Analytical method for estimation isotope yield under photonuclear production
The heuristic model for description space-energy characteristics of the high-energy bremsstrahlung has been developed. On its basis the method for analytical estimation photonuclear yield of isotopes in wide range of atomic number (Z=20-80) and size of a target as well as of the electron energy (40…...
Збережено в:
| Дата: | 2010 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2010
|
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/15708 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Analytical method for estimation isotope yield under photonuclear production / V.I. Nikiforov, V.L. Uvarov // Вопросы атомной науки и техники. — 2010. — № 2. — С. 145-149. — Бібліогр.: 6 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859617735221182464 |
|---|---|
| author | Nikiforov, V.I. Uvarov, V.L. |
| author_facet | Nikiforov, V.I. Uvarov, V.L. |
| citation_txt | Analytical method for estimation isotope yield under photonuclear production / V.I. Nikiforov, V.L. Uvarov // Вопросы атомной науки и техники. — 2010. — № 2. — С. 145-149. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| description | The heuristic model for description space-energy characteristics of the high-energy bremsstrahlung has been developed. On its basis the method for analytical estimation photonuclear yield of isotopes in wide range of atomic number (Z=20-80) and size of a target as well as of the electron energy (40…100 MeV) is proposed. The analysis of validity of the model assumptions has been executed by means of it comparison with the results of simulation using the program package PENELOPE/2006 [1] supplemented with database on the cross-sections of photonuclear reactions. It has been shown earlier that such simulation method provides close fit with the experimental results. As an example the reactions of practical interest 48Ti(γ,p)47Sc, 68Zn(γ,p)67Cu and 187Re(γ,n)186Re are presented.
Разработана эвристическая модель для описания пространственно-энергетических характеристик высокоэнергетичного тормозного излучения. Предложен метод с ее использованием для аналитической оценки фотоядерного выхода изотопов в широком диапазоне значений атомного номера (Z=20-80) и размеров мишени, а также энергии электронов (40…100 МэВ). Проведен анализ обоснованности допущений модели путем ее сопоставления с результатами моделирования на основе программной системы PENELOPE/2006, дополненной базой данных по сечениям фотоядерных реакций. Ранее было показано, что такой метод моделирования дает хорошее согласие с результатами эксперимента. В качестве примера рассмотрены представляющие практический интерес реакции 48Ti(γ,p)47Sc, 68Zn(γ,p)67Cu и 187Re(γ,n)186Re.
Розроблено евристичну модель для опису просторово-енергетичних характеристик високоенергетичного гальмівного випромінювання. Запропоновано метод з її використанням для аналітичної оцінки фотоядерного виходу ізотопів у широкому діапазоні значень атомного номера (Z=20-80) і розмірів мішені, а також енергії електронів (40…100 МеВ). Проведено аналіз обґрунтованості припущень моделі шляхом її порівнювання з результатами моделювання на основі програмної системи PENELOPE/2006, доповненої базою даних з перетинів фотоядерних реакцій. Раніше було показано, що такий метод моделювання дає добре погодження з результатами експерименту. Як приклад розглянуто реакції 48Tі(γ,p)47Sc, 68Zn(γ,p)67Cu і 187Re(γ,n)186Re, що мають практичний інтерес.
|
| first_indexed | 2025-11-28T22:10:49Z |
| format | Article |
| fulltext |
____________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2010. № 2.
Series: Nuclear Physics Investigations (53), p.145-149.
145
ANALYTICAL METHOD FOR ESTIMATION ISOTOPE YIELD
UNDER PHOTONUCLEAR PRODUCTION
V.I. Nikiforov, V.L. Uvarov
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
E-mail: uvarov@kipt.kharkov.ua
The heuristic model for description space-energy characteristics of the high-energy bremsstrahlung has been de-
veloped. On its basis the method for analytical estimation photonuclear yield of isotopes in wide range of atomic
number (Z=20-80) and size of a target as well as of the electron energy (40…100 MeV) is proposed. The analysis of
validity of the model assumptions has been executed by means of it comparison with the results of simulation using
the program package PENELOPE/2006 [1] supplemented with database on the cross-sections of photonuclear reac-
tions. It has been shown earlier that such simulation method provides close fit with the experimental results. As an
example the reactions of practical interest 48Ti(γ,p)47Sc, 68Zn(γ,p)67Cu and 187Re(γ,n)186Re are presented.
PACS: 07.85.-m, 81.40wx, 87.53-j, 87.53.Wz
1. INTRODUCTION
1.1. In the general case, the output devices of the
electron linac operated in the mode of isotope produc-
tion include a converter C in the form of a d thick plate
made from the material with great Z, and a target T in
the form of a cylinder of radius R and height H, which
is axially symmetric about the beam (see Fig.1). As a
result of the interaction between accelerated electrons
and the converter, a flux of bremsstrahlung photons (or
X-ray) escapes from the converter. The photon energy ω
is continuously distributed in the spectrum in the range
0 < ω ≤ ωmax=E0. Simultaneously, a flux of electrons
escapes from the converter. Their number and spectral
distribution being determined by the E0 value, and also,
by the converter material and thickness. Thus, a flux of
mixed e,X-radiation is formed in the converter and the
target, which is responsible for thermophysical and ra-
diation conditions of these devices [2].
e e′
C
Tn
n
n
n
R
d a H
γ
γ
z
Fig.1. Arrangement of basic elements for photonuclear
production of isotopes
In addition, as a result of (γ,n) reactions occurring in
the converter, a quasi-isotropic photoneutron flux es-
capes from the converter. As an example of these reac-
tions that occur in the natural tungsten converter we
mention the 182W(γ,n)181W and 186W(γ,n)185W reactions.
The photoneutrons may also initiate the yield of differ-
ent isotopes in the target [3]. In the context of the given
problem, we restrict ourselves to the consideration of
(γ,N) reactions only, because (γ,2n), (γ,np), (γ,α), (e,e’),
(n,γ) and other channels generally have substantially
lower cross section values.
1.2. The processes of high-energy photon transfer in
material media are generally described with the use of
the attenuation coefficient μ(Z,ω) [4]. In particular, the
intensity of the “narrow” photon beam dies away in the
target depth in proportion to exp[-μ(Z,ω)⋅z]. The μ–1
value characterizes the so-called “free path” of photons.
So, strictly speaking, the reactions with photon partici-
pation can occur in the whole half-space behind the
converter (R→∞, H→∞). With an increasing target size
the total yield of the isotope product in the i-type reac-
tion (normalized to one accelerated electron) tends to its
theoretical limit 0( )iy E∞ . As an example, Fig.2 shows
the simulated distribution of 47Sc nuclei that are pro-
duced in a large titanium target (R=10 cm, H=15 cm)
under the action of bremsstrahlung.
-10 -8 -6 -4 -2 0 2 4 6 8 10
0
2
4
6
8
10
12
14
μ-1(ωi)
H, см
R, см
Fig.2. Distribution of 47Sc nuclei in the Ti target
(Е0=100 MeV)
Thus, at the initial stage of developing the photonuclear
technology, the main task consists in estimating the iso-
tope yield for real parameters of the accelerator (elec-
tron energy E0, the average beam current I and beam
size), and also, in optimizing the target dimensions (R,
H) with regard to the total and specific activity. The key
parameters of the problem are as follows:
• electron beam density distribution on the converter;
• converter’s material and thickness d;
• value of gap a between the converter and the target.
1.3. The number of new nuclei in the target per one
accelerated electron can be described in the general case
by the following formula:
0
,
( , ) ( ) ,
i th
E
A
i T T i
V
Ny dV r d
A
γ
ω
ν ρ ω σ ω ω
• →
= ⋅ Φ∫ ∫ (1)
146
where ( , )rγ ω
• →
Φ is the differential fluence of
bremsstrahlung photons of energy ω that are generated
by a single electron in the target volume element having
the radius-vector r
→
; ( )iσ ω – i-reaction cross section;
ω i,th – i-reaction energy threshold; Tν – relative con-
centration of isotope-target nuclei; nT – bulk concentra-
tion of nuclei in the target; V – target volume.
Thus, the problem reduces to analytic representation
of the functions ( , )rγ ω
• →
Φ , ( )iσ ω and to calculation of
integral (1). From its form it follows, in particular, that
in our calculations it will be sufficient to take into ac-
count only the high-energy part of the photon spectrum
ωi,th =ωmin≤ ω ≤ E0. Those photons will be referred to as
“effective”.
2. DESCRIPTION OF BREMSSTRAHLUNG
2.1. PHOTON ENERGY DISTRIBUTION
It follows from the simulation data that the depend-
ence of the spectral bremsstrahlung intensity on photon
energy ω for a thick converter can be described in the
linear approximation by the following expression
0( , , )
.
N E d
b cγ ω
ω ω
ω
∂
−
∂
(2)
By extending this approximation to the whole pho-
ton energy range 0 < ω ≤ E0, it appears possible to de-
termine the coefficients b and c from the conditions
0
0E
Nγ
ωω =
∂
=
∂
, (2.1)
0
0 0
0
( , ) ,
E N
d E d Eγω ω η
ω
∂
=
∂∫ (2.2)
where η is the conversion coefficient. This coefficient is
defined as the ratio of the total energy of bremsstrah-
lung photons to the primary electron energy.
Thus, in the linear approximation, we can obtain the
following expressions for the spectral photon distribu-
tion in the 0 < ω ≤ E0 range
,1
0 0
0
1 1( , , ) 2 ( , ) ,
N
E d E d
E
γ ω η
ω ω
∂ ⎛ ⎞
= −⎜ ⎟∂ ⎝ ⎠
(3)
and also, for the “effective” photon yield (ωmin<ω≤E0)
min min
,1 0 min 0
0 0
( , , ) 2 ( , ) ln 1 .N E d E d
E Eγ
ω ωω η
⎡ ⎤⎛ ⎞
Δ = ⋅ − −⎢ ⎥⎜ ⎟
⎝ ⎠⎣ ⎦
(4)
Formula (4) provides the estimation of the “effec-
tive” photon yield from the conversion coefficient val-
ue. The last one can be determined experimentally with
the use of a thick-wall ionization chamber or a calo-
rimeter or by the simulation technique. So, Fig.3 shows
the conversion coefficient as a function of the W con-
verter thickness, and Table 1 lists the ΔNγ values for
different reactions, calculated by formula (4) and ob-
tained by the simulation technique (ωmin=7.2 MeV cor-
responds to the 186W(γ,n)185W reaction threshold, being
the lowest from among those considered in the present
work). From the data presented in Fig.3 it follows that
in the 40…100 MeV range the maximum conversion
coefficient value is within the limits of 0.42…0.51.
0 1 2 3 4 5 6 7 8 9
0,30
0,35
0,40
0,45
0,50 100
80
60
40η,
re
l.u
n.
d, mm
Fig.3. Energy conversion coefficient versus W converter
thickness. The figures indicate the electron energy E0
in MeV units
Table 1
“Effective” photon yields for different reactions (W converter, d=4 mm)
40 60 80 100 E0, MeV
Reaction ΔNγ1 ΔNγ ΔNγ1 ΔNγ ΔNγ1 ΔNγ ΔNγ1 ΔNγ
48Ti(γ,p)47Sc 0.4527 0.3772 0.7782 0.6895 1.027 0.9430 1.230 1.1572
68Zn(γ,p)67Cu 0.5482 0.4693 0.8945 0.8118 1.153 1.0831 1.362 1.3093
187Re(γ,n)186Re 0.7526 0.6813 1.136 1.0818 1.411 1.3884 1.631 1.6403
The analysis of the data in Table 1 shows that the li-
near approximation of the bremsstrahlung spectrum
gives an overestimated value of the “effective” photon
yield (up to 20%) at the lower boundary of the Z and E0
value ranges under consideration. At the same time, the
divergence practically disappears at the upper boundary
of the mentioned ranges. This is due to a certain radiant
energy redistribution between the lower and middle
parts of the spectrum at its linear approximation.
2.2. SPACE-ANGULAR DISTRIBUTION
OF PHOTONS
The peculiarity of electron dynamics in the linear
accelerator lies in the limitation of the cross-sectional
size of the beam by the aperture of the accelerating
structure along the whole path of beam formation.
Therefore, the angular divergence of electrons on the
front surface of the converter can be neglected. The
probability density function of their radial distribution is
commonly described by the Gaussian law [5]
2
2 2
1 exp ,
2 2
e
e e
dP r
dS πδ δ
⎛ ⎞
= −⎜ ⎟
⎝ ⎠
(5)
where δе is the standard deviation of the distribution.
The generation of bremsstrahlung photons and the
angle of their escape from the converter are determined
by the processes of accelerated-electron multiple scat-
tering in the converter. Therefore, we shall assume that
147
the radial and angular photon distributions behind the
converter can also be described by the Gaussian distri-
bution with the standard deviations δγ,r(E0,d) and
δγ,θ(E0,d), respectively.
The simulation method was used to calculate the ra-
dial and angular distributions of “effective” photons
(ωmin=7.2 MeV) for the W converter of different thick-
ness at various E0 values. The distributions were ap-
proximated by the Gaussian functions with the result
that the following standard deviation δγ,r as functions of
the converter thickness d ranging from 0 to 1 cm was
obtained:
3
2
, 0( ) ( ) .r ed k E dγδ δ= + ⋅ (6)
For the 0.4 cm thick W converter the coefficient
k(E0) value is variable from 0.053 (E0 = 40 MeV) to
0.029 (E0 = 100 MeV).
As an estimate of the average exit angle of “effective”
photons from the converter ⎯θ(Е0,d), we take
0 , 0 , 0( , ) 2ln2 ( , ) 1.177 ( , ) ,E d E d E dγ θ γ θθ δ δ= (7)
which corresponds to the half-width at half-height of the
θ distribution. From simulation results it follows that for
the 0.4 cm thick converter the θ value lies within the
range from 7.2° (Е0=40 MeV) to 3.8° (Е0=100 MeV).
So, the standard deviation of the radial photon flux dis-
tribution behind the converter in the plane with the co-
ordinate z (z = 0 corresponds to the front surface of the
converter) is given by
3
2
, 0 0 0( , , ) ( ) ( ) ( , ) .r eE d z k E d z d tg E dγδ δ θ= + ⋅ + − ⋅ (8)
Henceforth, to take into account the photon flux
density variation along the target axis owing to the an-
gular divergence of the flux, we shall use the δγ,r value
at the target half-height or at z = d + a + H/2.
3. THE PHOTONUCLEAR YIELD OF
ISOTOPES IN THE CYLINDRICAL TARGET
3.1. To express analytically the photonuclear reac-
tion cross section σi(ω), we make use of the customary
form of description of the giant dipole resonance [6]:
2
max
2 2 2 2
( )( ) ,
( ) ( )
i
i i
i i
ωσ ω σ
ω ω ω
Γ
= ⋅
− + Γ
(9)
where Гі is the excitation function width at half-height,
ωi is the photon energy corresponding to the cross sec-
tion peak max
iσ .
Table 2 gives the characteristics of both the cross
sections for the reactions under consideration and the
target material of natural isotopic composition.
Table 2
Parameters of target materials and excitation functions
Reaction ρТ,
гg/cm3
νТ ωi
th,
MeV
σi
max,
mb
ωi,
MeV
Γi,
MeV
48Ti(γ,p)47Sc 4.54 0.738 11.6 6.8 21.3 7.32
68Zn(γ,p)67Cu 7.133 0.188 9.99 10.76 23.16 8.82
187Re(γ,n)186Re 21.02 0.626 7.38 424.65 13.19 3.67
3.2. For the case of the cylindrical target axially
symmetric with radiant flux formula (1) can be rewritten
as
0
0
0
( ) 2 ( , , ) ( ) .
th
Ed a H R
A
i T T i
d a
Ny E dz rdr Ф z r d
A
γ
ω
ν ρ π ω σ ω ω
+ + •
+
= ⋅∫ ∫ ∫ (10)
At linear approximation of the spectrum (3), the expres-
sion for the normalized differential fluence of “effec-
tive” photons with allowance made for attenuation of
their flux in the target material can be represented as
2
0
,1 2 2
, 0 ,
( , ) 1 1( , , ) exp ( ) ( ) ,
( ) 2 ( )r r
E d rÔ z r z d a
z E zγ
γ γ
ηω μ ω
πδ ω δ
• ⎧ ⎫⎡ ⎤⎛ ⎞ ⎪ ⎪= − ⋅ − + ⋅ − −⎢ ⎥⎨ ⎬⎜ ⎟
⎢ ⎥⎝ ⎠ ⎪ ⎪⎣ ⎦⎩ ⎭
(11)
where , ( )r zγδ is determined by formula (6).
3.3. According to the simulation results, in the
10≤ω≤50 MeV range overlapping the giant dipole reso-
nance region, the photon attenuation coefficient μ(ω)
varies only very slightly practically for all the materials.
Taking also into account the form of the excitation func-
tion σi(ω), in the further calculations we can put
μ(ω)=μ(ωi). Then, substituting eq. (9), (11) into formula
(10) and integrating over r and z we obtain
[ ]
max 2
0
2
,
,1 0
( , )2 1 exp
2 ( 2)
1 exp ( )
( ) ,
( )
i A
i T T
r
i
i
i
E d N Ry
A d a H
H
S E
γ
η σν ρ
δ
μ ω
μ ω
⎡ ⎤⎛ ⎞⋅ ⋅
= ⋅ − − ⋅⎢ ⎥⎜ ⎟⎜ ⎟+ +⎢ ⎥⎝ ⎠⎣ ⎦
− − ⋅
⋅ ⋅ (12)
where
0
,
2
,1 0 2 2 2 2
0
( )( ) 1 .
( ) ( )
i th
E
i
i
i i
dS E
Eω
ω ω ω
ω ω ω ω
⎛ ⎞Γ
= ⋅ − ⋅⎜ ⎟− + Γ ⎝ ⎠
∫ (13)
After replacement of the variables
,
i
ωε =
Γ
,i
i
i
ωε =
Γ
0
0 ,
i
Eε =
Γ
,
, ,i th
i th
i
ω
ε =
Γ (14)
formula(13) takes on the form
0
,
,1 0 2 2 2 2
0
0 ,
( ) 1
( )
( ) ( ) ,
i th
i
i
i th
S E d
ε
ε
ε ε ε
ε ε ε ε
ε ε
⎛ ⎞
= ⋅ − =⎜ ⎟− + ⎝ ⎠
= Ψ −Ψ⎡ ⎤⎣ ⎦
∫
(15)
where
1 2 2
0
1( ) ( ) ( ) ( ) ,
2 D
ε ε ε ε
ε
− +⎡ ⎤Ψ = Ψ − Ψ −Ψ⎣ ⎦ (16)
2 2
1
1 2( ) 1( ) ,iarctg
D D
ε εε
⎡ ⎤− +
Ψ = ⎢ ⎥
⎣ ⎦
(17)
± 2 2
2
1( ) ln( ±D ) (2 ±D) ,
2 i D arctgε ε ε ε εΨ = + + ⋅
24 1 .iD ε= −
(18)
Finally, the expression for the normalized yield of
isotopes in the cylindrical target can be represented in
the following form
[ ]{ }
2
0 2
,
0
( ) 1 exp
2 ( 2)
1 exp ( ) ( ) ,
i
r
i i
Ry E
d a H
H y E
γδ
μ ω ∞
⎧ ⎫⎡ ⎤⎪ ⎪= − − ⋅⎢ ⎥⎨ ⎬+ +⎢ ⎥⎪ ⎪⎣ ⎦⎩ ⎭
⋅ − − ⋅ ⋅
(19)
where the yield in the semi-infinite target is given by
max 0
0 0 ,
( , )( ) 2 [ ( ) ( )] .
( )
A
i T T i i th
i
N E dy E
A
ην ρ σ ε ε
μ ω
∞ = ⋅ ⋅ ⋅ Ψ −Ψ (20)
3.4. The maximum volume velocity of isotope prod-
uct generation falls on the front surface of the target in
the neighborhood of the target axis (z=d+a; r=0), where
148
the photon flux density is the highest. For this region,
the normalized specific yield of the isotope can be de-
termined as
maxmax
max0
2
,
0 ,
( , )
( )
[ ( ) ( )] .
i A c
i T i
T r
i th
dy N E ty
dm d aA γ
ην σ
πδ
ε ε
⎛ ⎞
= = ⋅⎜ ⎟ +⎝ ⎠
⋅ Ψ − Ψ
(21)
3.5. With formulas (19)-(21) it is easy to estimate
the total activity of the target and its peak specific activ-
ity after the time of exposure τ at an average electron
beam current I as
0( ) ln 2( ) 1 exp ,i
i
i
I y EA
e T
τ τ
⎡ ⎤⎛ ⎞⋅
= − − ⋅⎢ ⎥⎜ ⎟
⎝ ⎠⎣ ⎦
(22)
where e is the electron charge, Ti is the half-life of the isotope.
3.6. Figs.4 to 6 show the normalized photonuclear
yields of 47Sc, 67Cu and 186Re isotopes as functions of
the electron energy E0 (δe=0.25 cm; d=0.4 cm) for the
targets from natural materials, measuring 2RxH (cm).
40 50 60 70 80 90 100
0,0
2,0x10
-5
4,0x10
-5
6,0x10
-5
8,0x10
-5
1,0x10
-4
1,2x10
-4
1,4x10
-4
Ti, 1x3
E0
y i,
re
l.u
n.
40 50 60 70 80 90 100
0,0
1,0x10
-4
2,0x10
-4
3,0x10
-4
4,0x10
-4
5,0x10
-4
6,0x10
-4
7,0x10
-4
8,0x10
-4
9,0x10
-4
Ti, d→∞, H→∞
E0
y i,
re
l.u
n.
Fig.4. Sc-47 yield from the Ti target
40 50 60 70 80 90 100
0,0
1,0x10-5
2,0x10-5
3,0x10-5
4,0x10-5
5,0x10-5
6,0x10-5
7,0x10-5
Zn, 1x3
E0
y i,
re
l.u
n.
40 50 60 70 80 90 100
0,0
5,0x10-5
1,0x10-4
1,5x10-4
2,0x10-4
2,5x10-4
E0
Zn, d→∞, H→∞
y i,
re
l.u
n.
Fig.5. Cu-67 yield from the Zn target
40 50 60 70 80 90 100
0,000
0,001
0,002
0,003
0,004
0,005
0,006
Re, 1x3
E0
y i,
re
l.u
n.
40 50 60 70 80 90 100
0,000
0,002
0,004
0,006
0,008
0,010
E0
Re, d→∞, H→∞
y i,
re
l.u
n.
Fig.6. Re-186 yield from the Re target
The data were obtained through calculations by for-
mulas (19), (20), and also through simulation with due
regard for the excitation functions measured experimen-
tally [6]. The last ones are denoted in the figures by the
■ symbol. The 0 ,[ ( ) ( )]i thε εΨ − Ψ function values for
the reactions are listed in Table 3.
Table 3
The 0 ,[ ( ) ( )]i thε εΨ −Ψ function values
Е0, MeV
Reaction 40 60 80 100
48Ti(γ,p)47Sc 0.1995 0.2829 0.3265 0.3532
68Zn(γ,p)67Cu 0.2026 0.3011 0.3532 0.3853
187Re(γ,n)186Re 0.2474 0.2922 0.3150 0.3288
CONCLUSIONS
The high-energy bremsstrahlung flux, to which the
processing target is exposed, is substantially inhomoge-
neous. The radiation intensity and its distribution in the
target volume are governed not only by the electron
energy and the average beam current, but also by the
beam size, the converter thickness and material, as well
as by the target size and location. As a rule, the target
interacts only with a part of the photon flux, and as a
result, an uncertainty arises between the target activity
and the electron beam charge. It is just here lies the vital
difference between photoactivation and the heavy parti-
cle activation, when practically the whole beam charge
is localized in the target. Therefore, the normalization of
the isotope yield to the beam charge (accepted in accel-
erator technologies) without a detailed description of
activation conditions, appears not quite correct, as ap-
plied to the photonuclear method.
The analysis of the data in Figs. 4 to 6 shows that the
proposed model gives overestimated isotope yield val-
ues for the targets with Z<30. The discrepancy de-
creases till the coincidence of the results is attained in
the region of Z ≈ 40, E0 ≈ 50 MeV. With an increase in
the electron energy the model starts to give underesti-
149
mated yield values. The discrepancy becomes greater at
Z → 80 (see Fig.6).
The mentioned difference between the analytical es-
timation data and the simulation data can be explained
by the fact that the proposed approximation of the
bremsstrahlung spectrum (see formula (3)) gives overes-
timated (up to 20%) “effective” photon yield values for
all the reactions at E0 < 100 MeV, the discrepancy de-
creasing with an increase in Z and E0 (see Table 1). The
reversal of the sign of discrepancy between the isotope
yield data in the region of Z>40, E0>50 is due to the fact
that the proposed model takes into account the channel
of isotope production only under the action of photons
generated in the converter. At the same time, as the Z
value of the target and the electron energy increase,
there grows the contribution from the reactions due to
photons produced in the target itself by the high-energy
part of the electron flux that has passed through the
converter.
REFERENCES
1. F. Solvat, J.M. Fernandez-Varea, I. Sempau.
PENELOPE-2006 a Code System for Monte-Carlo
Simulation of Electron and Photon Transport.
OECD Nucl. Ener. Agency (Issyles – Moulineous)
France. 2006.
2. V.I.Nikiforov, V.L.Uvarov. Analysis of Mixed e,X
Radiation along the Extraction Facilities of Electron
Accelerators // Atomic Energy. 2009, v.106, №4,
p.220-224.
3. N.P. Dikiy, A.N. Dovbnya, V.L. Uvarov. Electron
Accelerator Based Soft Technology for Medical Im-
aging Isotopes Production // Proc. 8-th Europ. Part.
Accel. Conf. EPAC’02. Paris (France), June 3-7,
2002, p.2760-2762.
4. I.H. Hubbel. Photon Mass Attenuation and Energy-
absorption Coefficients from 1 keV to 20 MeV // Int.
J. Appl. Rad. Isot. 1982, v.33, №12, p.1269-1290.
5. Radiation Dosimetry: Electron Beams with Energies
between 1 and 50 MeV // ICRU Report 35, 1984.
6. Handbook on photonuclear data for Applications //
Final report of coordinated researched projects.
IAEA. TECDOC. Draft N 3 (Culham). 11 February
2000.
Статья поступила в редакцию 02.12.2009 г.
АНАЛИТИЧЕСКИЙ МЕТОД ОЦЕНКИ ВЫХОДА ИЗОТОПОВ ПРИ ФОТОЯДЕРНОМ
ПРОИЗВОДСТВЕ
В.И. Никифоров, В.Л. Уваров
Разработана эвристическая модель для описания пространственно-энергетических характеристик высо-
коэнергетичного тормозного излучения. Предложен метод с ее использованием для аналитической оценки
фотоядерного выхода изотопов в широком диапазоне значений атомного номера (Z=20-80) и размеров ми-
шени, а также энергии электронов (40…100 МэВ). Проведен анализ обоснованности допущений модели пу-
тем ее сопоставления с результатами моделирования на основе программной системы PENELOPE/2006, до-
полненной базой данных по сечениям фотоядерных реакций. Ранее было показано, что такой метод модели-
рования дает хорошее согласие с результатами эксперимента. В качестве примера рассмотрены представ-
ляющие практический интерес реакции 48Ti(γ,p)47Sc, 68Zn(γ,p)67Cu и 187Re(γ,n)186Re.
АНАЛІТИЧНИЙ МЕТОД ОЦІНКИ ВИХОДУ ІЗОТОПІВ ПРИ ФОТОЯДЕРНОМУ ВИРОБНИЦТВІ
В.І. Нікіфоров, В.Л. Уваров
Розроблено евристичну модель для опису просторово-енергетичних характеристик високоенергетичного
гальмівного випромінювання. Запропоновано метод з її використанням для аналітичної оцінки фотоядерно-
го виходу ізотопів у широкому діапазоні значень атомного номера (Z=20-80) і розмірів мішені, а також енер-
гії електронів (40…100 МеВ). Проведено аналіз обґрунтованості припущень моделі шляхом її порівнювання
з результатами моделювання на основі програмної системи PENELOPE/2006, доповненої базою даних з пе-
ретинів фотоядерних реакцій. Раніше було показано, що такий метод моделювання дає добре погодження з
результатами експерименту. Як приклад розглянуто реакції 48Tі(γ,p)47Sc, 68Zn(γ,p)67Cu і 187Re(γ,n)186Re, що
мають практичний інтерес.
|
| id | nasplib_isofts_kiev_ua-123456789-15708 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-11-28T22:10:49Z |
| publishDate | 2010 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Nikiforov, V.I. Uvarov, V.L. 2011-01-31T16:17:15Z 2011-01-31T16:17:15Z 2010 Analytical method for estimation isotope yield under photonuclear production / V.I. Nikiforov, V.L. Uvarov // Вопросы атомной науки и техники. — 2010. — № 2. — С. 145-149. — Бібліогр.: 6 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/15708 The heuristic model for description space-energy characteristics of the high-energy bremsstrahlung has been developed. On its basis the method for analytical estimation photonuclear yield of isotopes in wide range of atomic number (Z=20-80) and size of a target as well as of the electron energy (40…100 MeV) is proposed. The analysis of validity of the model assumptions has been executed by means of it comparison with the results of simulation using the program package PENELOPE/2006 [1] supplemented with database on the cross-sections of photonuclear reactions. It has been shown earlier that such simulation method provides close fit with the experimental results. As an example the reactions of practical interest 48Ti(γ,p)47Sc, 68Zn(γ,p)67Cu and 187Re(γ,n)186Re are presented. Разработана эвристическая модель для описания пространственно-энергетических характеристик высокоэнергетичного тормозного излучения. Предложен метод с ее использованием для аналитической оценки фотоядерного выхода изотопов в широком диапазоне значений атомного номера (Z=20-80) и размеров мишени, а также энергии электронов (40…100 МэВ). Проведен анализ обоснованности допущений модели путем ее сопоставления с результатами моделирования на основе программной системы PENELOPE/2006, дополненной базой данных по сечениям фотоядерных реакций. Ранее было показано, что такой метод моделирования дает хорошее согласие с результатами эксперимента. В качестве примера рассмотрены представляющие практический интерес реакции 48Ti(γ,p)47Sc, 68Zn(γ,p)67Cu и 187Re(γ,n)186Re. Розроблено евристичну модель для опису просторово-енергетичних характеристик високоенергетичного гальмівного випромінювання. Запропоновано метод з її використанням для аналітичної оцінки фотоядерного виходу ізотопів у широкому діапазоні значень атомного номера (Z=20-80) і розмірів мішені, а також енергії електронів (40…100 МеВ). Проведено аналіз обґрунтованості припущень моделі шляхом її порівнювання з результатами моделювання на основі програмної системи PENELOPE/2006, доповненої базою даних з перетинів фотоядерних реакцій. Раніше було показано, що такий метод моделювання дає добре погодження з результатами експерименту. Як приклад розглянуто реакції 48Tі(γ,p)47Sc, 68Zn(γ,p)67Cu і 187Re(γ,n)186Re, що мають практичний інтерес. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Применение ускорителей Analytical method for estimation isotope yield under photonuclear production Аналитический метод оценки выхода изотопов при фотоядерном производстве Аналітичний метод оцінки виходу ізотопів при фотоядерному виробництві Article published earlier |
| spellingShingle | Analytical method for estimation isotope yield under photonuclear production Nikiforov, V.I. Uvarov, V.L. Применение ускорителей |
| title | Analytical method for estimation isotope yield under photonuclear production |
| title_alt | Аналитический метод оценки выхода изотопов при фотоядерном производстве Аналітичний метод оцінки виходу ізотопів при фотоядерному виробництві |
| title_full | Analytical method for estimation isotope yield under photonuclear production |
| title_fullStr | Analytical method for estimation isotope yield under photonuclear production |
| title_full_unstemmed | Analytical method for estimation isotope yield under photonuclear production |
| title_short | Analytical method for estimation isotope yield under photonuclear production |
| title_sort | analytical method for estimation isotope yield under photonuclear production |
| topic | Применение ускорителей |
| topic_facet | Применение ускорителей |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/15708 |
| work_keys_str_mv | AT nikiforovvi analyticalmethodforestimationisotopeyieldunderphotonuclearproduction AT uvarovvl analyticalmethodforestimationisotopeyieldunderphotonuclearproduction AT nikiforovvi analitičeskiimetodocenkivyhodaizotopovprifotoâdernomproizvodstve AT uvarovvl analitičeskiimetodocenkivyhodaizotopovprifotoâdernomproizvodstve AT nikiforovvi analítičniimetodocínkivihoduízotopívprifotoâdernomuvirobnictví AT uvarovvl analítičniimetodocínkivihoduízotopívprifotoâdernomuvirobnictví |