Precision method for the determination of neutrino mixing angle
Based on the properties of the cascade statistics of reactor antineutrinos the effective method of neutrino oscillations searching is offered. The determination of physical parameters of this statistics, i.e., the average number of fissions and the average number of antineutrinos per fission, does n...
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nasplib_isofts_kiev_ua-123456789-794762025-02-09T23:50:39Z Precision method for the determination of neutrino mixing angle Прецизионный метод определения угла смешивания для нейтрино Rusov, V.D. Zelentsova, T.N. Tarasov, V.A. Shaaban, I. Electrodynamics of high energies in matter and strong fields Based on the properties of the cascade statistics of reactor antineutrinos the effective method of neutrino oscillations searching is offered. The determination of physical parameters of this statistics, i.e., the average number of fissions and the average number of antineutrinos per fission, does not require a priori knowledge of geometry and characteristics of the detector, the reactor power and composition of nuclear fuel. 2001 Article Precision method for the determination of neutrino mixing angle / Precision method for the determination of neutrino mixing angle // Вопросы атомной науки и техники. — 2001. — № 6. — С. 157-160. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 14.60.Pq; 25.85.Ec https://nasplib.isofts.kiev.ua/handle/123456789/79476 en Вопросы атомной науки и техники application/pdf Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Electrodynamics of high energies in matter and strong fields Electrodynamics of high energies in matter and strong fields |
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Electrodynamics of high energies in matter and strong fields Electrodynamics of high energies in matter and strong fields Rusov, V.D. Zelentsova, T.N. Tarasov, V.A. Shaaban, I. Precision method for the determination of neutrino mixing angle Вопросы атомной науки и техники |
| description |
Based on the properties of the cascade statistics of reactor antineutrinos the effective method of neutrino oscillations searching is offered. The determination of physical parameters of this statistics, i.e., the average number of fissions and the average number of antineutrinos per fission, does not require a priori knowledge of geometry and characteristics of the detector, the reactor power and composition of nuclear fuel. |
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Article |
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Rusov, V.D. Zelentsova, T.N. Tarasov, V.A. Shaaban, I. |
| author_facet |
Rusov, V.D. Zelentsova, T.N. Tarasov, V.A. Shaaban, I. |
| author_sort |
Rusov, V.D. |
| title |
Precision method for the determination of neutrino mixing angle |
| title_short |
Precision method for the determination of neutrino mixing angle |
| title_full |
Precision method for the determination of neutrino mixing angle |
| title_fullStr |
Precision method for the determination of neutrino mixing angle |
| title_full_unstemmed |
Precision method for the determination of neutrino mixing angle |
| title_sort |
precision method for the determination of neutrino mixing angle |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2001 |
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Electrodynamics of high energies in matter and strong fields |
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https://nasplib.isofts.kiev.ua/handle/123456789/79476 |
| citation_txt |
Precision method for the determination of neutrino mixing angle / Precision method for the determination of neutrino mixing angle // Вопросы атомной науки и техники. — 2001. — № 6. — С. 157-160. — Бібліогр.: 7 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT rusovvd precisionmethodforthedeterminationofneutrinomixingangle AT zelentsovatn precisionmethodforthedeterminationofneutrinomixingangle AT tarasovva precisionmethodforthedeterminationofneutrinomixingangle AT shaabani precisionmethodforthedeterminationofneutrinomixingangle AT rusovvd precizionnyimetodopredeleniâuglasmešivaniâdlâneitrino AT zelentsovatn precizionnyimetodopredeleniâuglasmešivaniâdlâneitrino AT tarasovva precizionnyimetodopredeleniâuglasmešivaniâdlâneitrino AT shaabani precizionnyimetodopredeleniâuglasmešivaniâdlâneitrino |
| first_indexed |
2025-12-01T22:48:18Z |
| last_indexed |
2025-12-01T22:48:18Z |
| _version_ |
1850347931818786816 |
| fulltext |
PRECISION METHOD FOR THE DETERMINATION
OF NEUTRINO MIXING ANGLE
V.D. Rusov, T.N. Zelentsova, V.A. Tarasov, I. Shaaban
Odessa National Polytechnic University, Odessa, Ukraine
e-mail: siiis@te.net.ua
Based on the properties of the cascade statistics of reactor antineutrinos the effective method of neutrino
oscillations searching is offered. The determination of physical parameters of this statistics, i.e., the average number
of fissions and the average number of antineutrinos per fission, does not require a priori knowledge of geometry and
characteristics of the detector, the reactor power and composition of nuclear fuel.
PACS: 14.60.Pq; 25.85.Ec
1. INTRODUCTION
The hypothesis of massive neutrino mixing
stimulated the experiments on searching oscillations of
reactor electron antineutrinos eν~ [1]. The oscillation
effect χνν →e
~
can be manifested as spectrum
deformation and change of eν~ flux from distances R
according to the dependence [2]:
( )[ ]LRII πϑ 2cos12sin2
11 2
0 −−= , (1)
where I0 is the intensity in absence of oscillations; ϑ is
the mixing angle; L=2.5Eν/∆2 is the length of
oscillations, m; Eν is the neutrino energy, MeV; ∆2=m1
2
– m2
2 is the squares of masses difference, eV2.
The inverse β–decay reaction was used for this
purpose in series of papers:
nepe +→+ +ν~ . (2)
In the oscillation absence the counting rate of
detector is connected to reactor heat-generation power
W by relation:
,
4 2
0
νν
π
γ ε
∑⋅⋅⋅= p
f
N
RE
W
n (3)
where
∫∑ ==
max
,)(,
E
E
p
пор
dEEMM νννννν ρσ
∫∫=
maxmax
;)()()(
E
E
E
Е
pp
порпор
dEEdEEE ννννννν ρρσσ (4)
<Еν>=∑(αi⋅Еνi) is the average energy absorbed in
reactor per fission at given fuel composition; αi is
contribution from i-th isotope (i=5,9,8,1) in total fission
cross-section, which depends on mode of spectrum ρ (E
ν) determination [3]; (4π<R>2)-1 is the effective solid
angle with allowance for real distribution of energy-
gene-ration in reactor core volume; Np and γε0 are the
detector characteristics (number of hydrogen atoms in a
target and detection efficiency with allowance for the
part of detected neutrons γ corresponding to the reaction
(2)); ∑ν and <σνp> are neutrino reaction cross-sections,
and their dimensions are cm2/fission and cm2/ν-particles
accordingly; ∑ν =∑(αi⋅∑νi) at given fuel composition; M
ν is number of electron antineutrinos per fission; ρ(Eν)=
∑(αi⋅ρνi) is antineutrino energy spectrum (MeV-1⋅
fission-1) emitted by fission-products of all fuel
components (actinides); σνp(Eν) is the interaction cross-
section of monoenergetic (with an energy Eν)
antineutrinos with allowance for recoil, weak
magnetism and radiation corrections.
The cascade type of antineutrino statistics makes it
possible to modify Eq. (3) by the following way. It is
obvious, that the statistics of the reactor antineutrinos is
formed due to two-cascade stochastic process. Primary
random process (number of fissions <λ>) generates
secondary random process (β-decays chain or number
of antineutrinos per fission <ε>). Then due to well-
known Burgess theorem the mathematical expectation <
nν> and variance var(nν) of antineutrinos connected by
such relations [4]:
ελν =n , (5)
( ) ( ) ( ) 2varvarvar ελελν +=n , (6)
Substituting Eq. (5) in Eq. (3) and using the ratio of
two counting rates in the same antineutrino flux we
have
2
1
2
1
ν
ν
ε
ε
M
M
= , (7)
where <ε>1 and <ε>2 can be determined either
theoretically or experimentally depending on
experiment strategy (one-detector or two-detector
measurement scheme).
But in any case at the large distances from reactor
Eq.(1) with allowance for Eq.(7) can be re-written in
form:
( ) ( )ϑ
ε
ε
2sin211 2
2
1 −= . (8)
Eq. (8) is interesting for two nontrivial reasons.
Firstly, the ratio of average numbers of antineutrinos
(being statistically fine sensitive value) does not depend
neither on geometry and properties of the detector nor
from reactor power and isotope composition of nuclear
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2001, № 6, p. 157-160. 157
mailto:siiis@te.net
fuel. Secondly, it is obvious, that for determination of <
ε> by solution of the system of momental equations (as
Eqs. (5)-(6)) the a priori information about reactor
antineutrino statistics type is extremely necessary.
The determination of the type of reactor antineutrino
statistics, which properties could become base for the
development of precision method for determination of
neutrinos mixing angle, was the main purpose of our
research.
2. STATISTICS OF REACTOR ELECTRON
ANTINEUTRINO PRODUCTION.
THEORY AND EXPERIMENT
We suppose that the statistics of reactor
antineutrinos is formed due to two-cascade stochastic
process, in which the primary and secondary random
processes are Poisson. Then, by virtue of obvious
equality of expectation <n⋅> and variance var(n) of each
of random processes, Eqs. (5)-(6) have following
concrete form:
ελ=n , (9)
( )ε+= 1)var( nn , (10)
where sampling average <n>, variance var (n) of
antineutrinos are determined experimentally.
Using the method of generating functions it is easy
to found the probability density distribution of
antineutrino random number:
( ) ( ) ( ) ( )
∑
∞
=
−
⋅
−
=
0 !
exp
!
exp
k
kn
kn
kk
np
λλεε
, (11)
which exactly coincides with Neyman type A two-
parametrical distribution [4].
It is easy to show also that Neyman type A
distribution is the particular case of Saleh-Teich
distribution [5] and with <n>→ ∞ it goes to Gauss
distribution [4]. But in any case it keeps possibility for
the determination of very important parameters of our
distribution, i.e., average number of fissions <λ> and
average number of antineutrinos per fission, by the
system of momental equations (9)-(10).
Despite the abundance of publications devoted to the
reactor antineutrino detection we could find only one
experiment (Fig. 1a) [6] containing data, which suffice
for plotting the experimental distribution of detected
reactor antineutrinos (Fig. 1b). Due to small sample of
measurements corresponding to one reactor campaign
(approximately 40-90 measurements [6,7]) Fig.1b
reflects only qualitative goodness of fit of the
experimental distribution with Neyman distribution,
which asymptotically transforms to Gauss distribution.
Let us note that the Neyman's statistics works well
under conditions of low event intensity but large sample
of the measurements [4]. In this case the oscillatory
nature of Neyman cascade distribution can be exhibited
(Fig. 2).
If the statistics of reactor electron antineutrinos is
described by Neyman distribution, the average number
of electron antineutrinos per fission should be
approximately identical, i.e. <ε> ≈ const, for reactors of
different heat power but with same fuel composition.
Moreover, only a third of 6-7 antineutrinos produced by
fissioned nucleus has an energy above 1.8 MeV
(threshold of the reaction (2)) therefore rough
estimation gives value <ε>≈2-2.3. The obtaining
quantitative estimation of this value was the main
purpose of indirect check goodness of fit of the
experimental reactor electron antineutrino distribution
with Neyman distribution. We used experimental data
with same type nuclear reactors (Rovno, Ukraine and
Bugey, France [6,7]) for 1984 -1995 period.
Fig. 1. Counting rate of integral detector (for 105
s). a) Experiments №1 and №2 [6] with operating
and stopped reactor; b) Neyman () and Gauss (⋅⋅⋅)
distributions of reactor antineutrinos in experiment №1
158
The results of these experiments handling are
presented in Table 1. The analysis of data shows that,
firstly, average number of antineutrinos per fission in
averaged fuel, not only approximately equal in different
experiments with the same reactor (Rovno, Ukraine [6])
but has also (with allowance for an averaging)
physically acceptable value <ε>≈2.66. Secondly, the
average number of antineutrinos in different
experiments with the same type reactors having the
different power [6,7] coincides to within 5%. It
confirms the known supposition that the same type
reactors have small differences of nuclear fuel
composition.
Table 1. Experimental and calculated parameters of reactor antineutrino statistics
Parameters Rovno NPP [6]
Experiment N 1 Experiment N 2
Bugey-5 [7]
Np 1.152⋅1028 1.591⋅1028 4.953⋅1028 ± 0,5 %
ε0 0.540 0.568 0.549 ± 0.3 %
W, MW 1379 1371 2735 ± 0.6 %
R, m 18 17.96 14.882 ± 0.3 %
N 33* 17** 88.47
T, s 105 105 8.6⋅104
<nν> 386 561.5 3022 ± 11 ± 12 ± 12
var(n) 1409.34 2062.5 10704.87***
<ε> 2.65 ± 0.37 2.67 ± 0.51 2.54 ± 0.21
<λ> 145.66 210.3 1189.76
* from sample of experimental data N 1 four record measurements were excepted.
** from sample of experimental data N 2 two record measurements were excepted.
*** was determined from expression: var(n)/N = δ2, where δ is statistical error
of value <nν> equal to ± 11
Fig. 2. Simulation of Neyman distribution with <ε
>=2.65 and different <n>: 1 - 5; 2 – 10; 3 - 20
Let us adduce the relation for estimation of value <ε
> relative error. From Eq. (10) follows that with passage
from differentials to increments:
[ ] [ ] [ ]
nn
n
n
n
nn
n
−
∆
+
−
∆=∆
)var(
)var(
)var(
)var(
ε
ε
.
Then, using the estimation of sampling mean-square
error of random value <n> (by central limit theorem)
and error of sampling variance var(n) (by Bessel
approximation formula), we get
[ ]
+
−−
=∆ 2/12/1 )var(1
1
2
)var(
)var(
N
n
nNnn
n
ε
ε
.
3. DISCUSSION AND CONCLUSIONS
On the base of all totality of known now
experimental data for the first time it is shown that the
reactor antineutrino statistics is described with a high
accuracy by two-cascade Neyman type А distribution.
Nontrivial properties of the moments of this distribution
make it possible to determinate the important
parameters of electron antineutrino source, i.e., average
number of fissions <λ> and average number of
antineutrinos per fission <ε>. Let us consider below the
obvious consequences of the cascade-stochastic
properties of reactor antineutrinos statistics, which can
essentially intensify the experimental possibilities and
the quality of the researches of fundamental tasks in
neutrino physics.
Firstly, the knowledge of value <λ> makes it
possible to determine such important characteristics of
electron antineutrino source as normalised antineutrino
energy spectrum ρ(Eν), which can be obtained by a
normalization of the calculated antineutrino spectrum
N(Eν) on average number of fissions <λ>:
159
( ) ( )νν λ
ρ ENE 1= . (12)
Here calculated antineutrino spectrum N(Eν) is
obtained by solution of an integral equation relative to
«true» positron spectrum N(Те):
( ) ( ) ( ) eeeee dTETTNEN ,ℜ⋅= ∫ (13)
with a consequent shift of obtained spectrum N(Те) on
value of energy threshold of the reaction (2), which
connects a positron kinetic energy Те to antineutrino
energy Еν by the following relation
ne rTE ++= 804.1ν
where 1.804 MeV is threshold of reaction (2), rn (<< Eν)
is average recoil energy transmitted to neutron; N(Ее) is
an observable positron spectrum obtained, for instance,
by spectrometry method [3], Ее is an energy detected by
spectrometer; ℜ(Те,Ее) is the spectrometer response
function [3].
Secondly, such way of ρ(Eν) determination, in it
turn, enables to determine the inverse β– decay reaction
cross-section:
( ) ( )∫ ⋅=∑ ννννν σρ EEdE p . (14)
Here we note that at observance of certain known
conditions this way can be used also in some dynamic
neutrino experiments.
Thirdly, taking in consideration physical
equivalence of values <ε> and integral Mν (Eq. (4)), we
obtain new method of the determination of parameters
αi (describing the relative contribution from i-th isotope,
for instance, i = 5; 9; 8; 1, in total fission cross-section)
based on the following obvious system of equations:
( )
( ) ( )
=α
σ⋅ρα=∑
α=ε
ρα=ρ
∑
∑ ∫
∑
∑
ννννν
ν
ν
.1
,
,
,
i
pii
ii
ii
EEdE
M
E
(15)
Here as partial antineutrino energy spectra ρi(Eν) is
expedient using so-called “converted” antineutrino
spectra [2]. Let us note, that further the role of these
spectra will increase as in the field of applied researches
(for instance, for neutrino diagnostics of inside-reactor
processes and fuel-containing masses [3,7]) and in the
fundamental researches (in particular, at the analysis of
the reaction (2) for the determination of an axial
constant of the weak charged current of nucleons and
reactor antineutrino polarization [7]).
It is obvious, that the cascade-stochastic approach to
αi parameters determination has all necessary properties
of an independent and absolute method. This is very
actual method for remote on-line diagnostics of basic
parameters of reactor core (starting from the
determination of current heat power and heat-generation
up to the dynamics of concentration of everyone
actinide component of nuclear fuel and daughter fission
products during reactor operation). In the elementary
case of the reactor power determination it looks like this
∑∑ ⋅=⋅= λα iifiif ECEW . (16)
The universality of the offered method for
experimental determination of restrictions on the
neutrino mixing parameters consists in obtaining more
fine additional information about physical nature of the
compound statistics of reactor antineutrinos. It, in turn,
allows using the values reflecting higher degree
approximation to the investigated process dynamics. For
instance, taking into account the properties of Neyman
statistics moments (9)-(10) and Eqs. (4), (15) in case of
one-detector measurement scheme Eq. (8) can be
modified like this
[ ]
( )
( )ϑ
ραε
ε
νν
νν 2sin211
1)var( 2exp −=
−
=
∫∑ dEE
nn
iitheor
. (17)
Eq. (17) makes it possible to measure probable
periodic changes of electron antineutrino intensity (due
to detection only eν~ from the reaction (2)) by simple
but effective procedure of the determination of
statistical characteristics <ε>exp, i.e., average number of
electron antineutrinos per fission. Here <ε>theor is the
same value but in oscillations absence. In this case
indeterminacy of experiment due to the geometry and
characteristics of the detector and also parameters of
reactor (as source of antineutrinos) are excluded
practically completely.
Finally, we note that our conclusions based on the
found regularities, which describe type, structure and
properties of reactor antineutrino distribution, by virtue
of importance of the considered problem require the
additional confirmation in the special test experiments.
REFERENCES
1. C.N. Ketov, I.N. Machulin, L.A. Mikaelyan
et al. Experiment in new statement on searching of
neutrino oscillations at the reactor // JETP Lett.
1992, v. 55, p. 44-552.
2. S.V. Bilen'ky, B.M. Pontekorvo. The theory
of neutrino oscillations // Rev. Mod. Phys. 1977,
v. 123, p. 181-194.
3. V.I. Kopeikin, L.A. Mikaelyan, V.V. Sinev.
Energy spectrum of reactor antineutrinos // Nucl.
Phys. 1997, v. 60, №2, p. 230-234 (in Russian).
4. V.D. Rusov. The probability-stochastic
models of ionizing radiation detection by solid
state detectors of nuclear tracks: identification and
quantitative analysis. Doctor of Math. & Phys.
Thesis, MIPhI, Moscow, 1992.
5. V.D. Rusov, T.N. Zelentsova, S.I. Kosenko,
M.M. Ovsyanko, I.V. Sharf. Cascade
parametrization of multiplicity distributions in
inelastic pp- and pp -inter-actions of energy
interval in c.m.s. √s=20-1800 GeV // Phys. Lett.
2001, v. B504, p. 213-217.
6. A.I. Afonin, S.N. Ketov, V.I. Kopeikin, L.A.
Mikaelyan, M.D. Skorokhvatov,
S.V. Tolokonnikov. Investigation of the
160
nepe +→+ +ν~ reaction in a nuclear reactor //
JETP. 1988, v. 94, №2, p. 1-17.
7. V.N. Vyrodov, Y. Declais, H. de Kerret et al.
Precision measurement of cross-section of the
reaction nepe +→+ +ν~ at the Bugey reactor
(France) // JETP Lett. 1995, v. 61, p. 161-167.
161
Table 1. Experimental and calculated parameters of reactor antineutrino statistics
REFERENCES
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