Test of beta and antineutrino spectra symmetry in beta-decay
aa r X i v : . [ h e p - ph ] F e b Test of beta and antineutrino spectra symmetry inbeta-decay
S. V. Silaeva and V. V. Sinev
Institute for Nuclear Research of Russian Academy of Sciences, Moscow, RussiaE-mail: [email protected]
Abstract.
The mechanism of beta decay in nature is not understood yet. Mirrored energyspectra of electron and antineutrino can clarify the situation. A special experiment is neededto measure antineutrino spectrum from known beta-decaying isotope to compare it with thebeta one. One of ongoing experiments with large volume detector can be chosen to make theexperiment. Another possibility is to make a special experiment close to a powerful source ofmixture of known beta-decaying isotopes. If sufficient differences in shape will be observed themethod of antineutrino spectrum calculation should be revised.
1. Introduction
In beta decay one nucleus is transformed into another one with the emission of electron (positron)and antineutrino (neutrino). Also a nucleus can capture one of own atomic electrons fromelectron shell and emit monoenergetic neutrino. β − : ( A, Z ) → ( A, Z + 1) + e − + ¯ ν e , Q β − = M p − M d (1) β + : ( A, Z ) → ( A, Z −
1) + e + + ν e , Q β + = M p − M d − m e (2)Electron capture (EC) : ( A, Z ) + e − → ( A, Z −
1) + ν e , E ν = Q β , (3)where M p and M d masses of parent and daughter nuclei.Where inside the nucleus electron and antineutrino are born is unknown. E. Fermi createdtheory of beta-decay [1] and postulated that electron and antineutrino are born together exactlyin the moment of beta-decay. Electron and antineutrino energy spectra are mirrored to eachother relatively to the point in the middle of the spectrum ( T / T ≈ Q β ).We can regard beta decay from another point of view. Electron is a particle that massiveand charged in contrast with antineutrino that is neutral and uncharged. It is understood whyelectron spectrum while transforming by nucleus electric field becomes softer − it passes throughCoulomb field of daughter nucleus and interacts with it. But antineutrino should escape from anucleus without any visible interaction due to the absence of charge and magnetic moment.Antineutrino spectrum from individual isotope was never measured up to now. Only thespectrum containing thousands of individual spectra was measured in experiments with reactorantineutrinos (see for example last high statistical experiments [2] − [4]). But using this spectrumis impossible to check if antineutrino spectrum is exactly mirrored relatively to the electron one.he test on the mirror symmetry of antineutrino spectrum and electron one can bedone by measuring antineutrino spectrum directly using any known beta beta-decayingisotope and comparing it with the beta one. Modern detector techniques allows to measureantineutrino spectrum from some individual isotope. The progress in antineutrino detection inexperiments with reactor antineutrino spectrum makes it possible to measure individual isotopesantineutrinos. The problem is only to get a powerful antineutrino source of pure beta-decayingisotope.We propose to make an experiment on measuring antineutrino spectrum using high activityradioactive Sr − Y source (1 −
2. Beta and antineutrino spectra shapes
Beta spectrum shape P e ( E ¯ ν , E , Z ) can be written as P e ( E e , E , Z ) = K · p e E e · ( E − E e ) · F ( Z, E e ) · C ( Z, E e ) · (1 + δ ( Z, A, E e )) , (4)where K − is normalization factor, p e and E e − are momentum and energy of electron, F ( Z, E e ) − Fermi function accounting Coulomb field of the daughter nucleus, C ( Z, E e ) − the factoraccounting momentum dependence of nucleus matrix element and δ ( Z, A, E e ) − is correctionfactor to the spectrum shape.The antineutrino spectrum shape P ¯ ν ( E ¯ ν , E , Z ) can be expressed the same way as betaspectrum shape by changing E e by E − E ¯ ν .It is accounted that electron and antineutrino are born in the same moment in the nucleusand therefore all corrections should be applied to the electron and the same way (mirrored) tothe antineutrino. But why? In reality we do not know how electron and antineutrino appearinside a nucleus, what is just understood that they appear simultaneously somewhere inside anucleus and leave it in opposite directions. Electron moves in the direction opposite to nucleusspin [5]. Electron and antineutrino share energy Q β of parent nucleus relatively to the daughterone. The energy Q β can be calculated as a difference between atomic masses of parent anddaughter atoms what is equivalent to difference of mass excesses. Mass excess is differencebetween nucleus mass and sum of nucleons masses. Q β = ∆ M parent − ∆ M daughter , (5)where ∆ M parent and ∆ M daughter − are mass excesses for parent and daughter nuclei. Q β determines maximal electron (antineutrino) kinetic energy T . For example, for Y we have∆ M Y = -86494.1 keV and for the daughter nucleus Zr ∆ M Zr = -88772.5 keV. The differenceis 2278.4 keV what is exactly maximal energy of Y electron spectrum.At figure 1 one can see calculated antineutrino spectrum from Y. There are shown twospectra: one spectrum was calculated using all corrected factors equal to unit and the other oneused Fermi function F ( Z, E e ) that was applied to calculated spectrum. Other factors were nottaken into account. We note that when using (4) with F ( Z, E e ) the spectrum has sharp edge at T . In case of F ( Z, E e ) = 1 spectrum goes to ”0” smoothly. Sr − Y source for large detectors in ongoing experiments
To measure individual isotope antineutrino spectrum one needs a powerful enough source. Theusing of powerful ( ∼
10 MCi) Sr − Y source for testing of Standard Model and looking forsterile neutrinos was proposed in [6]. The sources in 200 −
300 kCi activity are using as electricpower suppliers for some needs in hardly reached places. ν E00.10.20.30.40.50.60.70.8 - M e V ν ) e without F(Z,E) e with F(Z,E Figure 1.
Antineutrino spectrum from Y without using correction factor for electrons F ( Z, E e ) (blue line) and with application of F ( Z, E e ) (red line). Figure 2.
Possible position of Sr − Y source on the top of KamLAND detector. C oun t s pe r b i n Figure 3. Y antineutrino spectrum that can be observed in a detector with the use of Sr − Y source 1 MCi by KamLAND during 3 years of data taking. Blue line − spectrumwith application of Fermi function F ( A, E e ), red line − the spectrum without Fermi function.Energy resolution 200 ph.e. per MeV.An array of sources in 200-300 kCi each (1 − Sr − Y source at a distance 13 m from the KamLAND detector center. At figure3 the spectrum from Sr − Y source, that can be observed in a detector is presented. Rightside of the spectrum should be pure energy resolution of the detector in case of sharp spectrumedge. If it smoothly goes to zero the shape will be different what is seen at the figure. At thefigure the difference ∼ −
150 keV in maximum positions can be seen as well as difference inright slope.Statistics that can be achieved in one year with 1 MCi source in KamLAND detector is ∼ ∼ − events.The same antineutrino source can be applied also at SNO+ detector [8]. But the distanceto the center is appeared slightly larger ( ∼
14 m) than that for the KamLAND detector.Correspondingly the events number becomes less, ∼ Sr − Y source at large scintillation detectors is also useful for othergoals, not only for testing the shape of antineutrino spectrum. In [6] was shown how this sourcecan be used for Standard Model testing and measuring of sin θ W with high accuracy. If tomeasure in one experiment recoil (with the same antineutrino source) recoil electrons spectrumfrom ( ¯ ν e , e − )-reaction and cross section of inverse beta decay reaction (IBD), the recoil electronsspectrum normalized on IBD cross section will not depend on the source parameters but onlyn sin θ W . W S ( T ) N νp = g F G V + G A · F ( T, sin θ W ) · n e n p , (6)where W S ( T ) − recoil electrons spectrum, N νp − IBD events number, T − recoil electrons kineticenergy, F ( T, sin θ W ) − normalized on IBD events recoil electron spectrum and n e and n p − electron and proton densities in the scintillator.With statistics more than 10 events in recoil electrons spectrum sin θ W accuracy could beless than 1%. It is important to stress that the Weinberg angle value can be measured at verylow energy in compare with accelerator experiment. If KamLAND or SNO+ detectors can seerecoil electrons from antineutrino-electron scattering the test of Standard Model can be done.
4. Small detector in vicinity of spent fuel storage
The test of antineutrino energy spectrum shape can be also made by using a small detector ( ∼ − ) placed in some room under the reactor spent fuel storage (water pool) at a distance lessthan 20 m from the center of the storage. If there is no room in the same building, the specialtunnel can be done that goes under the storage building.At NPP the spent fuel storage is placed in neighboring to the reactor building. It is water poolwhere spent fuel assemblies are placed after the use during 3 years in a reactor core. Normallyit contains a number of assemblies accumulated in 5 years, sometimes more. Fuel amount inspent fuel storage corresponds to 1.7 reactor cores as minimum. At Neutrino-2020 Double Chozzcollaboration presented the poster [9] where the results of measuring residual neutrinos emissionfrom two cores were shown. The registered by near detector ∼
80 events during ∼
20 days whenboth reactor cores were off (one can summarize four points at the plot for near detector). It is ∼ . If weassume roughly the equal input in this counting rate from both stopping cores and spent fuelstorages we get ∼ Y, Pr and
Rh. At figure 4 spent fuel spectrum isshown. It is calculated by summing the spectra with weights of parts of nuclei numbers for theseisotopes.We can recalculate 1 event per day for 30 m to a small detector 1 m placed at 15 m fromthe center of spent fuel pool. Then we have ∼ ∼
700 events per day if a core at adistance 60 m).The effect is about 2% of the background but it is concentrated in energy region below3.5 MeV of antineutrino energy. So, it can be seen in a similar way as geoneutrino signal inKamLAND detector. Reactor antineutrino spectrum is well known, can be easily fitted and thenbe subtracted from measured data.At figure 5 we show how spent fuel spectrum looks like in case of finite energy resolution atstatistics 8500 events (1.5 years of data taking). Here we also see by eye the difference in spectrain spite of energy resolution.
5. Conclusion
In this work we propose to check if antineutrino spectrum is really mirror symmetric to the betaone. There may be different experiments done to check the symmetry of antineutrino and betaspectra from one isotope.We propose to make an experiment with artificial radioactive source Sr − Y. Using thissource of 1 − .5 1 1.5 2 2.5 3E_visible, MeV05101520253035 r e l a t i v e un i t s with F(A,E)no F(A,E) Figure 4.
Spent fuel storage antineutrino spectrum as a mixture of the spectra produced by Y, Pr and
Rh. Black line with application of F ( A, E e ) function to antineutrino spectrum,blue line without using F ( A, E e ). C oun t s pe r b i n Figure 5.
Spent fuel storage antineutrino spectrum simulated for the detector energy resolution(200 ph.e. per 1 MeV). Blue line with F ( A, E e ) function and red line without F ( A, E e ). Energyresolution 200 ph.e. per MeV.pectrum shape. The experiment with Sr − Y source is convenient also for testing StandardModel. Weinberg angle can be measured with high accuracy as shown in [6].Test of antineutrino energy spectrum shape can be also done with a small detector at NPP ifto place a detector under spent fuel pool building. The background of antineutrino from reactorcore can be subtracted. In several years of measuring necessary statistics can be accumulated.
Acknowledgements
We would like to thank L. B. Bezrukov for fruitful discussions and valuable remarks.
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