Photonuclear production of F-18
¹⁸F is one of the most important positron emitters which are routinely used in the positron emission tomography (PET). The recoil nuclei method in the ¹⁹F(Ɣ,n)¹⁸F reaction was used for the production of ¹⁸F free carrier. The sufficiently high energy of recoil nuclei in this reaction can be up to 20...
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irk-123456789-1473062019-02-15T01:24:58Z Photonuclear production of F-18 Dikiy, N.P. Dovbnya, A.N. Krasnoselsky, N.V. Lyashko, Yu.V. Medvedeva, E.P. Medvedev, D.V. Uvarov, V.L. Fedorets, I.D. Применение ядерных методов ¹⁸F is one of the most important positron emitters which are routinely used in the positron emission tomography (PET). The recoil nuclei method in the ¹⁹F(Ɣ,n)¹⁸F reaction was used for the production of ¹⁸F free carrier. The sufficiently high energy of recoil nuclei in this reaction can be up to 200 keV. The mixture of 180 nanometer CaF₂ nanoparticles and an acceptor in the form of a nanoparticle of food salt was irradiated with bremsstrahlung with a maximum energy of 13.5 MeV. Irradiated samples were placed in distilled water to dissolve the sodium chloride. The yield of the ¹⁸F isotope in the solution was 30.2% of the total activity of the sample. The estimation of the ¹⁸F production on an electron accelerator with a power of 10 kW and an energy of 35 MeV can be up to 1 Ci for 4 hours. ¹⁸F є один з найважливіших позитронних випромінювачів, який зазвичай використовується в позитронній емісійній томографії (ПЕТ). Мета нашого дослідження полягала в тому, щоб розвинути метод ядер віддачі в реакції ¹⁹F(Ɣ,n)¹⁸F для виробництва вільного ¹⁸F. Досить висока енергія ядер віддачі в цій реакції може досягати 200 кеВ. При підготовці отримання ¹⁸F використовувалася суміш наночастинок CaF₂ , а також хлорат натрію чи кліноптілоліту як донор і акцептор, відповідно, які були опромінені гальмівним випромінюванням з максимальною енергією 13,5 МеВ. Вихід ізотопу ¹⁸F в розчині становив 30,2% від загальної активності зразка. Оцінка виробництва ¹⁸F на електронному прискорювачі потужністю 10 кВт і енергією 25 МеВ може становити до 1 Кі протягом 4 годин. Показано, що фотоядерний метод виробництва ¹⁸F більш ефективний, ніж отримання ¹⁸F на циклотронах. ¹⁸F один из самых важных позитронных излучателей, который обычно используется в позитронной эмиссионной томографии (ПЭТ). Цель нашего исследования состояла в том, чтобы развить метод ядер отдачи в реакции ¹⁹F(Ɣ,n)¹⁸F для производства свободного ¹⁸F. Достаточно высокая энергия ядер отдачи в этой реакции может достигать 200 кэВ. При подготовке получения ¹⁸F использовалась смесь наночастиц CaF₂, а также хлорат натрия или клиноптилолита как донор и акцептор соответственно, которые были облучены тормозным излучением с максимальной энергией 13,5 МэВ. Выход изотопа ¹⁸F в растворе составлял 30,2% от общей активности образца. Оценка производства ¹⁸F на электронном ускорителе мощностью 10 кВт и энергией 25 МэВ может составлять до 1 Ки в течение 4 часов. Показано, что фотоядерный метод производства ¹⁸F более эффективен, чем получение ¹⁸F на циклотронах. 2018 Article Photonuclear production of F-18 / N.P. Dikiy, A.N. Dovbnya, N.V. Krasnoselsky, Yu.V. Lyashko, E.P. Medvedeva, D.V. Medvedev, V.L. Uvarov, I.D. Fedorets // Вопросы атомной науки и техники. — 2018. — № 3. — С. 146-149. — Бібліогр.: 16 назв. — англ. 1562-6016 PACS: 28.60.+s; 87.53.Jw http://dspace.nbuv.gov.ua/handle/123456789/147306 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
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Применение ядерных методов Применение ядерных методов |
spellingShingle |
Применение ядерных методов Применение ядерных методов Dikiy, N.P. Dovbnya, A.N. Krasnoselsky, N.V. Lyashko, Yu.V. Medvedeva, E.P. Medvedev, D.V. Uvarov, V.L. Fedorets, I.D. Photonuclear production of F-18 Вопросы атомной науки и техники |
description |
¹⁸F is one of the most important positron emitters which are routinely used in the positron emission tomography
(PET). The recoil nuclei method in the ¹⁹F(Ɣ,n)¹⁸F reaction was used for the production of ¹⁸F free carrier. The sufficiently high energy of recoil nuclei in this reaction can be up to 200 keV. The mixture of 180 nanometer CaF₂ nanoparticles and an acceptor in the form of a nanoparticle of food salt was irradiated with bremsstrahlung with a maximum energy of 13.5 MeV. Irradiated samples were placed in distilled water to dissolve the sodium chloride. The
yield of the ¹⁸F isotope in the solution was 30.2% of the total activity of the sample. The estimation of the ¹⁸F production on an electron accelerator with a power of 10 kW and an energy of 35 MeV can be up to 1 Ci for 4 hours. |
format |
Article |
author |
Dikiy, N.P. Dovbnya, A.N. Krasnoselsky, N.V. Lyashko, Yu.V. Medvedeva, E.P. Medvedev, D.V. Uvarov, V.L. Fedorets, I.D. |
author_facet |
Dikiy, N.P. Dovbnya, A.N. Krasnoselsky, N.V. Lyashko, Yu.V. Medvedeva, E.P. Medvedev, D.V. Uvarov, V.L. Fedorets, I.D. |
author_sort |
Dikiy, N.P. |
title |
Photonuclear production of F-18 |
title_short |
Photonuclear production of F-18 |
title_full |
Photonuclear production of F-18 |
title_fullStr |
Photonuclear production of F-18 |
title_full_unstemmed |
Photonuclear production of F-18 |
title_sort |
photonuclear production of f-18 |
publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
publishDate |
2018 |
topic_facet |
Применение ядерных методов |
url |
http://dspace.nbuv.gov.ua/handle/123456789/147306 |
citation_txt |
Photonuclear production of F-18 / N.P. Dikiy, A.N. Dovbnya, N.V. Krasnoselsky, Yu.V. Lyashko, E.P. Medvedeva, D.V. Medvedev, V.L. Uvarov, I.D. Fedorets // Вопросы атомной науки и техники. — 2018. — № 3. — С. 146-149. — Бібліогр.: 16 назв. — англ. |
series |
Вопросы атомной науки и техники |
work_keys_str_mv |
AT dikiynp photonuclearproductionoff18 AT dovbnyaan photonuclearproductionoff18 AT krasnoselskynv photonuclearproductionoff18 AT lyashkoyuv photonuclearproductionoff18 AT medvedevaep photonuclearproductionoff18 AT medvedevdv photonuclearproductionoff18 AT uvarovvl photonuclearproductionoff18 AT fedoretsid photonuclearproductionoff18 |
first_indexed |
2025-07-11T01:49:50Z |
last_indexed |
2025-07-11T01:49:50Z |
_version_ |
1837313389936771072 |
fulltext |
ISSN 1562-6016. ВАНТ. 2018. №3(115) 146
PHOTONUCLEAR PRODUCTION OF F-18
N.P. Dikiy
1,3
, A.N. Dovbnya
1
, N.V. Krasnoselsky
2
, Yu.V. Lyashko
1,3
, E.P. Medvedeva
1,3
,
D.V. Medvedev
1,3
, V.L. Uvarov
1
, I.D. Fedorets
3
1
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine;
2
S.P. Grigorev Institute of Medical Radiology, Kharkov, Ukraine;
3
V.N. Karazin Kharkiv National University, Kharkov, Ukraine
E-mail: ndikiy@kipt.kharkov.ua
18
F is one of the most important positron emitters which are routinely used in the positron emission tomography
(PET). The recoil nuclei method in the
19
F(,n)
18
F reaction was used for the production of
18
F free carrier. The suffi-
ciently high energy of recoil nuclei in this reaction can be up to 200 keV. The mixture of 180 nanometer CaF2 nano-
particles and an acceptor in the form of a nanoparticle of food salt was irradiated with bremsstrahlung with a maxi-
mum energy of 13.5 MeV. Irradiated samples were placed in distilled water to dissolve the sodium chloride. The
yield of the
18
F isotope in the solution was 30.2% of the total activity of the sample. The estimation of the
18
F pro-
duction on an electron accelerator with a power of 10 kW and an energy of 35 MeV can be up to 1 Ci for 4 hours.
PACS: 28.60.+s; 87.53.Jw
INTRODUCTION
The advantage of the PET method, in comparison
with other methods of instrumental medical diagnostics,
is the possibility of obtaining information about the fate
of radionuclides in the body that correspond to the basic
elements-organogenes included in the composition of
biologically significant molecules. Positron emitters are
used to label various radiopharmaceuticals. The signifi-
cant advantages of PET are realized in the study of cer-
ebral blood flow and cerebral blood volume, regional
metabolism of carbohydrates and oxygen, in neuro-
chemical studies to obtain data on the density of indi-
vidual receptors and their functioning in the healthy and
diseased brain of man [1].
To detect abnormalities in the metabolism of oxygen,
a positron emitter of
15
О is used. This is important in the
treatment of epilepsy, brain tumors, ischemic lesions, etc.
To evaluate the neurotransmitter systems, in particu-
lar dopamine, a number of radiotracers are used, among
which L-DOPA, and its radiofluorinated analogue
18
F-6-
fluorideDOPA. To assess the activity of various recep-
tor systems, their antagonists are most often used, which
are capable of more or less irreversibly binding to them.
As radio raisers, isotope analogs of known radiophar-
maceuticals are often used: phenothiazines
(chlorpramazine), benzamides (raclopride), as well as
various benzodiazepines, opiates, acetylcholine deriva-
tives, etc.
In cardiology, the most popular positron radiators
are
13
N in the form of NH3, and
82
Rb in the form of
RbCl (for evaluating regional perfusion of the heart
muscle) and fatty acids labeled with carbon-11 (for
evaluating the regional metabolism of fatty acids) [1].
The most widely used in PET are
11
C,
13
N,
15
O, and
18
F. An important circumstance is that the listed iso-
topes, except for
18
F, are isotopes of biogenic elements.
Various biomolecules (including simple alcohols, sug-
ars, amino acids, steroids, alcaloids and host drugs) can
be carried with positron emitters without altering their
bio-chemical and physiological activities. We note that
the close Van der Waals radii of H and F allow us, with
some reservations, to introduce
18
F into labeled com-
pounds instead of hydrogen without major disturbances
in the geometry of the radiotracer.
In addition to widely used isotopes
11
C,
13
N,
15
O, and
18
F, other isotopes are also used, which significantly ex-
pands PET capabilities for diagnosis of various diseases
(Tabl). The maximum spatial resolution that can be ob-
tained by the PET method is limited to the range of posi-
trons in the object under study. The values of the positron
ranges in water are given in table. As follows from the
data in the table, the values of the positron ranges are
significantly different, which introduces an error in de-
termining the place of the event, which in principle can-
not be corrected. It can be seen that the minimum value
of the positron range is realized for
18
F. However, for
some applications, these isotopes have significant ad-
vantages (for example, cardiac studies using
82
Rb).
Although
18
F is not a significant element in living
organisms, its nuclear properties make its use in label-
ling of significant value. At present, in the overwhelm-
ing majority of PET centers, the
18
O(p,n)
18
F reaction is
used to produce fluorine-18 in the form of a fluoride
ion, which occurs when protons irradiated with water
enriched with oxygen-18.
Most PET use
18
F, which is obtained in the reaction
18
O(p,n)
18
F. Nevertheless, other methods of obtaining
18
F are being developed. Using brake gamma radiation
of 140 MeV electrons with an intensity of 80 μA,
Brinkman and Wyand [2] attempted to use the
18
F
photonuclear reaction of
19
F(,n)
18
F in targets filled with
liquid fluorinated hydrocarbons. Depending on the type
of hydrocarbon, the activity extracted by water ranged
from 11 to 68%. Of the total induced activity. Given the
correct choice of the irradiated material, it was possible
to achieve activities of
18
F-up to 100 mCi. At the same
time, it was shown that the extractable fluoride contains
an admixture of radioactive organic fluorinated com-
pounds, both used for irradiation, and products of reac-
tions of recoil atoms. Due to the strong radioactive de-
composition, the mole activity of fluoride did not ex-
ceed 0.25 Ci/mmol.
In [3], attempts were made to obtain
18
F on a linear
electron accelerator, which is used to irradiate cancer
patients. The high cost of obtaining
18
F on cyclotrons
prompted the appearance of work [4], where studies
were made of its production on a linear accelerator of
electrons with an energy of 55 MeV.
ISSN 1562-6016. ВАНТ. 2018. №3(115) 147
Isotope
T1/2,
hours
Mean and maximum energy -particles,
keV (intensity, %)
E, keV (intensity, %)
R90 of
+
,
mm
11
C 20.96 385.7, 960.4 (99.77) 511 (199.5) 1.68
13
N 9.97 491.8, 1198.5 (99.80) 511 (199.6) 2.26
15
O 2.037 735.28, 1735.0 (99.9) 511 (199.8) 3.61
18
F 109.77 249.8, 633.5 (96.73) 511 (193.4) 0.94
62
Cu 9.673 772.1, 1763.9 (0.138);
1320.7, 2936.9 (97.60)
511 (196);
1172.7 (0.35)
7.26
64
Cu 12.7 278.2, 653 (17.6);
188.85, 573 (38)
511 (35.2);
1347 (0.55)
1.04
62
Zn 9.255 255.4, 597.5 (8.2) 511 (15.8); 40.8 (22.6); 507.6 (14.8);
548.35 (15.3); 596.6 (26)
0.96
68
Ga 67.71 352.6, 821.7 (1.19); 836.0, 1899 (87.7) 511 (178.4); 1077.3 (3.2) 3.94
75
Br 96.7 514, 1181 (3.6); 601.4, 1376 (3.3);
708.1, 1612 (4.9); 772, 1753 (53);
904, 2040 (4)
511 (150.8); 141.2 (6.6); 286.5 (88);
431.8 (3.97)
3.78
76
Br 16.2 336, 781 (6.3); 427.2, 990 (5.2);
1532, 3382 (25.8); 1800, 3941 (6)
511 (109); 559.2 (74); 657 (15.9);
1853.7 (14.7)
8.35
82
Rb 1.2575 527.7, 1206.7 (0.32); 843.2, 1903 (0.12);
1167.6, 2601 (13.1); 1534.6, 3378 (81.8)
511 (189); 777 (12.5); 1395 (0.47) 7.65
86
Y 14.74 535.4, 1221 (11.9); 681.1, 1545 (5.6);
883.3, 1988 (3.6); 1436.8, 3141 (2.0)
511 (64); 443.1 (16.9); 627.7 (32.6);
703.3 (15.4); 777.4 (23); 1076.6
(82.5); 1153 (31.3); 1920.7 (21.3)
3.34
89
Zr 78.41 395.5, 902.3 (22.74) 511 (45.89); 909.1 (99.86); 1712
(0.86)
1.72
82
Rb 1.2575 527.7, 1206.7 (0.32); 843.2, 1903 (0.12);
1167.6, 2601 (13.1); 1534.6, 3378 (81.8)
511 (189); 777 (12.5); 1395 (0.47) 7.65
94m
Tc 52 404.5, 917 (0.92); 639.3, 1446 (0.93);
1094.2, 2439 (67.6)
511 (140.3); 871 (94.2); 1522 (4.5);
1868.7 (5.7)
5.79
110
In 69.1 1014.7, 2260 (60.7) 511 (122.5); 657.75 (97.7) 5.37
124
I 4.176 687.04, 1534.9 (11.7);
974.7, 2137.6 (10.7)
511 (45); 602.7 (62.9); 722.8 (10.36);
1591 (11.15)
4.24
134
La 6.45 946.9, 2104 (1.56); 1224.4, 2709, (62) 511, (127.2); 604.7 (5.04) 6.44
Also note the work of the Polish group, which are
developing alternative methods for obtaining
18
F on
neutrons [6] and protons [6]. Works on a production of
18
F and neutrons [7, 8] are known.
The purpose of the present article is the production
of a high specific activity
18
F on the basis of nanoparti-
cles of calcium fluoride and the effect of Szilard-
Chalmers.
RESULTS AND DISCUSSION
For the production of
18
F with high specific activity
was used Szilard-Chalmers method [9]. Nanoparticles
CaF2 and white salt were used as donor and acceptor,
respectively. For the concentration of recoil nuclei in
among donor (white salt), nanoparticle sizes CaF2, con-
taining an activatable element, must be less than or
equal to the range of the recoil nuclei (Fig. 1).
The evaporation model for compound nuclei pre-
dicts that the emitted neutron energy distribution ap-
proaches the form of a Maxwell distribution [10, 11]:
)exp()(
2
nn
n
EE
constEw ,
where θ = [(Eγ Bn)/a]
1/2
; Bn – separation energy of
neutron; Eγ – bremsstrahlung energy. The constant a
definition of the speed of ascending of a density of lev-
els of a nucleus at increasing of energy. The experi-
mental estimate of this constant is а ≈ A/15 МэВ
-1
.
However, in light nuclei, a structure is observed in
the cross section of the photonuclear reaction (Fig. 2).
The cross section for the
19
F(,n)
18
F reaction up to a
photon energy of 26 MeV is realized due to a small
number of single-particle dipole transitions, which can
take place in this nucleus [12]. These properties also
appear in the spectra of emitted neutrons. In Fig. 3
shows the spectra of neutrons from the
19
F(,n)
18
F reac-
tion, which correspond to transitions in the
18
F nucleus
to the ground, excited, and solid states [14 - 16]. It can
be seen that the neutron spectrum has a structure that is
related to the discrete states of the final nucleus.
0 20 40 60 80 100
0
50
100
150
200
R
a
n
g
e
1
8
F
i
n
C
a
F
2
,
n
m
18
F ion energy, keV
Fig. 1.
18
F ranges in natural calcium fluoride
ISSN 1562-6016. ВАНТ. 2018. №3(115) 148
10 20 30 40 50
0,000
0,005
0,010
0,015
c
ro
s
s
s
e
c
ti
o
n
,
b
n
E
, MeV
19
F(,n)
18
F
Fig. 2. Cross section of reaction
19
F(,n)
18
F [13]
Procedure of deriving calcium fluoride in nanosize
state was the following: the grinding of calcium fluoride
in an agate mortar for a long time, the precipitation of
powder in the distilled water. The velocity of subsid-
ence of calcium fluoride particles was being determined
out of the equation:
9
)(2 2rg
V o
,
where , o density of calcium fluoride particles and
water, accordingly; g acceleration of free falling; r
particle radius; dynamic viscosity of water. After
3.5 hours of precipitation the solution was decanted. A
solution of calcium fluoride particles was then precipi-
tated for 85 hours. In the obtained sediment were nano-
particles of calcium fluoride in the size from 0.5 to
2.5 m. In the second case, a solution of calcium fluo-
ride precipitated in the cylinder 434 hours. The superna-
tant of a solution of calcium fluoride was then evapo-
rated. This allowed obtaining nanoparticles of calcium
fluoride with an average size of 180 nm.
The mixture of CaF2 nanoparticles and an acceptor
in the form of nanoparticles of a food salt was irradiated
with bremsstrahlung with a maximum energy of
13.5 MeV.
After activation of samples and standards the activi-
ty of radioisotopes obtained in reactions
19
F(,n)
18
F has
been measured by Ge(Li)-detector with volume 50 cm
3
and with energy resolution 3.2 keV in the area of
1332 keV (Fig. 4).
1 2 3 4 5 6
0
20
40
60
80
100
y
ie
ld
,
re
l.
u
n
it
s
E
n
, MeV
GROUND-STATE
EXCITED-STATE
TOTAL SUM OF GROUND STATE
AND EXCITED-STATE
19
F(,n)
18
F
Fig. 3. Photoneutrons from Teflon;
pulse height spectra (E (max) = 21 MeV) [16]
The estimate of the average energy of neutrons for a
gamma radiation with the maximum energy of
13.5 MeV of reaction reaches 3 MeV. Therefore, the
average energy of recoil nuclei of
18
F is equal 80 keV.
Recoil nuclei
18
F can leave nanoparticles of CaF2 from a
depth of 150 nm (see Fig. 1). For the average radius of
CaF2 nanoparticles 1.5 m the part of recoil nuclei,
which can go out into a solution, is 4.75%. The yield of
18
F out of extractable phase amounted 3.03%.
For the average radius of CaF2 nanoparticles 180 nm
the part of recoil nuclei, which can go out into a solu-
tion, is %. Yield of
18
F out of extractable phase
amounted 30.2%.
1000 2000 3000 4000
10
100
1000
10000
number channel
c
o
u
n
ts
18
F
65
Zn 1116 keV
511 keV
Fig. 4. The spectrum of
18
F, Emax = 13.5 MeV
The estimation of the
18
F production on an electron
accelerator with a power of 10 kW and an energy of
35 MeV can be up to 1 Ci for 4 hours.
CONCLUSIONS
1. The possibility of photonuclear production of car-
rier free
18
F by using recoil nuclei of calcium fluoride
nanoparticles that produced by reaction
19
F(,n)
18
F has
been found.
2. The mixture of CaF2 nanoparticles and an accep-
tor in the form of a nanoparticle of a food salt was irra-
diated by bremsstrahlung with a maximum energy of
13.5 MeV. Irradiated samples were placed in a distilled
water to dissolve the sodium chloride.
3. The maximum yield of the
18
F isotope in the solu-
tion was 30.2% of the total activity of the sample.
4. The estimation of the
18
F production on an elec-
tron accelerator with a power of 10 kW and an energy
of 35 MeV can be up to 1 Ci for 4 hours.
REFERENCES
1. M.V. Korsakov. Guide to PET Radiochemistry.
St. Petersburg: “Theza”, 2002, 180 p.
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Article received 05.02.2018
ФОТОЯДЕРНЫЙ МЕТОД ПРОИЗВОДСТВА F-18
Н.П. Дикий, A.Н. Довбня, Н.В. Красносельский, Ю.В. Ляшко, Е.П. Медведева, Д.В. Медведев,
В.Л. Уваров, И.Д. Федорец
18
F один из самых важных позитронных излучателей, который обычно используется в позитронной
эмиссионной томографии (ПЭТ). Цель нашего исследования состояла в том, чтобы развить метод ядер отда-
чи в реакции
19
F(,n)
18
F для производства свободного
18
F. Достаточно высокая энергия ядер отдачи в этой
реакции может достигать 200 кэВ. При подготовке получения
18
F использовалась смесь наночастиц CaF2, а
также хлорат натрия или клиноптилолита как донор и акцептор соответственно, которые были облучены
тормозным излучением с максимальной энергией 13,5 МэВ. Выход изотопа
18
F в растворе составлял 30,2%
от общей активности образца. Оценка производства
18
F на электронном ускорителе мощностью 10 кВт и
энергией 25 МэВ может составлять до 1 Ки в течение 4 часов. Показано, что фотоядерный метод производ-
ства
18
F более эффективен, чем получение
18
F на циклотронах.
ФОТОЯДЕРНИЙ МЕТОД ВИРОБНИЦТВА F-18
М.П. Дикий, A.М. Довбня, М.В. Красносельський, Ю.В. Ляшко, О.П. Медведєва, Д.В. Медведєв,
В.Л. Уваров, І.Д. Федорець
18
F є один з найважливіших позитронних випромінювачів, який зазвичай використовується в позитронній
емісійній томографії (ПЕТ). Мета нашого дослідження полягала в тому, щоб розвинути метод ядер віддачі в
реакції
19
F(,n)
18
F для виробництва вільного
18
F. Досить висока енергія ядер віддачі в цій реакції може дося-
гати 200 кеВ. При підготовці отримання
18
F використовувалася суміш наночастинок CaF2, а також хлорат
натрію чи кліноптілоліту як донор і акцептор, відповідно, які були опромінені гальмівним випромінюванням
з максимальною енергією 13,5 МеВ. Вихід ізотопу
18
F в розчині становив 30,2% від загальної активності
зразка. Оцінка виробництва
18
F на електронному прискорювачі потужністю 10 кВт і енергією 25 МеВ може
становити до 1 Кі протягом 4 годин. Показано, що фотоядерний метод виробництва
18
F більш ефективний,
ніж отримання
18
F на циклотронах.
http://www.sciencedirect.com/science/article/pii/0020708X6590150X#!
http://www.sciencedirect.com/science/article/pii/0020708X6590150X#!
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