Usage of the fission reaction for the measurement of the polarization degree of photon beam
The e±ciency of photofission of ²³²Th and ²³⁸U for the measurement of the polarization degree of photon beam has been compared with the conventional reaction of the deuterium photodisintegration.
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irk-123456789-1112652017-01-10T03:02:45Z Usage of the fission reaction for the measurement of the polarization degree of photon beam Denyak, V.V. Khvastunov, V.M. Paschuk, S.A. Schelin, H.R. Ядерная физика и элементарные частицы The e±ciency of photofission of ²³²Th and ²³⁸U for the measurement of the polarization degree of photon beam has been compared with the conventional reaction of the deuterium photodisintegration. У роботі проведено оцінку ефективності використання реакції фотоподілу ізотопів ²³²Th и ²³⁸U для вимірювання ступеня поляризації фотонного пучка у порівнянні з традиційно використовуємою реакцією фоторозщеплення дейтерія. В работе проведена оценка эффективности использования реакции фотоделения изотопов ²³²Th и ²³⁸U для измерения степени поляризации фотонного пучка по сравнению с традиционно применяемой реакцией фоторасщепления дейтерия. 2009 Article Usage of the fission reaction for the measurement of the polarization degree of photon beam / V.V. Denyak, V.M. Khvastunov, S.A. Paschuk, H.R. Schelin // Вопросы атомной науки и техники. — 2009. — № 3. — С. 47-50. — Бібліогр.: 11назв. — англ. 1562-6016 PACS: 29.27.Hj, 24.70.+s, 25.85.Jg http://dspace.nbuv.gov.ua/handle/123456789/111265 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Ядерная физика и элементарные частицы Ядерная физика и элементарные частицы |
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Ядерная физика и элементарные частицы Ядерная физика и элементарные частицы Denyak, V.V. Khvastunov, V.M. Paschuk, S.A. Schelin, H.R. Usage of the fission reaction for the measurement of the polarization degree of photon beam Вопросы атомной науки и техники |
| description |
The e±ciency of photofission of ²³²Th and ²³⁸U for the measurement of the polarization degree of photon beam has been compared with the conventional reaction of the deuterium photodisintegration. |
| format |
Article |
| author |
Denyak, V.V. Khvastunov, V.M. Paschuk, S.A. Schelin, H.R. |
| author_facet |
Denyak, V.V. Khvastunov, V.M. Paschuk, S.A. Schelin, H.R. |
| author_sort |
Denyak, V.V. |
| title |
Usage of the fission reaction for the measurement of the polarization degree of photon beam |
| title_short |
Usage of the fission reaction for the measurement of the polarization degree of photon beam |
| title_full |
Usage of the fission reaction for the measurement of the polarization degree of photon beam |
| title_fullStr |
Usage of the fission reaction for the measurement of the polarization degree of photon beam |
| title_full_unstemmed |
Usage of the fission reaction for the measurement of the polarization degree of photon beam |
| title_sort |
usage of the fission reaction for the measurement of the polarization degree of photon beam |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2009 |
| topic_facet |
Ядерная физика и элементарные частицы |
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http://dspace.nbuv.gov.ua/handle/123456789/111265 |
| citation_txt |
Usage of the fission reaction for the measurement of the polarization degree of photon beam / V.V. Denyak, V.M. Khvastunov, S.A. Paschuk, H.R. Schelin // Вопросы атомной науки и техники. — 2009. — № 3. — С. 47-50. — Бібліогр.: 11назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-08T01:52:50Z |
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| fulltext |
USAGE OF THE FISSION REACTION FOR THE
MEASUREMENT OF THE POLARIZATION DEGREE OF
PHOTON BEAM
V.V. Denyak1∗, V.M. Khvastunov1, S.A. Paschuk2, H.R. Schelin2
1National Science Center ”Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine
2Federal University of Technology - Parana, Curitiba, 80230-901, Brazil
(Received December 22, 2009)
The efficiency of photofission of 232Th and 238U for the measurement of the polarization degree of photon beam has
been compared with the conventional reaction of the deuterium photodisintegration.
PACS: 29.27.Hj, 24.70.+s, 25.85.Jg
1. INTRODUCTION
The experimental investigations of the photofission of
even-even nuclei showed that its cross section value
is sensitive to the direction of the polarization vector
for photon energies Eγ < 20 MeV [1, 2, 3, 4]. Such
result opens up possibility to use the photofission re-
action for the measurement of the beam polarization
degree [5].
In this work the comparison of the efficiency of pho-
todisintegration of deuterium, which is usually used
in this energy region, with photofission of 232Th and
238U was made.
2. PRECISION OF THE
DETERMINATION OF THE
POLARIZATION DEGREE
To evaluate the efficiency of one or other nuclear reac-
tion in determination of the polarization degree (P) of
the photon beam it is necessary to find the formula in
which the precision the of the determination of P de-
pends from the reaction characteristics - cross section
(σ) and asymmetry (Σ) (in the case of photofission
this quantity is called ”analyzing power”).
The polarization degree is usually defined as:
P =
N‖ −N⊥
N‖ + N⊥
,
where N‖ (N⊥) - the number of photons with electric
field vector parallel (perpendicular) to the reaction
plane. At the same time the total number of photons
passed through the target is Nγ = N‖ + N⊥. In this
case such formulas are true:
N‖ =
Nγ
2
(1 + P ),
N⊥ =
Nγ
2
(1− P ). (1)
The cross section asymmetry (analyzing power) asso-
ciated with the change of the polarization direction
is defined as:
Σ(θ) =
dσ‖
dΩ (θ)− dσ⊥
dΩ (θ)
dσ‖
dΩ (θ) + dσ⊥
dΩ (θ)
,
where dσ‖,⊥/dΩ(θ) - differential cross section of the
reaction induced by photons with polarization paral-
lel and perpendicular to the reaction plane. In this
case the cross section with unpolarized photons is:
dσ
dΩ
(θ) =
dσ‖
dΩ (θ) + dσ⊥
dΩ (θ)
2
.
For such definitions the given formulas are true:
dσ‖
dΩ
(θ) =
dσ
dΩ
(θ)(1 + Σ(θ)),
dσ⊥
dΩ
(θ) =
dσ
dΩ
(θ)(1− Σ(θ)). (2)
In the analysis of the experimental data the value of
Σ(θ) is determined by the formulae:
Σ(θ) =
1
P
· Y‖(θ)− Y⊥(θ)
Y‖(θ) + Y⊥(θ)
,
where Y(θ)‖,⊥ - the reaction yield in the plane par-
allel and perpendicular to the polarization plane. In
this case:
P =
1
Σ(θ)
· Y‖(θ)− Y⊥(θ)
Y‖(θ) + Y⊥(θ)
.
Quantity Y‖(θ) represent the sum of the reaction
yields for photons with polarization parallel and per-
pendicular to the reaction plane:
Y‖(θ) = Nn∆Ωε(N‖
dσ‖
dΩ
(θ) + N⊥
dσ⊥
dΩ
(θ)),
∗Corresponding author E-mail address: denyak@gmail.com
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2009, N3.
Series: Nuclear Physics Investigations (51), p.47-50.
47
where Nn - the number of nuclei in the target, ∆Ω -
the solid angle of the detector, ε - detector efficiency.
In the case of Y⊥(θ) we have the similar formulae only
N‖ and N⊥ change their places. For the reaction yield
in the plane perpendicular to the polarization plane
N⊥ photons are parallel and N‖ - perpendicular.
Y⊥(θ) = Nn∆Ωε(N⊥
dσ‖
dΩ
(θ) + N‖
dσ⊥
dΩ
(θ)).
Using (1) and (2) it is easy to obtain
Y‖(θ) = Nn∆ΩεNγ
dσ
dΩ
(θ)(1 + PΣ(θ)),
and
Y⊥(θ) = Nn∆ΩεNγ
dσ
dΩ
(θ)(1− PΣ(θ)).
The relative error of the determination of the polar-
ization value is:
∆P
P
=
1
PΣ(θ)
∆
(
Y‖(θ)− Y⊥(θ)
Y‖(θ) + Y⊥(θ)
)
=
1
PΣ(θ)
√(
∆(Y‖(θ)− Y⊥(θ))
Y‖(θ) + Y⊥(θ)
)2
+
(
(Y‖(θ)− Y⊥(θ))∆(Y‖(θ) + Y⊥(θ))
(Y‖(θ) + Y⊥(θ))2
)2
=
1
PΣ(θ)
√
(∆(Y‖(θ)− Y⊥(θ)))2(Y‖(θ) + Y⊥(θ))2 + (Y‖(θ)− Y⊥(θ))2(∆(Y‖(θ) + Y⊥(θ)))2
(Y‖(θ) + Y⊥(θ))4
.
Using the obtained expressions for Y‖,⊥(θ), and considering the error of Y‖,⊥(θ) as a square root of its
value we have:
Y‖(θ) + Y⊥(θ) = Nn∆ΩεNγ
dσ
dΩ
(θ)(1 + PΣ(θ) + 1− PΣ(θ)) = 2Nn∆ΩεNγ
dσ
dΩ
(θ),
Y‖(θ)− Y⊥(θ) = Nn∆ΩεNγ
dσ
dΩ
(θ)(1 + PΣ(θ)− (1− PΣ(θ))) = 2Nn∆ΩεNγ
dσ
dΩ
(θ)PΣ(θ),
∆(Y‖(θ) + Y⊥(θ)) = ∆(Y‖(θ)− Y⊥(θ)) =
√
(∆Y‖(θ))2 + (∆Y⊥(θ))2 =
√
Y‖(θ) + Y⊥(θ) =
√
2Nn∆ΩεNγ
dσ
dΩ
(θ).
Thus the relative error of measured polarization degree can be presented as:
∆P
P
=
1
PΣ(θ)
√
2Nn∆ΩεNγ
dσ
dΩ (θ)(2Nn∆ΩεNγ
dσ
dΩ (θ))2 + (2Nn∆ΩεNγ
dσ
dΩ (θ)PΣ(θ))22Nn∆ΩεNγ
dσ
dΩ (θ)
(2Nn∆ΩεNγ
dσ
dΩ (θ))4
=
√
1 + P 2Σ(θ)2
2Nn∆ΩεNγ
dσ
dΩ (θ)P 2Σ(θ)2
=
1√
2Nn∆ΩεNγP 2
√
1 + P 2Σ(θ)2
dσ
dΩ (θ)Σ(θ)2
,
(3)
where information about the nuclear reaction is in the second factor only.
3. RESULTS AND DISCUSSION
It was shown in the experimental investigations [1, 2,
3, 4] of the fission of even-even nuclei with polarized
photons that in the energy region Eγ < 20 MeV this
process is described completely by the electric dipole
excitation. In this case according to the equations
of [6] the analyzing power of the photofission can be
presented as:
Σ (θ = 90◦) =
b
a + b
,
where a and b may be obtained from the analysis of
the cross section angular distribution for unpolarized
photons:
W (θ) = a + b sin2(θ).
To obtain the values of dσ/dΩ(90◦) and Σ(90◦) the
results of following works were used: [7, 8] - 232Th,
[8, 9] - 238U, [10, 11] - 2H. Numerical values were
taken from the data base EXFOR (http://www-
nds.iaea.org/exfor/exfor00.htm). To eliminate the
fluctuations produced by the statistical dispersion of
the data the approximation of the energy dependence
of each experimental value with smooth curve was
done. The example of such approximation for 232Th
is given in Fig.1.
As it is seen from formula (3) the precision of the
determination of the polarization degree depends on
Σ(θ) and product dσ/dΩ(θ)Σ2(θ). For polarization
P¿1 term P2Σ2(θ) in the numerator of the second
factor became significantly smaller than 1. In this
case the only value the relative error of P depends on
is product dσ/dΩ(θ)Σ2(θ):
∆P
P
∼ 1√
dσ
dΩ (θ)Σ2(θ)
.
48
Fig.1. Approximation of the cross section and
analyzing power of 232Th with smooth curves
Fig.2 shows the energy dependence of
dσ/dΩ(90◦)Σ2(90◦) for 232Th and 238U photofission
and photodisintegration of deuterium. Since the error
is inversely as square root of this quantity it is evi-
dent that in the energy region Eγ ∼ 5.9 ... 6.4 MeV
for 238U and Eγ ∼ 6.0 ... 7.3 MeV for 232Th the
photofission reaction is preferable against the pho-
todisintegration of deuterium. The usage of the
photofission of 232Th should give stronger positive
effect and in broader energy region in comparison
with 238U.
To evaluate how the relative error depends on the
value of the polarization itself in the case when it
isn’t possible to ignore the second term in the nu-
merator of the formula (3) the calculations were
carried out for polarization degree 10% and 100%.
The result is present in Fig.3.
As it is seen from Fig.3 the usage of photofission of
232Th is preferable for the measurements of polar-
ization as compared with the photodisintegration of
deuterium. But this advantage isn’t big. The relative
error can be reduced up to ∼25% for P = 10% and
up to ∼30% for P = 100%. With the decrease of the
polarization degree the energy region of the positive
effect also became smaller from Eγ ∼ 6.0 ... 7.6 MeV
for P = 100% to Eγ ∼ 6.0 ... 7.3 MeV for P = 10%.
The photofission of 238U gives smaller effect
not only in absolute value but in more nar-
row energy region also. But for the polar-
ization close to 100% the new energy region
of positive effect, that is absent in photofis-
sion of 232Th, is opened - Eγ ∼ 7.6 ... 8.3 MeV .
Fig.2. Energy dependence of the product of cross
section and square of asymmetry (analyzing power)
for θ = 90◦.
Solid circles - photodisintegration of deuterium.
Open circles - photofission of 232Th.
Stars - photofission of 238U
Fig.3. Relative error of the polarization degree of
photon beam.
Solid circles - photodisintegration of deuterium.
Open circles - photofission of 232Th.
Stars - photofission of 238U
49
4. CONCLUSIONS
The carried out investigation shows that the usage
of 232Th and 238U photofission for the determina-
tion of the polarization degree of the photon beam
offers certain advantage compared with the conven-
tional reaction of the deuterium photodisintegration.
In spite of the fact that the positive effect doesn’t ex-
ceed 30% these reactions are very perspective taking
into account that the registration of the fission frag-
ment is much easier task than the detection of the
deuterium photodisintegration products. The essen-
tial weakness of the method is the impossibility of its
usage for non-monochromatic photon beam.
References
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1982, A308, p.63-71.
2. F. Steiper, T. Frommhold, W. Henkel, et al. Mass
dependence of fragment angular distributions in
the fission of 232Th and 236U induced by polar-
ized photons //Nucl. Phys. 1993, A563, p.282-
300.
3. V.M.Khvastunov, V.V.Denyak, I.G.Evseev, et al.
Fission of 232Th nucleus by linearlt polarized
photons //Phys. At. Nucl. 1994, v.57, p.1858-
1892.
4. V.M.Khvastunov, V.V.Denyak. 236U and 238U
fission induced by linearly polarized photons in
the region of giant dipole resonance //Phys. At.
Nucl. 2001, v.64, p.1269-1272.
5. V.M. Khvastunov. Polarimeter based on the reac-
tion of photofission of thorium nucleus //PAST.
Series ”General and Nuclear Physics”. 2000,
v.2(36), p.46-47 (www.kipt.kharkov.ua)
6. V. Bellini, M. Di Toro, S. Lo Nigro, and
G.S. Pappalardo. Fission induced by linearly
polarized photons on even-even nuclei //Lett.
Nuovo Cimento. 1979, v.26, p.173-179.
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4A, p.421-430.
8. V.V. Varlamov, N.N. Peskov. Evaluation of
(γ,xn), (γ,sn), (γ,n), (γ,2n), and (γ,f), reac-
tions cross sections for actinides nuclei 232Th,
238U, 237Np, and 239Pu: consistency between
data obtained using quasimonoenergetic annihila-
tion and bremsstrahlung photons. Moskow State
University, Institute of Nuclear Physics, Report,
2007-8/829, 2007, 17p.
9. A. Manfredini, L. Fiore, C. Ramorino, et al. An-
gular distribution of 238U fission fragments for
12 different mono-energetic γ-rays //Nucl. Phys.
1969, A123, p.664-672.
10. Y. Birenbaum, Z. Berant, A. Wolf, et al. Differ-
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11. V.P. Likhachev, M.N. Martins, Yu.A. Kasatkin,
et al. Disintegration of the deuteron by linearly
polarized photons at low energies //Nucl. Phys.
1998, A628, p.597-606.
ИСПОЛЬЗОВАНИЕ РЕАКЦИИ ДЕЛЕНИЯ ДЛЯ ИЗМЕРЕНИЯ СТЕПЕНИ
ЛИНЕЙНОЙ ПОЛЯРИЗАЦИИ ФОТОННОГО ПУЧКА
В.В. Деняк, В.М. Хвастунов, С.А. Пащук, У.Р. Счелин
В работе проведена оценка эффективности использования реакции фотоделения изотопов 232Th и
238U для измерения степени поляризации фотонного пучка по сравнению с традиционно применяемой
реакцией фоторасщепления дейтерия.
ВИКОРИСТАННЯ РЕАКЦIЇ ПОДIЛУ ДЛЯ ВИМIРЮВАННЯ СТУПЕНЯ ЛIНIЙНОЇ
ПОЛЯРИЗIЦIЇ ФОТОННОГО ПУЧКА
В.В. Деняк, В.М. Хвастунов, С.А. Пащук, У.Р. Счелiн
У роботi проведено оцiнку ефективностi використання реакцiї фотоподiлу iзотопiв 232Th и 238U
для вимiрювання ступеня поляризацiї фотонного пучка у порiвняннi з традицiйно використовуємою
реакцiєю фоторозщеплення дейтерiя.
50
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