The mathematical model for decay curve of the nuclei-delayed neutron precursors in experiment at a pulsed electron linear accelerator
On the basis of the notion about six groups of nuclei as delayed neutron precursors, radioactive decay laws and the pulsed mode of accelerator operation, a relationship has been derived to describe the decay curve of nuclei-delayed neutron precursors as a function of the pulse rate of the accelera...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2009 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2009
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The mathematical model for decay curve of the nuclei-delayed neutron precursors in experiment at a pulsed electron linear accelerator / A.Yu. Buki, S.P. Gokov, O.A. Demeshko, V.I. Kasilov, K.S. Kokhnyuk, S.S. Kochetov, I.V. Mel’nitsky, I.L. Semisalov, A.A. Khomich, O.A. Shopen // Вопросы атомной науки и техники. — 2009. — № 5. — С. 95-100. — Бібліогр.: 9 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859717918441340928 |
|---|---|
| author | Buki, A.Yu. Gokov, S.P. Demeshko, O.A. Kasilov, V.I. Kokhnyuk, K.S. Kochetov, S.S. Mel’nitsky, I.V. Semisalov, I.L. Khomich, A.A. Shopen, O.A. |
| author_facet | Buki, A.Yu. Gokov, S.P. Demeshko, O.A. Kasilov, V.I. Kokhnyuk, K.S. Kochetov, S.S. Mel’nitsky, I.V. Semisalov, I.L. Khomich, A.A. Shopen, O.A. |
| citation_txt | The mathematical model for decay curve of the nuclei-delayed neutron precursors in experiment at a pulsed electron linear accelerator / A.Yu. Buki, S.P. Gokov, O.A. Demeshko, V.I. Kasilov, K.S. Kokhnyuk, S.S. Kochetov, I.V. Mel’nitsky, I.L. Semisalov, A.A. Khomich, O.A. Shopen // Вопросы атомной науки и техники. — 2009. — № 5. — С. 95-100. — Бібліогр.: 9 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | On the basis of the notion about six groups of nuclei as delayed neutron precursors, radioactive decay laws and the
pulsed mode of accelerator operation, a relationship has been derived to describe the decay curve of nuclei-delayed
neutron precursors as a function of the pulse rate of the accelerator, the exposure time, the observation time, the time
measurement interval and the number of measurement runs. A pilot experiment on thermal-neutron fission of 235U
has been conducted. The aim of the experiment was to check the hardware and the information readout computer
program. Based on the expressions derived, an analysis was performed and relative yields of delayed neutrons were
determined. The present results are compared to the data obtained by other authors. For further development of the
analysis, a question is brought up about the influence of additional conditions on the determination of relative delayedneutron
yields. These additional conditions can be represented by certain expressions laid down when measuring
delayed neutron yields directly between the accelerator pulses.
Виходячи з представлення про шiсть груп ядер-попередникiв запiзнiлих нейтронiв, законiв радiоактивного розпаду, i iмпульсного режиму роботи прискорювача, отримано спiввiдношення, що описує
криву розпаду ядер-попередникiв запiзнiлих нейтронiв у залежностi вiд частоти посилок прискорювача, часу експозицiї, часу спостереження, кроку вимiру за часом i кiлькостi циклiв вимiрiв. Проведено
пробний експеримент з подiлу 235U тепловими нейтронами. Мета експерименту - перевiрка апаратури
i комп’ютерної програми з’йому iнформацiї. На базi отриманих виражень проведено аналiз i визначено
вiдноснi виходи запiзнiлих нейтронiв. Результати порiвнюються з iншими роботами. Як перспектива
подальшого розвитку аналiзу, ставиться питання про вплив додаткових умов на визначення вiдносних
виходiв запiзнiлих нейтронiв. Такими додатковими умовами можуть бути деякi вирази, сформульованi
при вимiрi виходiв запiзнiлих нейтронiв безпосередньо мiж посилками прискорювача
Исходя из представления о шести группах ядер-предшественников запаздывающих нейтронов, законов
радиоактивного распада, и импульсного режима работы ускорителя, получено соотношение, описывающее кривую распада ядер предшественников запаздывающих нейтронов в зависимости от частоты
посылок ускорителя, времени экспозиции, времени наблюдения, шага измерения по времени и количества циклов измерений. Проведен пробный эксперимент по делению 235U тепловыми нейтронами.
Цель эксперимента - проверка аппаратуры и компьютерной программы съема информации. На базе
полученных выражений проведен анализ и определены относительные выходы запаздывающих нейтронов. Результаты сравниваются с другими работами. Как перспектива дальнейшего развития анализа, ставится вопрос о влиянии дополнительных условий на определение относительных выходов
запаздывающих нейтронов. Такими дополнительными условиями могут быть некоторые выражения,
сформулированные при измерении выходов запаздывающих нейтронов непосредственно между посылками ускорителя.
|
| first_indexed | 2025-12-01T08:35:45Z |
| format | Article |
| fulltext |
THE MATHEMATICAL MODEL FOR DECAY CURVE OF
THE NUCLEI-DELAYED NEUTRON PRECURSORS IN
EXPERIMENT AT A PULSED ELECTRON LINEAR
ACCELERATOR
A.Yu. Buki ∗, S.P. Gokov, O.A. Demeshko, V.I. Kasilov,
K.S. Kokhnyuk, S.S. Kochetov, I.V. Mel’nitsky, I.L. Semisalov,
A.A. Khomich, O.A. Shopen
National Science Center ”Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine
(Received July 24, 2009)
On the basis of the notion about six groups of nuclei as delayed neutron precursors, radioactive decay laws and the
pulsed mode of accelerator operation, a relationship has been derived to describe the decay curve of nuclei-delayed
neutron precursors as a function of the pulse rate of the accelerator, the exposure time, the observation time, the time
measurement interval and the number of measurement runs. A pilot experiment on thermal-neutron fission of 235U
has been conducted. The aim of the experiment was to check the hardware and the information readout computer
program. Based on the expressions derived, an analysis was performed and relative yields of delayed neutrons were
determined. The present results are compared to the data obtained by other authors. For further development of the
analysis, a question is brought up about the influence of additional conditions on the determination of relative delayed-
neutron yields. These additional conditions can be represented by certain expressions laid down when measuring
delayed neutron yields directly between the accelerator pulses.
PACS: 28.20-v
1. INTRODUCTION
The importance of the use of delayed neutrons in ap-
plied nuclear physics is widely recognized [1]. Among
the applications are the control and determination
of small amounts of fissile elements (uranium and
transuranium elements) in solid and liquid radioac-
tive wastes, in spent fuel elements, and also the
measurements of nuclear constants used in reac-
tor engineering (relative yield and half-life period
of certain groups of delayed neutrons). To determine
the nuclear-physical constants, the world practice
makes use of the fission processes of uranium, pluto-
nium and other nuclei in neutron/gamma-ray beams.
The beams may be both pulsed and continuous.
The neutron/gamma-ray beams can be generated in
different machines, including electron accelerators,
through the use of targets-converters. Work [2] can
serve an example of the use of a accelerator of con-
tinuous action . The electrostatic accelerator was
used there to obtain some nuclear-physical constants
necessary for the development of nuclear reactor en-
gineering. The research techniques for investigating
the composition of transuranium wastes with the use
of pulsed reactors are well developed in France [3].
Though the pulse techniques are more complicated
as compared to the continuous methods, yet they
have certain advantages. In the pulse technique,
delayed neutrons can be registered by two methods
during one measuring run. In the first method, de-
layed neutrons are registered between the machine
pulses in a certain time window chosen so as to reduce
the background. In the second method, the sample
is saturated with nuclei-delayed neutron precursors.
Then the beam is switched off and the decay curve
is measured. With machines of continuous action,
only the measurement of the decay curve is possible.
Since the delayed neutron yield registered between
the pulses and the decay curve are described by the
same parameters, the pulse technique is more infor-
mative, because it provides a joint analysis of the
data obtained by the two measuring methods. In our
papers [4-9], we have developed the methods for de-
termining fissile elements with the use of the pulsed
electron accelerator. These methods can find their
application in different countries (e.g., France, Rus-
sia, etc.), where nuclear engineering is developing.
Paper [8] was concerned with the first method of de-
layed neutron registration (between the accelerator
pulses). The present work is devoted to the second
method (decay curve measurement).
∗Corresponding author. E-mail address: khomichaa@kipt.kharkov.ua
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2009, N5.
Series: Nuclear Physics Investigations (52), p.95-100.
95
2. DERIVATION OF ANALYTIC
DEPENDENCE FOR THE DELAYED
NEUTRON YIELD UNDER THE DECAY
CURVE
2.1. Main assumptions and definitions
Let the accelerator pulse generate gi nuclei-
delayed neutron precursors of group i = (1, 2, ... , 6);
gi = const for all accelerator pulses; λi is the decay
constant of the group i precursor; f is the acceler-
ator pulse frequency (δt = 1/f is the time between
the pulses). We assume the machine pulse dura-
tion to be substantially shorter than the time be-
tween the pulses, therefore it will be neglected in our
further considerations. The last assumption follows
from the fact that the pulse duration is ≈ 1 · 10−6s,
while the interpulse interval at operating frequency
of 50Hz makes 0.02s. The computer program of
information readout and management is character-
ized by the exposure time texp = µδt, µ being the
number of pulses for the given time texp; the ob-
servation time tobs (in the general case we assume
texp 6= tobs); the time measurement interval tint (de-
cay curve integration step or the time observation
channel width), tint = const; the time observation
channel number-k; the number of measurement runs-
n. The measurement procedure includes the alter-
nating cycles of accumulation of nuclei-precursors for
the time texp = µδt and the cycles of observation
of delayed neutrons for the time tobs. The accumu-
lation cycle begins from the moment of accelerator
beam switching and ends as the time texp elapses with
the beam switched off. As the beam is switched off,
the observation cycle begins and lasts tobs seconds.
With the end of the observation cycle another accu-
mulation cycle starts, and so on. Under the above-
described assumptions, our task is to derive the ex-
pression, which describes the delayed neutron yield of
all groups in the k-th time channel for n cycles. We
divide the task into two stages. The first stage con-
sists in the derivation of expression for the number
of accumulated nuclei-precursors of the i-th group in
a certain arbitrary l-th cycle; the second stage lies in
the derivation of the final formula.
2.2. The number of accumulated
nuclei-precursors of the i-th group in an
arbitrary l-th cycle
We denote the unknown number of accumulated
nuclei-precursors of the i-th group in an arbitrary
l-th cycle as Nµl
i (this symbol indicates that the ac-
cumulation took place during µ accelerator pulses).
Let Nµ
i be the number of nuclei-precursors of the i-
th group, which were accumulated for µ accelerator
pulses in one cycle, and Nµ
i = const for all the cy-
cles. Then the number of precursors of group i, which
were accumulated in the first cycle is Nµ1
i = Nµ
i . The
number of precursors accumulated in the second cycle
is equal to
Nµ2
i = Nµ
i + Nµ
i e−λitobs = Nµ
i (1 + e−λitobs) .
For the third cycle we have:
Nµ3
i = Nµ
i (1 + e−λitobs + e−λi2tobs) .
Reasoning by induction, one can write down
Nµl
i = Nµ
i (1+e−λitobs +e−λi2tobs +...+e−λi(l−1)tobs) .
After finding the sum of geometrical progression, we
have:
Nµl
i = Nµ
i
1− e−λiltobs
1− eλitobs
. (1)
2.3. Derivation of the final formula
Using eq. (1), we find the number of i-th group de-
layed neutrons that came to the timing channel k in
the cycle l:
4Nµl
ik = Nµ
i
1− e−λiltobs
1− eλitobs
(e−λi(k−1)tint − e−λiktint) .
(2)
Summing expression (2) over l = (1, 2, . . . , n), we ob-
tain the number of i-th group delayed neutrons that
came to the timing channel k during all the given n
cycles:
4Nµ
ikn = Nµ
i
e−λi(k−1)tint − e−λiktint
1− e−λitobs
×
(n− e−λitobs − e−λi(n+1)tobs
1− e−λitobs
) . (3)
Summation of expression (3) over i gives the yield of
all the groups of delayed neutrons in the arbitrary
timing channel k for n measurement cycles
4Nµ
kn =
6∑
i=1
Nµ
i
e−λi(k−1)tint − e−λiktint
1− e−λitobs
×
(n− e−λitobs − e−λi(n+1)tobs
1− e−λitobs
) . (4)
It has been demonstrated in ref. [8] that Nµ
i can be
represented as:
Nµ
i = gi
e−λi/f
1− e−λi/f
(1− e−λiµδt) . (5)
In the following, formula (4) will be the basis for the
analysis of our preliminary experiment. If λi/f ¿ 1
for all neutron groups, then relation (5) can be rep-
resented in the following form:
Nµ
i = gi
f
λi
(1− e−λiµδt) = N0i(1− e−λiµδt), (6)
where N0i = limtexp→∞Nµ
i is the number of nuclei-
precursors of group i accumulated in the sample at
the cut-off time of the accelerator and at the start
of measuring the decay curve at a sufficiently great
texp. Practically, texp is approximately equal to 5T ,
where T is the half-life period of the most long-lived
group. In our experiment, f = 50 Hz and the con-
dition λi/f ¿ 1 can be fulfilled. So, in the analysis
of our preliminary experiment by formula (4) the Nµ
i
parameter was taken in the form of expression (6).
96
The aim of the analysis has been to estimate the rel-
ative yields of delayed neutrons under the decay curve
Di = N0i/
∑
N0i as well as the relative yields during
fission ai = gi/
∑
gi , and to compare them with the
available data. For further discussion we note that at
λi/f ¿ 1 these parameters can be represented as:
Di =
aiTi∑
aiTi
,
ai =
N0iλi∑
N0iλi
,
where Ti is the half-life period of the i-th group, the
other quantities being defined above.
3. EXPERIMENTAL SETUP AND THE
MEASURING TECHNIQUE
The experiment was performed at the NSC KIPT
300 MeV electron linear accelerator (LUE-300). The
main units of the facility include: the linear accel-
erator, the neutron-producing target, the sample to
be studied (a mixture of 238U and 235U with 2% of
235U), a polyethylene warmer, the Mac-Kiben detec-
tor to register neutrons (see for its details in ref. [9]).
A new element of the setup, as compared with the
cited work, is represented by a computer control of
both the process of information readout and the ex-
perimental conditions. The experiment on measuring
the decay curve of nuclei-delayed neutron precursors
was carried out at the energy of electrons incident
on the neutron-producing target E = 16 MeV , beam
current I = 34 µA, pulse frequency f = 50Hz. In
front of the sample there was placed a warmer, which
represented a polyethylene unit, 8cm in thickness. To
detect neutrons, the all-wave Mac-Kiben detector was
used. The program-controlled experimental condi-
tions were as follows: exposure time texp = 300 s, the
measurement interval tint = 1 s, the observation time
tobs = 300 s, the number of cycles n = 4. Considering
that the warmer was present in the experiment, in the
treatment of the experimental data it was assumed
that it was 235U which mainly fissioned. Figure
shows the results of decay curve measurements ver-
sus the time channel number (points with error bars).
Fig. The results of decay curve measurements
versus the time channel number
4. ANALYSIS OF THE EXPERIMENTAL
DATA AND PROSPECTS FOR
INVESTIGATIONS
Two analytic treatments have been performed. The
first treatment made use of the parameters ai taken
from work [2]. The aim of the given analysis was
to estimate N0i and the relative contributions from
different groups of delayed neutrons under the decay
curve Di = N0i/ΣN0i. The second direct determi-
nation of N0i from the analysis of the decay curve
made use of the least-squares method with a subse-
quent estimation of Di and ai. A question has been
brought up about additional conditions that exert
an influence on the determination of the sought-for
parameters. These additional conditions can be for-
mulated when registering delayed neutrons between
the accelerator pulses.
1. Using the relation ai = gi/
∑6
1 gi we write
down the parameters gi in terms of ai and substi-
tute the resuly into expression (6). Then formula (4)
takes on the form:
4Nµ
kn = βf
6∑
i=1
ai
λi
(1− e−λitexp)×
e−λi(k−1)tint − e−λiktint
1− e−λitobs
×
(n− e−λitobs − e−λi(n+1)tobs
1− e−λitobs
) , (7)
where β =
∑6
1 gi With the ai parameters for 235U
taken from ref. [2] and with the use of the least-
squares method, the model dependence was brought
into agreement with the experiment by varying the
parameter β, which physically presents (to an ac-
curacy of the proportionality factor) the number
of nuclei-precursors of all six groups generated by
one accelerator pulse. The fitting has resulted in
β = 16.71 ± 0.12,
∑
χ2
k/(N − 1) = 1.57, N = 78
being the number of points under the decay curve
(see Fig.1, solid curve). Note that in this analysis
only 78 experimental points were involved (we had
300 experimental values). This is explained by the
fact that the supplementation of experimental points
(more than 78) produces no essential effect on the de-
finable parameter β. With an increase in the number
of experimental points up to 300, the β value changes
only by 0.1%. and an experimental error in it of 0.7%.
The analysis under discussion well predicts the total
number of events under the decay curve. The ex-
periment gives the total number of events under the
decay curve to be 43087 ± 208. The model value
of this parameter can be estimated by the formula:
4 ·∑6
1 N0i, where N0i is the second column of Tab.1
(N0i = fai
∑
gi/λi, ai, λi are taken from ref. [2],∑
gi - our analysis). The fourth column of Table1
gives the relative yields of delayed neutron groups
under the decay curve: Di = N0i/
∑
N0i (N0i is the
second column of Table 1).
97
Table. 1. The number of nuclei-precursors of group i accumulated for one measurement cycle-N0i,
and the relative yield of the i-th group delayed neutrons under the decay curve-Di. Here we used the
following designations: Ng-Group number; N∗
0i-Calculated, using parameters from [2]; N∗∗
0i -Our data;
D∗
i -Calculated, using parameters from [2]; D∗∗
i -Our data
Ng N∗
0i N∗∗
0i D∗
i D∗∗
i
1 2476± 94 2469± 118 0.228± 0.09 0.246± 0.014
2 5685± 90 4941± 192 0.524± 0.010 0.492± 0.025
3 1523± 26 1561± 191 0.140± 0.003 0.155± 0.019
4 1078± 13 1007± 139 0.099± 0.002 0.100± 0.014
5 78± 2 68± 48 0.007± 0.0002 0.007± 0.005
6 6± 1 −3± 2.6
5± 4 0.0005± 0.0001 0.0005± 0.0004
2. For the analysis, formula (4) was taken in the
following form:
4Nµ
kn =
6∑
i=1
N0i
(
1− e−λitexp
)×
e−λi(k−1)tint − e−λiktint
1− e−λitobs
×
(
n− e−λitobs − e−λi(n+1)tobs
1− e−λitobs
)
, (8)
where N0i represents the sought-for parameters.
From the condition: ∂χ2/∂N0i = 0 a set of lin-
ear equations was formulated, and N0i was deter-
mined with the least-squares method. This analysis
has involved 240 experimental points. A further
increase in the number of experimental points for
the analysis does not change the N0i values. For
control, the set was solved in two ways using the
Cramer and the Gauss method. In this case, it ap-
peared that the quality of agreement between the
analytic curve and the experiment is characterized as∑
χ2
k/(N − P ) = 1, 1, (N = 240, P = 6). On finding
N0i, relative yields of delayed neutrons were deter-
mined both under the decay curve: Di = N0i/
∑
N0i
and under fission: ai = N0λi/
∑
N0λi. The N0i val-
ues are listed in the third column of Table 1. It can
be seen from the table that N06 = −3 ± 2.6, this
having, unfortunately, no physical meaning. The
estimation of N06 with physical meaning was per-
formed using the expression: N06 = N05λ5a6/λ6a5 ,
where N05 was taken from our analysis, while the
other parameters were taken from ref. [2]. The Di
values are presented in the fifth column of Table 1.
The comparison of the N0i and Di values obtained in
this section with similar values of the previous sec-
tion (see table 1) shows them to be coincident within
the experimental error (the exception is the second
group). A comparatively great error is caused by the
fact that in the preliminary experiment there were
only 4 measurement cycles. Table 2 gives the values
of relative yields ai. It is obvious from the table 2 that
within the experimental error the ai values agree very
closely with the results of ref. [2]. To conclude the
analysis, we formulate below possible additional con-
ditions for the search for the decay curve parameters.
Table 2. Relative delayed neutron yields of six
groups in thermal-neutron fission of 235U
Ng ai − our data ai − from[2]
1 0.041± 0.003 0.038± 0.001
2 0.197± 0.014 0.211± 0.004
3 0.217± 0.026 0.197± 0.004
4 0.397± 0.064 0.396± 0.005
5 0.123± 0.081 0.132± 0.004
6 0.025± 0.020 0.026± 0.001
5. ADDITIONAL CONDITIONS ON THE
SEARCH FOR THE DECAY CURVE
PARAMETERS
We now formulate additional conditions on the search
for the decay curve parameters that can be obtained
when registering neutrons between the accelerator
pulses. In the preliminary experiment considered
above, the measurements of delayed neutron yields
between the pulses were not performed. Therefore,
the conditions formulated below can be considered
as a prospect for further investigations of the decay
curve. At λi/f ¿ 1 , the following expressions are
valid:
∑
N0i = fT
∑
gi/ln 2, where T =
∑
aiTi, ai
are the relative yields of delayed neutrons, Ti are the
half-lives of nuclei-precursors. It has been demon-
strated in paper [8] that if, at least, two measure-
ments of delayed neutron yields are made with regis-
tration between the accelerator pulses with the times
of exposure t1 >> 1/λi and t2 >> 1/λi (for definite-
ness, we assume that t2 > t1), then T and
∑
gi can
be determined from the following equations:
N(t2)
N(t1)
=
t2 ln 2− T
t1 ln 2− T,
,
∑
gi =
(N(t2)−N(t1))δt
(tend − tin)(t2 − t1)f
,
where N(t1) and N(t2) are the delayed neutron yields
for the exposures t1 and t2, tend - tin is the time ob-
servation channel width, tin is the start time, tend
is the end time point (the time is computed from
the moment of the accelerator pulse), the remaining
parameters are described above. So, performing the
98
experiment between the pulses, we can formulate ad-
ditional conditions on the search for the parameters
of the decay curve in the following form:
∑
N0i − fT
∑
gi/ln 2 = 0, .
Besides, the delayed neutron yield registered between
the accelerator pulses for the time texp [8] can be an
additional condition in the search of the decay curve
parameters, because this yield and the decay curve
are described by the same parameters:
N(texp) =
∑
gi
e−λitin − e−λitend
1− e−λi/f
×
(
f · texp − e−λi/f
1− e−λi/f
(
1− eλitexp
))
. (9)
In finding the parameters by the least-squares
method at additional conditions, the accuracy of the
sought-for parameters often gets improved. In future,
we expect to investigate the influence of the men-
tioned additional conditions obtained between the ac-
celerator pulses on the accuracy of determination of
decay curve parameters. Technically, the task is re-
duced to finding the constrained minimum of the χ2
function and can be solved by the Lagrange method
of undetermined coefficients.
6. CONCLUSIONS
1. An analytic representation of the decay curve
has been obtained for the analysis and design of ex-
periments.
2. A preliminary experiment has been performed
to check the instrumentation and the computer infor-
mation readout program.
3. The results of experimental data analysis are
in agreement within the experimental error with the
data of paper [2].
4. The question has been brought up about ad-
ditional conditions that exert influence on the deter-
mination of decay curve parameters.
References
1. V.V. Frolov. Nuclear techniques to control
fissionable materials. M: ”Ehnergoatomizdat”
1989, 178p. (In Russian).
2. V.M. Piksaikin, L.E. Kazakov, G.G. Korolyov,
S.G. Isayev, V.A. Roshchenko, M.Z. Tarasko.
The relative yield and period of some delayed
neutron groups at fission of 233U , 235U , 239Pu
by epithermal neutrons // Atomnaya Ehnergiya.
2000, v.92, p.135-143 (In Russian).
3. A. Lyoossi, J. Romeyer-Dherbey, F. Jallu, et al.
Transuranic waste detection by photon interro-
gation and on-line delayed neutron counting //
Nuclear Instruments and Methods in Physics Re-
search. 2000, v.B160, p.280-289.
4. A.Yu. Buki, V.Y. Kasilov, V.V. Kirichenko, et al.
Development of the industrial technique to deter-
mine the fissionable material concentration using
the electron linac as the base // Atomna Ehner-
getika ta Promyslovist’ Ukrainy. 2000, N2, p.24-
25 (In Ukrainian).
5. V.I. Kasilov, V.V. Kirichenko, L.A. Makhnenko,
et al. About possible determination of the 238U
content in concrete samples by means of the elec-
tron linac. Atomna Ehnergetika ta Promyslovist’
Ukrainy. 2000, N2, p.50-51 (In Russian).
6. R.P. Slabospitsky, S.S. Kochetov, V.V.
Kirichenko. Rapid radioactive waste sorting
system using the electron linac. Preprint KhFTI
2002-1. Kharkov, NSC KIPT , 2002, 19p.(In
Russian).
7. S.S. Kochetov, R.P. Slabospitsky,
V.V. Kirichenko. The use of the electron
linac for determining fissionable materials in
radioactive wastes // Visnyk Kharkivs’kogo
Universytetu, ser. fizychna ”Yadra, chastynky,
polya”. 2002, v.B.2(20), N.574, p.71-80 (In
Russian).
8. A.A. Khomich, V.I. Kasilov, V.V. Kirichenko,
et al. The model of delayed neutron yield in
the experiment at the pulsed electron linac //
Visnyk Kharkivs’kogo Universytetu, ser. fizychna
”Yadra, chastynky, polya”. 2006, v.B2(30), N732,
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9. A.Yu. Buki , V.I.Kasilov , V.V. Kirichenko,
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prosy Atomnoj Nauki i Tekhniki. Ser. ”yaderno-
fizicheskaya”. 2000, v. 2(36), p.64-65.
МАТЕМАТИЧЕСКAЯ МОДЕЛЬ КРИВОЙ РАСПАДА ЯДЕР,
ПРЕДШЕСТВЕННИКОВ ЗАПАЗДЫВАЮЩИХ НЕЙТРОНОВ, В ЭКСПЕРИМЕНТЕ
НА ИМПУЛЬСНОМ ЛИНЕЙНОМ УСКОРИТЕЛЕ ЭЛЕКТРОНОВ
А.Ю. Буки, С.П. Гоков, О.А. Демешко, В.И. Касилов, К.C. Кохнюк, С.С. Кочетов,
И.В. Мельницкий, И.Л. Семисалов, А.A. Хомич, О.A. Шопен
Исходя из представления о шести группах ядер-предшественников запаздывающих нейтронов, законов
радиоактивного распада, и импульсного режима работы ускорителя, получено соотношение, описыва-
99
ющее кривую распада ядер предшественников запаздывающих нейтронов в зависимости от частоты
посылок ускорителя, времени экспозиции, времени наблюдения, шага измерения по времени и коли-
чества циклов измерений. Проведен пробный эксперимент по делению 235U тепловыми нейтронами.
Цель эксперимента - проверка аппаратуры и компьютерной программы съема информации. На базе
полученных выражений проведен анализ и определены относительные выходы запаздывающих ней-
тронов. Результаты сравниваются с другими работами. Как перспектива дальнейшего развития ана-
лиза, ставится вопрос о влиянии дополнительных условий на определение относительных выходов
запаздывающих нейтронов. Такими дополнительными условиями могут быть некоторые выражения,
сформулированные при измерении выходов запаздывающих нейтронов непосредственно между посыл-
ками ускорителя.
МАТЕМАТИЧНА МОДЕЛЬ КРИВОЇ РОЗПАДУ ЯДЕР, ПОПЕРЕДНИКIВ
ЗАПIЗНIЛИХ НЕЙТРОНIВ, В ЕКСПЕРИМЕНТI НА IМПУЛЬСНОМУ ЛIНIЙНОМУ
ПРИСКОРЮВАЧI ЕЛЕКТРОНIВ
О.Ю. Букi, С.П. Гоков, О.О. Демешко, В.Й. Касилов, К.C. Кохнюк, С.С. Кочетов,
I.В. Мельницький, I.Л. Семiсалов, А.A. Хомич, О.О. Шопен
Виходячи з представлення про шiсть груп ядер-попередникiв запiзнiлих нейтронiв, законiв радiоак-
тивного розпаду, i iмпульсного режиму роботи прискорювача, отримано спiввiдношення, що описує
криву розпаду ядер-попередникiв запiзнiлих нейтронiв у залежностi вiд частоти посилок прискорюва-
ча, часу експозицiї, часу спостереження, кроку вимiру за часом i кiлькостi циклiв вимiрiв. Проведено
пробний експеримент з подiлу 235U тепловими нейтронами. Мета експерименту - перевiрка апаратури
i комп’ютерної програми з’йому iнформацiї. На базi отриманих виражень проведено аналiз i визначено
вiдноснi виходи запiзнiлих нейтронiв. Результати порiвнюються з iншими роботами. Як перспектива
подальшого розвитку аналiзу, ставиться питання про вплив додаткових умов на визначення вiдносних
виходiв запiзнiлих нейтронiв. Такими додатковими умовами можуть бути деякi вирази, сформульованi
при вимiрi виходiв запiзнiлих нейтронiв безпосередньо мiж посилками прискорювача.
100
|
| id | nasplib_isofts_kiev_ua-123456789-96514 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-01T08:35:45Z |
| publishDate | 2009 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Buki, A.Yu. Gokov, S.P. Demeshko, O.A. Kasilov, V.I. Kokhnyuk, K.S. Kochetov, S.S. Mel’nitsky, I.V. Semisalov, I.L. Khomich, A.A. Shopen, O.A. 2016-03-17T20:49:39Z 2016-03-17T20:49:39Z 2009 The mathematical model for decay curve of the nuclei-delayed neutron precursors in experiment at a pulsed electron linear accelerator / A.Yu. Buki, S.P. Gokov, O.A. Demeshko, V.I. Kasilov, K.S. Kokhnyuk, S.S. Kochetov, I.V. Mel’nitsky, I.L. Semisalov, A.A. Khomich, O.A. Shopen // Вопросы атомной науки и техники. — 2009. — № 5. — С. 95-100. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 28.20-v https://nasplib.isofts.kiev.ua/handle/123456789/96514 On the basis of the notion about six groups of nuclei as delayed neutron precursors, radioactive decay laws and the pulsed mode of accelerator operation, a relationship has been derived to describe the decay curve of nuclei-delayed neutron precursors as a function of the pulse rate of the accelerator, the exposure time, the observation time, the time measurement interval and the number of measurement runs. A pilot experiment on thermal-neutron fission of 235U has been conducted. The aim of the experiment was to check the hardware and the information readout computer program. Based on the expressions derived, an analysis was performed and relative yields of delayed neutrons were determined. The present results are compared to the data obtained by other authors. For further development of the analysis, a question is brought up about the influence of additional conditions on the determination of relative delayedneutron yields. These additional conditions can be represented by certain expressions laid down when measuring delayed neutron yields directly between the accelerator pulses. Виходячи з представлення про шiсть груп ядер-попередникiв запiзнiлих нейтронiв, законiв радiоактивного розпаду, i iмпульсного режиму роботи прискорювача, отримано спiввiдношення, що описує криву розпаду ядер-попередникiв запiзнiлих нейтронiв у залежностi вiд частоти посилок прискорювача, часу експозицiї, часу спостереження, кроку вимiру за часом i кiлькостi циклiв вимiрiв. Проведено пробний експеримент з подiлу 235U тепловими нейтронами. Мета експерименту - перевiрка апаратури i комп’ютерної програми з’йому iнформацiї. На базi отриманих виражень проведено аналiз i визначено вiдноснi виходи запiзнiлих нейтронiв. Результати порiвнюються з iншими роботами. Як перспектива подальшого розвитку аналiзу, ставиться питання про вплив додаткових умов на визначення вiдносних виходiв запiзнiлих нейтронiв. Такими додатковими умовами можуть бути деякi вирази, сформульованi при вимiрi виходiв запiзнiлих нейтронiв безпосередньо мiж посилками прискорювача Исходя из представления о шести группах ядер-предшественников запаздывающих нейтронов, законов радиоактивного распада, и импульсного режима работы ускорителя, получено соотношение, описывающее кривую распада ядер предшественников запаздывающих нейтронов в зависимости от частоты посылок ускорителя, времени экспозиции, времени наблюдения, шага измерения по времени и количества циклов измерений. Проведен пробный эксперимент по делению 235U тепловыми нейтронами. Цель эксперимента - проверка аппаратуры и компьютерной программы съема информации. На базе полученных выражений проведен анализ и определены относительные выходы запаздывающих нейтронов. Результаты сравниваются с другими работами. Как перспектива дальнейшего развития анализа, ставится вопрос о влиянии дополнительных условий на определение относительных выходов запаздывающих нейтронов. Такими дополнительными условиями могут быть некоторые выражения, сформулированные при измерении выходов запаздывающих нейтронов непосредственно между посылками ускорителя. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Ядернo-физические методы и обработка данных The mathematical model for decay curve of the nuclei-delayed neutron precursors in experiment at a pulsed electron linear accelerator Математична модель кривої розпаду ядер, попередникiв запiзнiлих нейтронiв, в експериментi на iмпульсному лiнiйному прискорювачi електронiв Математическaя модель кривой распада ядер, предшественников запаздывающих нейтронов, в эксперименте на импульсном линейном ускорителе электронов Article published earlier |
| spellingShingle | The mathematical model for decay curve of the nuclei-delayed neutron precursors in experiment at a pulsed electron linear accelerator Buki, A.Yu. Gokov, S.P. Demeshko, O.A. Kasilov, V.I. Kokhnyuk, K.S. Kochetov, S.S. Mel’nitsky, I.V. Semisalov, I.L. Khomich, A.A. Shopen, O.A. Ядернo-физические методы и обработка данных |
| title | The mathematical model for decay curve of the nuclei-delayed neutron precursors in experiment at a pulsed electron linear accelerator |
| title_alt | Математична модель кривої розпаду ядер, попередникiв запiзнiлих нейтронiв, в експериментi на iмпульсному лiнiйному прискорювачi електронiв Математическaя модель кривой распада ядер, предшественников запаздывающих нейтронов, в эксперименте на импульсном линейном ускорителе электронов |
| title_full | The mathematical model for decay curve of the nuclei-delayed neutron precursors in experiment at a pulsed electron linear accelerator |
| title_fullStr | The mathematical model for decay curve of the nuclei-delayed neutron precursors in experiment at a pulsed electron linear accelerator |
| title_full_unstemmed | The mathematical model for decay curve of the nuclei-delayed neutron precursors in experiment at a pulsed electron linear accelerator |
| title_short | The mathematical model for decay curve of the nuclei-delayed neutron precursors in experiment at a pulsed electron linear accelerator |
| title_sort | mathematical model for decay curve of the nuclei-delayed neutron precursors in experiment at a pulsed electron linear accelerator |
| topic | Ядернo-физические методы и обработка данных |
| topic_facet | Ядернo-физические методы и обработка данных |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/96514 |
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