The journal of Nuclear Science and Technology - Volume 10, Number 1, March 2020
ISSN 1810-5408
Nuclear Science
and Technology
Volume 10, Number 1, March 2020
Published by
VIETNAM ATOMIC ENERGY SOCIETY
VIETNAM ATOMIC ENERGY INSTITUTE
NUCLEAR SCIENCE AND TECHNOLOGY
Volume 10, Number 1, March 2020
Editorial Board
Editor-in-chief
Tran Huu Phat (VINATOM)
Executive Editors
Vuong Huu Tan (VARANS)
Tran Chi Thanh (VINATOM)
Cao Dinh Thanh (VINATOM)
Hoang Anh Tuan (VAEA)
Editors
Nguyen Kien Cuong (VINATOM)
Nguyen Nhi Dien (VINATOM)
Nguyen Thi Kim Dung (VINATOM)
Ho Manh Dung (VINATOM)
Nguyen Nam Giang (VINATOM)
Trinh Van Giap (VINATOM)
Le Ngoc Ha (108 Military Central Hospital)
Phan Son Hai (VINATOM)
Le Hong Khiem (IOP)
Dao Tien Khoa (VINATOM)
Tran Hoai Nam (Duy Tan University)
Dang Duc Nhan (VINATOM)
Nguyen Hao Quang (VINATOM)
Nguyen Mong Sinh (VINATOM)
Tran Duc Thiep (IOP)
Dang Quang Thieu (VINATOM)
Le Ba Thuan (VINATOM)
Le Huy Ham (VAAS)
Nguyen Quoc Hien (VINATOM)
Le Van Hong (VINATOM)
Nguyen Trung Tinh (VARANS)
Tran Ngoc Toan (VINATOM)
Duong Thanh Tung (VARANS)
Nguyen Nu Hoai Vi (VARANS)
Nguyen Tuan Khai (VINATOM)
Pham Dinh Khang (VINATOM)
Science Secretary
Hoang Sy Than (VINATOM)
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Copyright: ©2008 by the Vietnam Atomic Energy Society (VAES), Vietnam Atomic Energy Institute
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Pusblished by
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Contents
Investigation of the same isomeric pair, produced from different nuclear reactions
Tran Duc Thiep, Truong Thi An, Bui Minh Hue, Phan Viet Cuong, Nguyen
01
11
Hong Ha, A. G. Belov, S. Mitrofanov……………………………………………..……..
Determination of thermal neutron flux distribution at the rotary rack served for
elemental concentration analysis using the k0-INAA method
Nguyen Thi Tho, Tran Tuan Anh, Trinh Van Cuong, Ho Van Doanh, Tran
Quoc Duong, Ho Manh Dung……………………………………………………………..
Evaluation of slip ratio correlations in two-phase flow
Thanh Tram Tran, Hyun Sik Park………………………………………………………….... 21
Deposition velocities of some natural radionuclides from the atmosphere at Ninh
Thuan and Dong Nai of Vietnam
Nguyen Van Phu, Le Nhu Sieu, Tran Dinh Khoa, Nguyen Dinh Tung, Nguyen Thi
31
Thanh Nga, Truong Y…………………………………………………………………………
Determination of recovery efficiency of 137Cs in seawaterusing co-precipitation method
Duong Duc Thang, Vuong Thu Bac, Bui Dac Dung, Duong Van Thang, Doan Thuy
Hau, Le Dinh Cuong, Nguyen Van Khanh, Nguyen Thi Thu Ha, Cao Duc Viet,
Nguyen Huyen Trang, Nguyen Thi Oanh, Le Thị Hoa.................................................. 40
Maillard reaction products of chitosan and glucosamine: antibacterial and
antioxidant activity
Le Anh Quoc, Dang Van Phu, Nguyen Ngoc Duy, Nguyen Quoc Hien, Ngo
47
Dai Nghiep…………………………………………………………………………………...
Nuclear Science and Technology, Vol.10, No. 1 (2020), pp. 01-10
Investigation of the same isomeric pair, produced from
different nuclear reactions
Tran Duc Thiep1, 2*, Truong Thi An1, Bui Minh Hue1, 2**, Phan Viet Cuong3,
Nguyen Hong Ha1, A. G. Belov4, S. Mitrofanov4
1Institute of Physics, VAST, 10 Dao Tan St., Ba Dinh Dist., Hanoi, Vietnam
2Grad. University of Science and Technology, VAST, 18 H. Q. Viet, Hanoi, Vietnam
3Danang Irradiation Center, VINATOM, Danang City, Vietnam
4Flerov Laboratory of Nuclear Reactions, JINR, 141980 Dubna, Moscow, Russia
*Corresponding author: <[email protected]>
(Received 05 March 2020, accepted 10 March 2020)
Abstract The isomeric ratio (IR) of isomeric pair 109m,gPd, produced in 110Pd(γ, n)109m,gCd reaction
and 108Pd(n, γ)109m,gPd neutron capture reactions, induced by thermal, epithermal and mixed
thermal-epithermal neutrons have been determined. The off-line activation technique using a
spectroscopic system consisting of a HPGe semiconductor detector with high energy resolution and
a PC based 8192 channel analyzer (CANBERRA) was applied. The investigated samples were
prepared from the 99.99 % purity PdO and irradiated at the electron accelerator Microtron MT-25
of the Joint Institute for Nuclear Research Dubna, Russia. The data analysis and necessary
corrections were made to upgrade the precision of the experimental method. The obtained results
were discussed, compared and combined with those from other authors to point out the role of the
reaction channels in nuclear reactions.
Keywords: Photonuclear reaction - neutron capture reactions - isomeric ratio – isomeric pair
109m,gPd – intake impulse – transfer momentum - reaction channel effect.
intermediate state structure, nuclear channel
effect, the contributions of direct and pre-
equilibrium processes and so on [1 - 16]. N.
Tsoneva et al [3] measured the IRs in (γ, n)
reactions in N = 81 isotone nuclei (137Ba, 139Ce,
141Ba and 143Ba) and showed that in the isotone
nuclei, the IRs depend on the mass numbers.
This is the so called nucleon configuration
effect and was also observed in [3 - 6]. In ref.
[4] we have studied the IRs of (γ, n) nuclear
reactions in Z = 56 isotopes of Ba and the
isomeric pairs 129m,gBa, 131m,gBa and 133Ba were
formed with the same spin ground state 1+/2
and isomeric states of spins 7+/2, 9-/2 and 11-/2,
respectively. The results showed that the IR
decreases with the increase of the isomeric
I. INTRODUCTION
The product of a nuclear reaction can
exist in the isomeric or ground states. The ratio
of the cross sections or the yields (in the case
of continuous excitation energy spectrum) of
these two states is the so called isomeric ratio
(IR), which furnishes important information on
nuclear level structure, level density, namely
the spin cut-off parameter σ and the level
density parameter a as well as nuclear reaction
mechanism. In fact this ratio is connected to
different nuclear effects as the excitation
energy, momentum transfer, spins of the
isomeric and ground states and their
dependence,
nucleon
configuration,
©2020 Vietnam Atomic Energy Society and Vietnam Atomic Energy Institute
INVESTIGATION OF THE SAME ISOMERIC PAIR, PRODUCED FROM ...
state spin. This effect is the so called isomeric
neutrons, gamma-rays, protons, deuterons,
tritons, helions, and alpha-particles, in the 1
keV - 200 MeV energy range. This work aims
at studying the isomeric pair 109m,gPd, produced
from 110Pd(γ, n)109m,gPd photonuclear reaction
and 108Pd(n, γ)109m,gPd neutron capture reaction,
induced by thermal, epithermal and mixed
thermal-epithermal neutrons. The obtained
experimental results could provide the data for
the nuclear model test as well as for practical
applications of nuclear technology.
state spin dependence. The other effect, which
is also concerned the spins is that the higher
the isomeric state spin, the smaller the IR can
be found in [7, 8]. M. Huber et al [9] and J. J
Carroll et al [10] pointed out the important role
of intermediate states on the mechanism of
population of the isomeric and ground states.
Up to now the famous statistical model of
Huizenga and Vandenbosch [1, 2] has been
applied to consider the IR in nuclear reactions
induced by different projectiles. S. Mukherjee
et al [11] studied the nuclear reaction induced
II. EXPERIMENTAL
93
by α particle on Nb nucleus and came to the
A. Irradiation sources and sample preparation
conclusion that the angular momentum
removal in the pre-equilibrium emission play a
major role in the formation of the isomers and
hence in the measurement of IR. S. Sudar and
S. M. Qaim in [12] used the STAPRE code in a
In this study, the bremsstrahlung photon
flux, produced by the electron accelerator
Microtron MT-25 of the Flerov Laboratory of
Nuclear Reactions, JINR Dubna, Russia [22]
was used for performing the photonuclear
reaction. This accelerator produces 10 to 25
MeV electron beam with 1 MeV energy step
and the energy spread of the accelerated
electrons is small (30- 40 keV for up to 600 W
of average beam power) allows the
measurement of the IR at strictly defined end-
point energy bremsstrahlung.
combination
of
the
Hauser-Feshbach
(statistical model) and exciton model (pre-
equilibrium effects) formalisms to consider
their experimental results for the excitation
functions and IRs in nuclear reactions, induced
3
by α and He particles. They showed that the
level density parameters and the spin of
residual nucleus play important role in the
calculated IRs as well as in formation of the
isomeric states. All most the researches in
photonuclear reactions in the giant dipole
resonant (GDR) region show that the IR of
high spin state to that of low spin state
increases with the increase of end-point
bremsstrahlung energy [3 - 6, 13 - 16].
The source of thermal, epithermal and
mixed thermal-resonant
neutrons
was
constructed at the Microtron MT-25 by using
a graphite cub as depicted in Fig. 1. The
neutron beam was obtained by (γ, n) reactions
with Be and U and (γ, f) fission reaction of U
when the electron beam was directed to a
uranium electron-photon converter. The
uranium-beryllium converter was also served
as a main neutron moderator to thermal and
epithermal energy neutrons. The thermal
neutron flux at the center of the cube was
4.108 neutrons/s.cm2 with an electron energy
of 25 MeV and a current of 20 μA. The
Recently, the study of IR has been an
effective tool to check different models of
nuclear reaction by computation programs, in
which it is worth mentioning the Talys
program [17] and its applications [18 - 21].
Talys code is a nuclear reaction program,
which simulates nuclear reactions that involve
2
TRAN DUC THIEP et al.
detailed construction of this neutron source
reactions, caused by the neutron background
from reactions on the accelerating structure
or the breaking target itself, the sample was
covered by cadmium foil of 2 mm thickness.
In the case of neutron capture reactions with
thermal, resonant and thermal-resonant
mixed neutrons, the sample was uncovered
or covered in Cd foil of 2 mm thickness and
placed at 40 cm distance from the center of
the graphite cube, where the Cd ratio was
2.5. In both bremsstrahlung and neutron
irradiations, the average electron current
was of 15 μA and the irradiation time – 90
min., which were estimated so that the
counts of the interested gamma rays of the
isomeric and ground states to ensure a good
count statistics.
can be found in refs. [23, 24].
The investigated samples were prepared
from the 99.99 % purity PdO, packed in
polyethylene wrap in disk shape with diameter
of 1.0 cm. The sample mass was chosen to be
of 0.3230 g, which was proper for the study of
both (γ, n) and (n, γ) capture reactions.
B. Sample irradiation and measurement
For 110Pd(γ, n)109m,gPd reaction
investigation, the sample was placed at the
axis of the electron beam with 2 cm from
the aluminum absorber of MT-25 and
irradiated by the bremsstrahlung flux of 24
MeV end-point energy for 30 minutes. To
avoid the interference from (n, γ) capture
Fig. 1. The scheme for production of thermal and epithermal neutron source.
After a definite cooling time, the γ-ray
to 1 - 2 %. The detailed information of the
measuring system can be found in [4 - 5].
activities of the investigated samples were
measured with
a
spectroscopic system
III. DATA ANALYSIS AND ISOMERIC
RATIO DETERMINATION
consisting of a coaxial p-type HPGe detector
with a diameter of 60.5 mm and a length of 31
mm, connected to a PC based 8192 channel
analyzer (CANBERRA) for the data
processing. The resolution of the detector
system was 1.8 keV FWHM at the 1332.5 keV
γ-ray photo-peak of 60Co. The efficiencies of
the detector were determined with a set of
standard single gamma ray sources calibrated
The 110Pd(γ, n) reaction, excited by
bremsstrahlung and 108Pd(n, γ) reactions,
induced by thermal, resonant and thermal-
resonant mixed neutrons produce the same
isomeric pair 109m,gPd. Fig. 2 depicts the
simplified decay schemes of isomeric and
ground states 109mPd and 109gPd.
3
INVESTIGATION OF THE SAME ISOMERIC PAIR, PRODUCED FROM ...
Fig. 2. The simplified schemes of the isomeric and ground states of 109m,gPd.
Table I. The decay characteristics and gamma rays used in the isomeric ratio calculation
of the isomeric pair 109m,gPd.
Nuclear
Reaction
Target
Spin, Parity
[Jπ]
Nuclear
state
Spin
Parity
[Jπ]
Decay
Mode
[%]
Half
Life
γ-ray
Energy
[keV]
Intensity
[%]
108Pd(n, γ)
0+
109mPd
11/2-
IT: 100
4.69 m
13.7 h
189.0
55.9
3.6
109mPd
108Pd(n, γ)
0+
109gPd
5/2+
β- : 100
88.04
109gPd
Table I shows the decay characteristics
and γ-rays used for the IR calculation of
isomeric pairs 109m,gPd and 111m,gPd. The
criterion for choosing the gamma rays in this
table were the followings: a/ Their intensities
are higher than that of other gamma rays, b/
They are separated in the gamma spectra and c/
They are free of the contributions from the
products of other nuclear reactions with natural
palladium. The data in this table were taken
from [25, 26].
(1)
(2)
t
1et
Fg
Where fi - the fraction of coincidence
photons of energy i in coincidence with the
gamma ray of interest and t (i) - the total
efficiency of the coincidence photon of energy
i and Cc - the correction factor; µ - the linear
attenuation coefficient, t - the sample thickness
and Fg is defined as the ratio of the true and
measured counts of the interested gamma rays.
In our experiment Cc was found to be 1.0 and
1.0; and Fg were 1.26 and 1.05 for 88.0 and
189.0 keV, respectively at the distance of 0 and
5 cm from the detector.
The losses of gamma ray activities due
to the self-absorption and coincident summing
effects, which lead to the error in the isomeric
ratio determination, were corrected by
formulas (1) and (2), taken from refs. [27, 28],
respectively as below:
4
TRAN DUC THIEP et al.
The IR was calculated based on the
counts of -rays characterizing the isomeric
and ground states measured for the definite
times of irradiation, cooling and counting. The
calculation procedure is the same, which has
been presented in refs. [16, 27] by using the
following expression:
The total uncertainty of the isomeric
ratio determination was estimated to be 10%. It
consists of the systematic errors, including
those from the distance from the detector to
sample, the gamma ray selection, the electron
beam variation, the irradiation and cooling
times and that, calculated by the error
propagation principle of the expression (3).
Sgm Im
369 158 358 367
Smg Ig
1
IV. RESULTS AND DISCUSSION
IR
258
(3)
Fig. 3 shows a typical spectrum of natural
Pd, irradiated with 24 MeV bremsstrahlung for
20 min. and measured for 10 min. after 40 min
cooling time. Fig. 4 presents a spectrum of
natural Pd irradiated by neutron for 1.5 h,
measured for 30 min and cooling time of 11 min.,
measured at 0 cm distance from the detector.
Where m and g - the isomeric and
ground states; S, and I - the counts, the
efficiencies and the intensities of the interested
gamma rays and Λi (i = 1 ~ 9) are expressions
related to the irradiation, cooling and
measurement times.
Fig. 3. A typical spectrum of natural Pd, irradiated with 24 MeV bremsstrahlung for 20 min. and measured
for 10 min. after 40 min cooling time, measured at 5 cm from the detector.
Natural palladium consists of 102Pd,
104Pd, 105Pd, 106Pd, 108Pd and 110Pd with the
abundances of 1.020, 11.14, 22.33, 27.33,
26.46 and 11.72%, respectively. Through
photonuclear reactions, only one isomeric pair
109m,gPd was formed in 110Pd(γ, n)109Pd
reaction, while two isomeric pairs 109m,gPd and
111m,gPd were produced in 108Pd(n, γ)109m,gPd
and 110Pd(n, γ)111m,gPd neutron capture
reactions. One can see that the characteristic
gamma rays of the isomeric and ground states
of the isomeric pairs 109m,gPd are seen very
clearly in the spectra. Table II presents the
IRs in 110Pd(γ, n)109m,gPd reaction, 108Pd(n,
5
INVESTIGATION OF THE SAME ISOMERIC PAIR, PRODUCED FROM ...
γ)109m,gPd capture reactions induced by
interpretation, the IRs for 110Pd(n, 2n)109Pd
reactions are also shown hereby [14, 31]. In
Table II are also presented the reaction
product excitation energies.
thermal, resonant and mixed thermal-resonant
neutrons, obtained in our experiments and
from other authors in refs. [29 - 30]. For the
Fig. 4. Spectrum of natural Pd irradiated by neutron for 1.5 h, electron current-15 µA, measured for 30 min
and cooling time -11 min., at 0 cm distance from the detector.
For the 108Pd(n, γ)109m,gPd neutron
capture reactions, the product excitation energy
is equal to the binding energy of 109Pd, taken
from [25]. The product excitation energy of
110Pd(γ, n)109Pd reaction is an effective value
Eeff due to the reaction with bremsstrahlung
and was calculated as following:
For (n, 2n) reaction, the product
excitation energy is as following:
Eprod.ex = Eex - S2n
(6)
Where Eprod.ex, Eex and S2n - the product,
the target excitation energies and the two
neutrons separation energy of the compound
nucleus, which were taken from ref. [25].
Eeff = Eex - Bn - Ɛn
(4)
From the Table II one can make the
following comments:
a/ For the neutron capture reactions, our
results are insignificantly lower than that in ref.
[29] and higher than the data in refs. [30]. This
may be since in the previous works, the authors
used scintillation detector [29, 30], while in
this work we used high resolution HPGe
semiconductor detector and the advanced data
processing program.
(5)
Where Bn - The binding energy of
neutron, taken from [25], Ɛn – the mean kinetic
energy of photo-neutrons, taken from [32], (E)
- the excitation function taken from [14] and
(E, E0) - the Schiff formula for the
bremsstrahlung photon flux described in ref.
[33], E0 - the electron energy and Eth - the
reaction threshold energy taken from ref. [25].
b/ The product excitation energies in (γ.
n) and (n, γ) reaction are insignificantly
6
TRAN DUC THIEP et al.
different, but the IRs in (γ, n) reactions are
d/ The investigated results show that the
IRs in different nuclear reactions are different
and depend on the projectile type, intake
impulse, excitation energy, spins of the
isomeric and ground states as well as the
nuclear reaction mechanisms. This is the
channel effect in nuclear reactions.
much higher than that in (n, γ) reactions
because the intake impulses in the (γ, n)
reactions are higher in the (n, γ) reactions. This
fact can be used to explain why the IRs in the
(n, 2n) reactions strongly exceed that in the (n,
γ) and (γ, n) reactions.
c/ In photonuclear reactions in the GDR
region and nuclear capture reactions by thermal
and resonant neutrons, the transfer momenta to
the target nuclei are very low, namely L = 1 and
1/2 ħ, respectively. Therefore, the compound
nuclei in both reaction kinds are with spins JC =
J0, J0 ± 1 and J0 ± 1/2 respectively. These effects
restrict the spin range of excited levels or in
other words, they restrict the excitation of high
spin states making the value of IR in the
photonuclear and thermal and resonant neutron
capture reactions lower in comparison with that
of other reactions.
e/ The Talys computation program
[17] has been applied to study many
problems of nuclear physics, in which study
of the cross sections and isomeric ratios in
nuclear reactions, produced by different
projectiles is one important research
direction, for example [17 - 21, 34 - 40] and
for test any model it is needed to carried not
one, but
a
series of measurements.
Therefore, in this meaning we do hope that
our results as additional data can be used for
the test of nuclear reaction models by the
mentioned program.
Table II. The IRs of 109m,gPd in photonuclear reaction, in neutron capture reactions with thermal, resonant
and mixed thermal-resonant neutrons and in other reactions.
Nuclear Reaction
and Product
Type of
Product Exc.
Energy, MeV
Isomeric Ratio
Projectile
IR
108Pd(n, γ)109m,gPd
Thermal
neutron
6.15
0.023 ± 0.002 [This work]
0.028 ± 0.005 [29]
0.018 ± 0.005 [30]
108Pd(n, γ)109m,gPd
108Pd(n, γ)109m,gPd
110Pd(γ, n)109m,gPd
110Pd(n, 2n)109m,gPd
Resonant
neutron
6.15
6.15
0.023 ± 0.002 [This work]
0.028 ± 0.005 [29]
Mixed Thermal-
Resonant neutron
0.023 ± 0.002 [This work]
24 MeV Bremstrahlung
25 MeV Bremsstrahlung
6.50
6.93
0.069 ± 0.007 [This work]
0.065 ± 0.003 [14]
14.1 MeV
neutron
5.28
0.410 ± 0.039 [14]
0.41 ± 0.03 [31]
photonuclear reaction, neutron capture
reactions, induced by thermal, resonant and
mixed thermal-resonant neutrons. The
obtained results show the nuclear reaction
V. CONCLUSIONS
We have studied the IRs of the same
isomeric pair 109m,gPd, formed from the
7
INVESTIGATION OF THE SAME ISOMERIC PAIR, PRODUCED FROM ...
Bremsstrahlungs With Endpoint Energies in
channel effect in IRs and could provide the
data to the Nuclear Data Bank for test of
nuclear reaction models as well as for nuclear
application uses. For interpretation of this
effect, this needs different nuclear reaction
models, which combine all nuclear reaction
mechanisms as statistical, direct and pre-
equilibrium processes.
The Giant Dipole Resonance Region”. J
Radioanal Nucl Chem V. 292, 89 – 96, 2012.
[5]. T. D. Thiep, T.T An, P.V. Cuong and N. T.
Vinh, “Study of The Isomeric Ratios In
Photonuclear Reactions of Natural Selenium
Induced by Bremsstrahlungs With Endpoint
Energies In The Giant Dipole Resonance
Region”, J. Radioanal. Nucl. Chem., V. 292,
N. 3, 1035 – 1042, 2012.
ACKNOWLEDGEMENT
[6]. T. D. Thiep, N. V. Do, T T An and N. N. Son,
“Nuclear Reactions With 14 Mev Neutrons and
Bremsstrahlungs in Giant Dipole Resonance
(GDR) Region Using Small Accelerators”,
Nucl Phys A V. 722, 568 – 572, 2003.
This work has been performed at the
Flerov Laboratory of Nuclear Reaction, Joint
Institute for Nuclear Research, Dubna, Russia.
The authors would like to express sincere
thanks to the MT-25 Microtron group for
operating the irradiation facility and the
Chemical Department of the Flerov
Laboratory of Nuclear Reaction for providing
the measurement system. The financial
support for the institute selected project, titled
“Study of the reaction channel effect in the
isomeric ratios in different nuclear reactions”
from the Institute of Physics, Vietnam
Academy of Science and Technology is
sincerely acknowledged.
[7]. A. G. Belov, Yu. P. Gangrsky et al,
“Excitation of high spin isomers in
photonuclear reactions”, Phys. Part. Nucl. Lett.
V.1, N.4, 47-52, 2004.
[8]. Tran Duc Thiep, Truong Thi An, Phan Viet
Cuong, Nguyen The Vinh, Bui Minh Hue, A.
G. Belov and O. D. Maslov, “The Study of
Isomeric Ratios in Photonuclear Reactions
Forming High Spin Isomers in the Giant
Dipole Resonance Region”, Communications
in Physics, V. 24, N. 4, 381, 2014.
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10
Nuclear Science and Technology, Vol.10, No. 1 (2020), pp. 11-20
Determination of thermal neutron flux distribution
at the rotary rack served for elemental concentration analysis
using the k0-INAA method
Nguyen Thi Tho1, Tran Tuan Anh1, Trinh Van Cuong1, Ho Van Doanh1,
Tran Quoc Duong1, Ho Manh Dung2
1Dalat Nuclear Research Institute, 01 Nguyen Tu Luc Street., Da Lat, Lam Dong.
2Center For Nuclear Techniques, 217 Nguyen Trai street, District 1, HCM City.
(Received 08 January 2020, accepted 24 February 2020)
Abstract: The accuracy of elements concentration determination using the k0-standardization method
directly depends on irradiation and measurement parameters including Non-1/E epithermal neutron
flux distribution shape (
), thermal-to-epithermal neutron flux ratio f, efficiency , peak
⁄
area… In the case of the irradiation position at the rotary rack of the Dalat Nuclear Research Reactor
(DNRR), the difference of thermal neutron flux between the bottom (3.541012 n.cm-2.s-1) and the top
(1.931012 n.cm-2.s-1) of the 15 cm aluminum container is up to 45%. Therefore, it is necessary to
accurately determine above-mentioned parameters in the sample irradiation position. The present
paper deals with the determination of the distribution of thermal neutron flux along the sample
irradiation container by using 0.1% Au–Al wire activation technique. The thermal neutron flux was
then used to calculate the concentration of elements in the Standard Reference Material 2711a and
SMELS type III using k0-INAA method at different positions in the container. The obtained results
with the neutron flux correction were found to be in good agreement with the certified values. In
conclusion, the proposed technique can be applied for activation analyses without sandwiching flux
monitors between samples during irradiations.
Keywords: K0-standardization method, Dalat nuclear research reactor, neutron spectrum parameters.
The advantages of k0-NAA in the applications
are a capability of the determination of multi-
element with high precision and accuracy as
well as a minimized sample preparation [1].
I. INTRODUCTION
Nuclear analytical techniques have been
developed for decades. It has been used to
solve
environmental
problems,
legal
investigations.... Since March 2012, the DNRR
has been continuously operated about 100130
hours per month at a nominal power of 500 kW
for radioisotopes production, activation
analysis and other researches. The k0-
standardization method (k0-NAA) has been
applied and developed at the DNRR over 17
years. Its main applications include the studies
in geology, bio-medicine, material, petroleum,
archaeology and environment among others.
At the DNRR, there are three irradiated
channels used for NAA (Fig.1): (1) The fast
pneumatic transfer system for very short
irradiation at the channel 13-2 and thermal
column (Tirr<45 sec); (2) The pneumatic
transfer system for short and medium
irradiations at the 7-1 channel (Tirr = 451200
sec); (3) The rotary rack with 40 irradiated
holes placed inside the graphite reflector for
long irradiation
(Tirr>20
min). The
©2020 Vietnam Atomic Energy Society and Vietnam Atomic Energy Institute
DETERMINATION OF THERMAL NEUTRON FLUX DISTRIBUTION AT THE ROTARY RACK ...
experiments for determination of thermal flux
were carried out at the sixth hole of the rotary
rack of the DNRR.
in NAA are parameters such as flux variation
within a sample and irradiation geometry in the
container. When the sample is irradiated with
neutrons, the activation rates depend on the
geometry effect due to the irradiation position
within the container, the variation and the
differences within the irradiation site [4].
In the determination of elemental
concentration in unknown samples using k0-
method, samples and flux monitors were
simultaneously irradiated together. The flux
monitors were usually positioned at the top,
middle and bottom of the containers.
Therefore, we proposed the technique that can
be applied for k0-method with suitable
accuracy without sandwiching flux monitors
between samples during irradiations. An
experimental determination of the thermal
neutron flux in the inner sample irradiation
container at the rotary rack of the DNRR
using foil activation technique was undertaken
in this work.
Fig. 1. Dalat research reactor cross-section.
The neutron spectrum parameters of the
DNRR were reported to be very stable which
permit the use of k0-NAA method [2].
Instrumental neutron activation analysis with
research
reactors
has
some
special
characteristics which makes it more attractive
to use for routine analysis. These include
multi-element capability, reproducibility of
the results and independence of the chemical
state of the element [3,4]. Thermal, epithermal
and fast neutron fluxes determination are
useful when characterizing the activation site
in instrumental neutron activation analysis. In
this perspective NAA using reactor neutrons
plays a vital role due to its high sensitivity
and detection limits for many elements in a
variety of matrices [5], but these could not be
achieved without proper knowledge of the
neutron flux [6].
II. CONTENT
A. Subjects and methods
In the absolute method, the thermal
neutron flux is given as [7]:
(1)
(2)
[
]
Where Asp is the specific activity, M is
It is necessary to measure thermal
neutron flux distribution at various points in
sample irradiation container and neutron flux
monitoring is, therefore, required to be carried
out regularly for any reactor for analytical
quality control. This is to guarantee continues
application of neutron activation analysis since
the main sources of measurement uncertainty
the atomic mass, is the isotopic abundance,
is the 2200 m.s-1 (n, γ) cross-section, γ is the
absolute gamma-intensity, Np is the number of
counts under the full-energy peak during the
counting time tm, w is the sample weight in
gram, S = l-exp(-tirr) is the saturation factor
with tirr being the irradiation time,
12
NGUYEN THI THO et al.
is the decay factor with td being decay time, C
= [l-exp(-tm) ]/tm is the measurement factor
correcting for decay during the measurement
time tm, is the decay constant, NA is the
[11]. This is due to the fact that the epithermal
flux is shown to deviate from the ideal situation
with a factor . Eq. (4) should, therefore, be
modified to take care of the flux-shaping factor
and thus we have a semi-empirical relationship
given as:
Avogadro’s number, p is the full energy peak
detection efficiency, f is the thermal to
epithermal neutron flux ratio, is the
epithermal neutron flux shape factor.
[ ]
(5)
Where is the characteristic of the
reactor irradiation position and was shown [11]
to be positive or negative depending on the
reactor epithermal spectrum. Eq.(5) was
proved to be satisfactory for instrumental
neutron activation analysis [6,11] and it
enables the correction of the resonance integral
to the deviating spectrum. Thus to preserve
accuracy in the k0-method, should be known
when calculating the concentration of an
element in a sample [6,12].
For ideal situation Q0 = I0/0, I0 -
resonance integral for an ideal (assumed 1/E)
epithermal neutron flux distribution.
For a non-ideal situation, the Q0(I0) need
to be modified with an -dependent term. The
conversions from the tabulated Q0(I0) values to
Q0() (or (I0()) are given by:
]
[
(3)
̅̅̅
The k0-standardization method was
Where ECd is the effective Cd cut-off
introduced in NAA [13]. In terms of the k0-
energy ( ECd=0.55 eV in standard conditions)
methodology,
adopting
the
Hødgdahl
and Er is the effective resonance energy,
convention [14], the concentration calculations
are based on the fundamental equation:
defined by Ryves [8]. The a term
(numerically unity) originates from the
definition of the epithermal neutron flux in a
1/E1+ distribution [9,10].
⁄
(6)
⁄
(
)
For an ideal reactor flux, the slowing
down neutrons after collision with the
moderator atoms, show an energy distribution
e(E) which varies as E-1. This means that the
epithermal neutron flux integrated over one
logarithmic energy interval can be represented
by a constant e since:
With k0 defined as:
(7)
SMELS type III [13] (a multi-element
synthetic material producing the long-lived
radionuclides when irradiated with neutrons)
and SRM-2711a (the certified reference
material from National Institute for Standard
and Technology - NIST) were used to calculate
the concentration of the elements at different
positions in the container using k0-INAA.
[ ]
(4)
However, it was found that applying a
single comparator method (k0-standardization)
with reactor neutrons, using Eq. (4) is
unacceptable from the standpoint of accuracy
13
DETERMINATION OF THERMAL NEUTRON FLUX DISTRIBUTION AT THE ROTARY RACK ...
In order to evaluate the laboratory
performance, the u-score test was used in
which the u-score is calculated according to the
following equation:
(9)
B. Experiment
For determination of the axial flux
distribution, the gold wire (Al-0.1%Au, =0.6mm)
was used. The 15 cm long Au wire was placed at
the center of the aluminum container. After
irradiation and suitable decay, it was cut in pieces
of 5 mm with the weight of about 2 - 6 mg. The
gold foils (Al-0.1%Au, d=0.1mm) and zirconium
foils (Zr-99.98%) were also placed at some
positions 1, 2, 6, 7, 12, 14 cm in order to determine
the thermal neutron flux and , f values.
(8)
√
Where xlab, ulab, xref, and uref are the
experimental and reference values and
uncertainties, respectively [2].
The relative bias between the
experimental result and the reference value is
calculated and expressed as a percentage:
Fig. 2. Typical aluminum sample irradiation container usually used at the rotary rack of the DNRR.
Table I. The irradiation, decay, counting times for Au wire/foil, Zr monitor, SRM-2711a, SMELS III.
Counting time
SRM/Monitor
Au wire
Irradiation time (tirr)
Decay time (td)
12d
(tm)
1739h
1h
1h/10h
1h
Au foil
34 d
10 15m
120m
Zr monitor
SRM-2711a
SMELS III
3d
1h/10h
10h
912d
215h
223h
1018d
After an appropriate decay time, the
Au wire was cut into sixteen pieces of 5mm
and measured on the HPGe coaxial detector
1.9 keV at 1332.5 keV. The full-peak
energy efficiency of the detector was
determined using standard gamma-ray
sources of 241Am, 133Ba, 109Cd, 137Cs, 60Co,
57Co and 152Eu.
(GMX30190), which has
a
relative
efficiency of 30% and energy resolution of
14
NGUYEN THI THO et al.
and the top (1.931012 n.cm-2.s-1) of the 15 cm
C. Results and discussion
aluminum container is up to 45%. The
measured results of and f at the rotary rack
of the DNRR were found of 0.088 and 39.5,
respectively. The values are in good agreement
with the previous measurements [16].
The thermal neutron flux distribution in
the sample irradiation container of the DNRR
was shown in Table II and Fig. 3. The
difference of thermal neutron flux between the
bottom (3.541012 n.cm-2.s-1) of the 0.75 cm
Table II. The axial thermal neutron flux profile in the sample irradiation container.
Thermal
neutron flux
(n.cm-2s-1)
Axial position in
the container
(cm)
Thermal
neutron flux
(n.cm-2s-1)
Axial position in the
container
Error
Error
(n.cm-2s-1)
(n.cm-2s-1)
(cm)
0.75
1.25
2.25
3.25
4.25
5.25
6.25
6.75
7.25
8.25
9.25
10.25
12.25
13.25
13.75
14.25
3.51E+12
3.43E+12
3.48E+12
3.28E+12
3.16E+12
3.08E+12
2.90E+12
2.86E+12
2.77E+12
2.71E+12
2.68E+12
2.55E+12
2.26E+12
2.13E+12
2.09E+12
1.98E+12
1.43E+11
1.39E+11
1.43E+11
1.32E+11
1.29E+11
1.25E+11
1.18E+11
1.17E+11
1.13E+11
1.15E+11
1.09E+11
1.04E+11
9.25E+10
8.63E+10
8.67E+10
8.16E+10
2(*)
7(*)
3.35E+12
2.84E+12
2.06E+12
3.51E+12
3.07E+12
2.27E+12
1.32E+11
1.13E+11
8.31E+10
1.38E+11
1.22E+11
9.11E+10
14(*)
1(**)
6(**)
12(**)
(*) Neutron flux in January 2019. (**) Neutron flux in February 2019.
4.0E+12
Thermal flux using Au wire
Thermal flux using Au foils *
3.5E+12
Thermal neutron using Au foils **
3.0E+12
2.5E+12
2.0E+12
1.5E+12
0
5
10
15
Position (cm)
Fig. 3. Thermal neutron flux distribution from the bottom to top of the container.
15
DETERMINATION OF THERMAL NEUTRON FLUX DISTRIBUTION AT THE ROTARY RACK ...
The thermal neutron flux distribution in
the sample irradiation container of the DNRR
also was simulated by MCNP code,
simulation results were shown in Fig. 4.
In this simulation (Fig. 5), it has been
shown that the difference of thermal neutron
flux within 2.4 cm of the diameter of the
aluminum container is about 20% and with
1.5 cm of the effection diameter of the sample
box is about 10%. This difference won’t affect
the accuracy of element analysis using k0-
INAA when irradiation samples are coaxially
arranged in the.
1.1
MCNP
1
Exp
0.9
0.8
0.7
0.6
0.5
0.4
The obtained neutron flux was then
used to calculate concentration of the
elements in the SRM-2711a and SMELS III
using k0-INAA method at different positions
in the container. The xlab/xref ratios, RB values
and u-scores were used to evaluate the
precision of data. The thermal neutron flux
distribution in the container were shown in
Table II and Fig. 3. The concentration of
elements Fe, Cr, Co, Sc in SRM-2711a were
compared with the reference values in which
the RB values are less than 5% in both cases
of sandwiching and linear interpolation at
difference positions in the container, except
for Cr were about 12% at the position of 14
cm. The u-score values were within ±1.64 for
all elements (see Tables III-IV).
0
5
10
Positon (cm)
15
20
Fig. 4. Obtained thermal neutron flux distribution
from the bottom to top of the container by
experiment and simulation.
Fig. 4 shows that within the error range
the obtained results from experiment are in
good agreement with simulation results.
The determination of thermal neutron
flux distribution along the diameter of the
container by experiment is quite difficult so
we have simulated this distribution by MCNP
code. Simulation result was seen in Fig. 5.
4.0E+12
3.9E+12
3.8E+12
3.7E+12
3.6E+12
3.5E+12
3.4E+12
3.3E+12
3.2E+12
3.1E+12
-1.8
-1.2
-0.6
0
0.6
1.2
1.8
Position (cm)
Fig. 5. Simulation of thermal neutron flux distribution along the diameter of the container by MCNP code.
16
NGUYEN THI THO et al.
Table III. The concentration of elements and uncertainties in mg/kg, xlab/xref ratios, RB and u-score values
for SRM-2711a at position 2cm in the container.
RB1 RB2
(%) (%)
1
2
1
2
Element
xlab±ulab
29621±1235 29258±1223 28200±400
54.2±3.2 53.5±3.2 52.3±2.9
10.31±0.55 10.19±0.54 9.89±0.18
8.6±0.4 8.5±0.3 8.5±0.1
xlab±ulab
xref±uref
xlab/xref xlab/xref
u-score1 u-score2
Fe
Cr
Co
Sc
1.05
1.04
1.04
1.01
1.04 5.04 3.75
1.02 3.63 2.29
1.03 4.25 3.03
1.00 1.18 0.00
1.09
0.44
0.73
0.24
0.82
0.29
0.52
-0.05
1 using sandwiching flux monitor
2 using linear interpolation
Table IV. The concentration of elements and uncertainties in mg/kg, xlab/xref ratios, RB and u-score values
for SRM-2711a at position 7 cm in the container.
RB1 RB2
(%) (%)
2.08 2.32 0.46
u-
u-
1
2
1
2
Element
xlab±ulab
xlab±ulab
xref±uref xlab/xref xlab/xref
1.02
1.00 -0.18 -4.06 0.47
score1 score2
Fe
Cr
Co
Sc
28786±1197 28854±1180 28200±400 1.02
0.53
0.5
54.1±2.6
10.25±0.47 9.85±0.44
8.6±0.4 8.3±0.3
52.0±2.5
54.2±2.6
9.89±0.18
8.6±0.4
1.00
1.04
1.00
1.00
0.97
3.64 -0.40 0.72
0.00 -3.49 0.32
0.78
0.38
Table V. The concentration of elements and uncertainties in mg/kg, xlab/xref ratios, RB and u-score values for
SRM-2711a at position 14 cm in the container.
RB1 RB2
u-
2
1
2
1
Element
xlab±ulab
xlab±ulab
xref±uref xlab/xrefxlab/xref
u-score2
score1
(%) (%)
28726±1234 28985±1223 28200±400 1.02 1.03 1.87 2.78
58.2±3.2 58.7±3.2 52.3±2.9
10.16±0.51 10.25±0.51 9.89±0.18 1.03 1.04 2.73 3.64
8.8±04 8.9±0.4 8.5±0.1 1.04 1.05 3.53 4.71
Fe
Cr
Co
Sc
0.41
0.61
1.49
0.67
0.95
1.11 1.12 11.28 12.24 1.37
0.49
0.73
Table VI. The concentrations of elements and uncertainties in mg/kg, xlab/xref ratios, and u-scores
for SMELS III at position 1 cm in the container.
RB1 RB2
(%) (%)
u-
u-
1
2
1
2
Element xlab±ulab
xlab±ulab
xref±uref
xlab/xref xlab/xref
score1 score2
Fe
Co
Cr
Sc
Cs
In
8672±358 8655±357
8200±190
1.06
1.05
1.04
1.06
1.05
1.04
1.06
1.08
1.10
1.07
1.10
1.09
1.11
1.07
1.09
1.07
5.76 5.55 1.16 1.12
4.94 4.73 1.09 1.05
4.04 3.81 0.76 0.72
6.14 6.14 1.16 1.12
8.56 8.32 1.80 1.76
10.28 10.17 1.69 1.66
7.03 6.64 1.37 1.33
10.69 9.92 1.61 1.57
9.31 9.09 1.79 1.75
10.69 10.69 1.88 1.84
7.30 7.30 1.40 1.36
9.18 8.70 1.76 1.72
6.96 6.80 1.49 1.44
25.50±1.04 25.45±1.04 24.3±0.33
90.2±3.79 90.0±3.8 86.7±2.6
1.21±0.05 1.21±0.01 1.140±0.031 1.06
22.58±0.92 22.53±0.92 20.80±0.34
1.09
1.10
1.07
1.11
1.09
1.11
1.07
1.09
1.07
510±21
54.8±2.2
145±6
509±21
54.6±2.2
144±6
462±19
51.2±1.3
131±6
Sb
Se
Sr
8909±375 8891±374
8150±200
26.2±0.9
23.3±0.7
20.7±0.5
618±11
Th
Tm
Yb
Zn
29±1
25±1
29±1
25±1
22.6±0.9
661±27
22.5±0.9
660±27
17
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