYING NUCLEI

CAPTURE ON EC DE-

The behavior of reaction 2 as a function of the -value can be divided in three categories: in case the neutrino capture process of reaction 2 has indeed no energy threshold since the -value is large enough to allow the creation of a positron in the final state even without the contribution of the electron mass in the initial state of the EC decay. On the other hand, if the -value satisfy the relation positron decay become energetically allowed; this case is described in details in [1] and will not be treated here. There exist thus a range of values of that is wide and that would allow the detection of antineutrino with an arbitrarily small energy. Transitions falling in this category

A.G. Cocco / Nuclear Physics B (Proc. Suppl.) 188 (2009) 34–36

would have the remarkable property of a unique signature: the positron in the final state of reaction 2 can be definitely used to disentangle the antineutrino capture interaction with respect to the spontaneously occurring EC decay. Finally, in the case of antineutrino captured on nuclei having reaction 2 presents a threshold on the energy of the incomdue to ing antineutrino given by the fact that the -value cannot compensate anymore the lack of the captured electron mass in the initial state and the creation of a positron in the final state. The energy of the outgoing positron is given in fact by . For what concerns reaction 3 the -value plays a reaccrucial role as well. In case tion 3 has no energy threshold; moreover, the nucleus is stable since the corresponding EC decay become energetically allowed only if . Thus, once again, it exists a region of -values that is wide and in which reaction 3 has no threshold on the energy of the incoming antineutrino. The process is also background free since the EC decay is energetically forbidden. Nevertheless, reaction 3, as it is, is forbidden by the lack of a suitable final state. Using the second Fermi golden rule ( ) it is easy to prove in fact that the cross section for this process depends on the number of available final states per unit energy ; this has only one possible solution in case of antineutrino at rest and . Despite that, we can still envisage at least two other cases in which the process might happen: there exists an excited state having energy ; in this case EC decay through the same channel would be forbidden due to energy conservation even in the limit of for non vanishing values of the neutrino mass; the captured electron is “off-mass shell” with an effective mass given by and this could happen for example in a metal when the nucleus captures an electron in the valence band, the mean binding energy of vabeing in this case lence electrons. In the case of reaction 3 could still be triggered by antineutrino having . an energy greater than

3.

35

CAPTURE CROSS SECTION

The electron capture process has been studied in detail in [2]. The rate of electron capture is given by (4) where the sum extends over all the atomic shells from which an electron can be captured, is the relative occupation number of that shell and is the nuclear shape factor relative to the given transition. The index labels the orbital electron wave-function via the variable given by the spherical waves deis the analogous of the composition. The function integrated Fermi function of the decay and is given . by the expression It can be shown that antineutrino capture cross section can be written as (5) where the variable depends only on the shape factors ratio. In particular, for reaction 2 it is given by (6) is where is the nuclear transition shape factor, the energy of the outgoing neutrino in the EC decay and the subscript ( ) refers to the positron in the final state of reaction 2. Similarly, in case of reaction 3 it is easy to prove that (7) is the energy of the incoming neutrino in where is written in analogy reaction 3 and to . The values of the cross section for nuclei having the largest product of cross section times lifetime for a specific value of the incoming neutrino energy are reported in table 1. The antineutrino cross section for reaction 3 can be easily written using expression 5; in the case of allowed transitions and electron captured from the K shell we can write (8)

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A.G. Cocco / Nuclear Physics B (Proc. Suppl.) 188 (2009) 34–36

Table 1 Pure EC decaying nuclei that present the largest product of for the process in expression 2. Cross section is evaluated for incoming antineutrino energy of 1 MeV above reaction threshold and in case of K shell capture. Allowed transitions (top) and forbidden unique (bottom) are shown. Isotope

Decay (

Be Be Fe Ge W Ca Kr Pd Te

)

(keV) 637.80 160.18 790.62 916.00 930.70 600.61 741.30 693.68 970.70

(

cm )

where and are, respectively, the outgoing neutrino momentum and the half–life of the nucleus EC decay. In the case of reactions 2 and 3 and using, respectively, equations 6 and 7 we can write the ratio between antineutrino capture and EC decay rate as where is the antineutrino density at the nucleus. 4. COSMOLOGICAL RELIC

DETECTION

The detection of the cosmological relic neutrino background (C B) using reaction 2 is of course problematic due to the presence of the energy threshold; neutrino of the C B have an energy of the order of the neutrino mass and thus in the electron-volt scale. A possible solution could be to use the C B as a target for accelerated nuclei; in this case the threshold energy could be accomplished by the center of mass energy of the accelerated nucleus and the steady neutrino. From simple kinematical considerations we have that the nucleus of mass should have a greater than . In the case of accelerated nuclei we have that the factor that enhances the antineutrino density ( ) in the reference frame of the steady nucleus is compensated by the same factor that

should be applied to in the C B rest frame; the relic antineutrino capture rate can thus be expressed as (9) is the decay’s proper time. The total rate where is obtained by multiplying the last expression by the where realistic total number of accelerated nuclei values for present storage rings are . Assuming a transition having a value of of the order of the electronvolt this would lead to an interaction rate in case of allowed transitions of the order of s , too slow to be effectively detected even in case of absence of background due to EC decay of the nucleus (ie using a fully ionized beam). The C B detection using reaction 3 appears even more difficult due to the fact that in the case of neutrino having very small energy the number of final states per unit energy is basically unknown. The atom in the final state has to accomplish an excess energy via electromagnetic or phonon emission (if the decaying atom is bounded in a solid). Photons emission can be due either to atomic electrons or to nuclear level transition; in the first case the typical energy lies in the ev-keV region and, being in the same energy range, this impose that only nuclei with a very small -value could be suitable for this detection. In the second case there should exist a nuclear level that matches the energy difference. In both cases the energy of these levels should match exactly the mass difference; moreover, to avoid the possibility that the channel opens up also for the spontaneous EC decay this level must be above the transition -value. On the other hand, being in this case the EC decay forbidden, there is a priori no easy way to evaluate the cross section for reaction 3. REFERENCES 1. A.G. Cocco et al., Journal of Cosmology and Astroparticle Physics 06 (2007) 015 2. W. Bambinek et al., Reviews of Modern Physics 49 (1977) 77