²³⁸U fission near the threshold
Using the data on angular distribution of fission fragments, a threshold has been determined in a dipole fission channel with J=1 spin projection to the nucleus symmetry axis. It has been shown that the peak observed in the ²³⁸U fission cross section is determined by the contribution from the quadru...
Збережено в:
| Опубліковано в: : | Вопросы атомной науки и техники |
|---|---|
| Дата: | 2020 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2020
|
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/194560 |
| 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: | ²³⁸U fission near the threshold / V.M. Khvastunov , V.I. Kasilov, S.S. Kochetov, A.A. Khomich // Problems of atomic science and tecnology. — 2020. — № 5. — С. 23-26. — Бібліогр.: 12 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-194560 |
|---|---|
| record_format |
dspace |
| spelling |
Khvastunov, V.M. Kasilov, V.I. Kochetov, S.S. Khomich, A.A. 2023-11-27T14:16:55Z 2023-11-27T14:16:55Z 2020 ²³⁸U fission near the threshold / V.M. Khvastunov , V.I. Kasilov, S.S. Kochetov, A.A. Khomich // Problems of atomic science and tecnology. — 2020. — № 5. — С. 23-26. — Бібліогр.: 12 назв. — англ. 1562-6016 PACS: 25.85.Jg, 27.90.+b, 24.70.+s https://nasplib.isofts.kiev.ua/handle/123456789/194560 Using the data on angular distribution of fission fragments, a threshold has been determined in a dipole fission channel with J=1 spin projection to the nucleus symmetry axis. It has been shown that the peak observed in the ²³⁸U fission cross section is determined by the contribution from the quadrupole excitation. Знайдено поріг у дипольному каналі діления з проекцією спіна J=1 на вісь симетрії ядра із даних кутового розподілу осколків діления. Показано, що пік, який спостерігається в перерізі ділення ²³⁸U біля порогу, зумовлений вкладом у ділення при квадрупольному збудженні. Определен порог в дипольном канале деления с проекцией спина J=1 на ось симметрии ядра из данных углового распределения осколков деления. Показано, что пик, наблюдаемый в сечении деления ²³⁸U около порога, обусловлен вкладом в деление при квадрупольном возбуждении. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Nuclear physics and elementary particles ²³⁸U fission near the threshold Ділення ²³⁸U біля порогу Деления ²³⁸U у порога Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
²³⁸U fission near the threshold |
| spellingShingle |
²³⁸U fission near the threshold Khvastunov, V.M. Kasilov, V.I. Kochetov, S.S. Khomich, A.A. Nuclear physics and elementary particles |
| title_short |
²³⁸U fission near the threshold |
| title_full |
²³⁸U fission near the threshold |
| title_fullStr |
²³⁸U fission near the threshold |
| title_full_unstemmed |
²³⁸U fission near the threshold |
| title_sort |
²³⁸u fission near the threshold |
| author |
Khvastunov, V.M. Kasilov, V.I. Kochetov, S.S. Khomich, A.A. |
| author_facet |
Khvastunov, V.M. Kasilov, V.I. Kochetov, S.S. Khomich, A.A. |
| topic |
Nuclear physics and elementary particles |
| topic_facet |
Nuclear physics and elementary particles |
| publishDate |
2020 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Ділення ²³⁸U біля порогу Деления ²³⁸U у порога |
| description |
Using the data on angular distribution of fission fragments, a threshold has been determined in a dipole fission channel with J=1 spin projection to the nucleus symmetry axis. It has been shown that the peak observed in the ²³⁸U fission cross section is determined by the contribution from the quadrupole excitation.
Знайдено поріг у дипольному каналі діления з проекцією спіна J=1 на вісь симетрії ядра із даних кутового розподілу осколків діления. Показано, що пік, який спостерігається в перерізі ділення ²³⁸U біля порогу, зумовлений вкладом у ділення при квадрупольному збудженні.
Определен порог в дипольном канале деления с проекцией спина J=1 на ось симметрии ядра из данных углового распределения осколков деления. Показано, что пик, наблюдаемый в сечении деления ²³⁸U около порога, обусловлен вкладом в деление при квадрупольном возбуждении.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/194560 |
| citation_txt |
²³⁸U fission near the threshold / V.M. Khvastunov , V.I. Kasilov, S.S. Kochetov, A.A. Khomich // Problems of atomic science and tecnology. — 2020. — № 5. — С. 23-26. — Бібліогр.: 12 назв. — англ. |
| work_keys_str_mv |
AT khvastunovvm 238ufissionnearthethreshold AT kasilovvi 238ufissionnearthethreshold AT kochetovss 238ufissionnearthethreshold AT khomichaa 238ufissionnearthethreshold AT khvastunovvm dílennâ238ubílâporogu AT kasilovvi dílennâ238ubílâporogu AT kochetovss dílennâ238ubílâporogu AT khomichaa dílennâ238ubílâporogu AT khvastunovvm deleniâ238uuporoga AT kasilovvi deleniâ238uuporoga AT kochetovss deleniâ238uuporoga AT khomichaa deleniâ238uuporoga |
| first_indexed |
2025-11-24T06:57:25Z |
| last_indexed |
2025-11-24T06:57:25Z |
| _version_ |
1850843377520607232 |
| fulltext |
238U FISSION NEAR THE THRESHOLD
V.M.Khvastunov∗, V. I. Kasilov, S. S.Kochetov, A.A.Khomich
National Science Center ”Kharkiv Institute of Physics and Technology”, 61108 Kharkiv, Ukraine
(Received June 3, 2019)
Using the data on angular distribution of fission fragments, a threshold has been determined in a dipole fission channel
with J = 1 spin projection to the nucleus symmetry axis. It has been shown that the peak observed in the 238U
fission cross section is determined by the contribution from the quadrupole excitation.
PACS: 25.85.Jg, 27.90.+b, 24.70.+s
1. INTRODUCTION
Studies of angular distribution of fission fragments
provide important information on the properties of
fission barriers for heavy nuclei as well as on quantum
numbers of lower excitation states. In photofission,
low-spin states are excited [1]. At small photon ener-
gies fission is determined mainly by the electric dipole
(E1) excitation and by the much smaller contribution
of the electric quadrupole (E2) excitation. These ex-
periments provide information on the angular distri-
bution of fission fragments. Using this information
and the new technique, we have determined the fis-
sion barrier height of 238U in the dipole channel with
spin projection on the nuclear symmetry axis K = 1.
Angular distributions of fission fragments from E1
and E2 of the excited states are well described by
the equation (1).
W (θ) = a+ b sin2(θ) + c sin2(2θ) . (1)
Coefficients a, b, c are determined by the con-
tributions from 5 channels with quantum numbers
(Jπ, K) = (1−, 0), (1−, 1), (2+, 0), (2+, 1), (2+, 2),
where J and π are spin and parity of the excited state
of the nucleus, respectively, and K is the projection
of spin J to the nucleus symmetry axis. θ is the angle
between the photon beam direction and the direction
of exiting fragments (these two directions determine
the plane of the reaction). Coefficients a and b are
connected with dipole and quadrupole contributions,
and coefficient c is connected with quadrupole contri-
butions only. From the fit of expression (1) to the ex-
perimental data obtained three quantities, a, b, and
c, so for the data analysis respectively employs three
main fission channels, (1−, 0), (1−, 1), (2+, 0), while
the contributions of channels (2+, 1), (2+, 2) are ig-
nored.
In references [2-7] linearly polarized photons
have been used for the studies of photofission of
heavy nuclei. In these experiments, the new in-
dependent quantity has been obtained, namely, the
Σ-asymmetry, which characterizes the analyzing ca-
pacity of the photonuclear reaction.
Theoretical formalism for the analysis of fission
by polarized photons has been developed in [2,3].
Within this approach, quantity Σ(θ) is defined as
Σ(θ) =
1
Pγ
W (θ, φ = 0)−W (θ, φ = π/2)
W (θ, φ = 0) +W (θ, φ = π/2)
, (2)
where Pγ is the degree of photon beam polarization,
W (θ, φ) is the angular distribution of fission frag-
ments, φ is the angle between the polarization vector
of the photon and the plane of the reaction.
The angular distribution of fragments from the
fission by linearly polarized photons is given for the
total moment g ≤ 2 by the following expression [3],
W (θ, φ) = a+ b sin2(θ) + c sin2(2θ) +
ω Pγ cos(2φ)(d sin2(θ)− 4c sin4(θ)) , (3)
where ω = +1 for the electric excitations and ω = −1
for the magnetic excitations. The coefficient d is con-
nected with dipole and quadrupole contributions. In
this case, expression for Σ(θ) has the form
Σ(θ) = ω
d sin2(θ)− 4c sin4(θ)
a+ b sin2(θ) + c sin2(2θ)
. (4)
For θ = π/2
Σ
(
θ =
π
2
)
= ω
d− 4c
a+ b
. (5)
It is known from the analysis of angular distribu-
tion of fragments from fission by nonpolarized pho-
tons (Pγ = 0 in Eq.(3)) that the contribution from
the quadrupole fission in the energy range from 5 to
10MeV is small, i.e. the process is determined by
the dipole excitation only. As shown in [3] the value
of analyzing capacity Σ(θ) is determined in case of
purely dipole transition (ω = +1, c = 0) by coeffi-
cients a and b only, because d = b. This allows one to
compare the result obtained in the experiment with
polarized photons with the value of Σ(θ) computed on
∗Corresponding author E-mail address: Khvastunov@kipt.kharkov.ua
ISSN 1562-6016. PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2020, N5(129).
Series: Nuclear Physics Investigations (74), p.23-26.
23
the basis of the results of angular distribution mea-
surements for nonpolarized photon beam. It can be
seen from Eq.(3) that also in this case (Pγ = 0, c = 0)
the angular distribution is determined only by coeffi-
cients a and b, and the expression for Σ(θ) takes the
form
Σ
(
θ =
π
2
)
=
b
a+ b
. (6)
In paper [8] is shown, that the coefficients of angu-
lar distribution of fragments from fission are related
to the cross-sections of dipole channels of fission as
follows
b
a
=
σγ,f (1
−, 0)
σγ,f (1−, 1)
− 1
2
. (7)
2. ANALYSIS OF EXPERIMENTAL DATA
[10,11]
Putting expression (7) into (6) it was got
Σ
(
θ =
π
2
)
=
2σγ,f (1
−, 0)− σγ,f (1
−, 1)
2σγ,f (1−, 0) + σγ,f (1−, 1)
. (8)
Thus the size of Σ(π/2) is determined both
through the coefficients of a, b and through the sec-
tions of σ(1−, 0), σ(1−, 1). From a formula evi-
dently, that if present contribution only cross-section
of σ(1−, 0), then the size of Σ(π/2) is equal +1, and if
a contribution is cross-section of σ(1−, 1) only, then
Σ(π/2) is equal −1.
Using Eq.(6), the values of Σ-asymmetry for 238U
nucleus have been obtained. Experimental values
of angular distribution of fission fragments for 238U
nucleus were measured in [9,10], and numerical val-
ues of coefficients of a and b Eq.(1) were defined
in [11]. Values of Σ-asymmetry in the photon en-
ergy range from 5.0 to 6.8MeV are shown in Fig.1.
4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
S
-a
sy
m
m
e
tr
y
Eg, MeV
Fig.1. Σ-asymmetry of 238U photofission as ob-
tained from the data [10] (circles) and [11] (squares).
In absence of error bars, these bars are smaller than
the symbol size. The straight horizontal line shows
the Σ-asymmetry value egual to 1 determined only
by contribution of the cross-section in the channel
(1−, 0). The dotted line represents Σ = P/E4
γ .
The dash-dotted line shows the crossing point of
horizontal and dotted lines, which corresponds to the
barrier height of 238U fission in the channel (1−, 1)
From Fig.1 it is visible that at small energy
Eγ size of Σ-asymmetry is close to +1, that is Σ-
asymmetry in this area Eγ is defined only by fis-
sion through dipole (1−, 0) – the channel, and other
channels of fission, within experiment errors, have no
impact on Σ-asymmetry size. In the energy range
from 5 to 6.09MeV average size of experimental
data of Σ-asymmetry 238U (see Fig.1) is equal to
0.9645 ± 0.014533. This value differs from unit for
3.55%. Such difference can be caused by dispersion
of experimental data and a contribution of fission at
quadrupole excitation. This contribution doesn’t ex-
ceed 3.55% and it, is generally shown at low energy in
this range of energy. Therefore influence of this con-
tribution on value Σ-asymmetry at increase in energy
will be even less where to be shown, generally only
a fission contribution via the dipole channel with a
projection a back K = 0 on an axis of symmetry of a
nucleus.
From Fig.1 it is also visible that with increase
in energy Eγ size of Σ-asymmetry decreases. It fol-
lows from Eq.(8) than Σ-asymmetry is positive and
equal to +1 for the channel (1−, 0), and negative
and equal to −1 for the channel (1−, 1). The val-
ues of Σ-asymmetry obtained from the experiments
have positive values, i.e. they are mainly determined
by the (1−, 0) fission channel. In the region where
Σ-asymmetry is equal +1, only the channel (1−, 0)
contributes, i.e. Σ-asymmetry in it the Eγ areas
is defined only by fission through the dipole (1−, 0)
channel, and other channels of fission, within errors,
have no impact on the size Σ-asymmetry. The ap-
pearance of (1−, 1) channel contribution leads to the
reduction of Σ-asymmetry value. This means that
the energy, for which Σ-asymmetry becomes smaller
than +1, determines the height of 238U photofission
barrier through the (1−, 1) channel. It can be seen
from Fig.1 that at energy above 6.1MeV , the Σ-
asymmetry becomes less than +1.
To determine more precisely the energy height of
the photofission barrier E of the 238U nucleus, five
curves
Σ = P/E2
γ , Σ = P/E3
γ , Σ = P/E4
γ ,
Σ = P/E5
γ , Σ = P/E6
γ , (9)
where P is an adjustable parameter and Eγ is the
incident photon energy, were least-squares fitted to
the Σ-asymmetry values in the (1−, 1)-channel. For
this purpose we minimized the functional χ2 =∑
ωi (Σi − Σm,i)
2
, where Σi denotes the experimen-
tal Σ-asymmetry values in the energy range from 6.37
to 6.8MeV , where these values are less than +1 (Ta-
ble 1); Σm,i denotes the Σ-asymmetry values calcu-
lated from curves (8); ωi = 1/(∆Σi)
2 is the statisti-
cal weight Σi, ∆Σi is the mean square error of Σi.
24
Table 1. These values of Eγ ,
Σ-asymmetry and ∆Σ
Eγ , MeV Σ ∆Σ
6.37 0.819 0.040
6.42 0.803 0.110
6.71 0.68 0.050
6.75 0.64 0.090
6.80 0.427 0.1
The fitting results for the five curves (9) are given
in Table 2. It is apparent from Table 2, that the
least χ2 value was obtained for the curve Σ = P/E4
γ .
Since for the (1−, 0)-channel the Σ-asymmetry is pos-
itive and is equal to +1, then the energy, at which
the Σ = P/E4
γ curve with P = 1331 ± 49 is equal
to +1, determines the photofission barrier height of
the 238U nucleus in the (1−, 1)-channel. By mak-
ing P/E4 equal to 1, we have obtained E = P 1/4 =
(6.04±0.06)MeV . This value represents the photofis-
sion barrier height of the 238U nucleus in the (1−, 1)-
channel.
Table 2. The fitting results for the five curves (9)
Eq.(8) P +∆P χ2/(n− 1) E +∆E
MeV
P/E2 31.33± 1.17 2.04 5.6± 0.10
P/E3 204.5± 7.6 1.4 5.89± 0.07
P/E4 1331± 49 1.035 6.04± 0.06
P/E5 8659± 322 1.09 6.13± 0.05
P/E6 57083± 2108 1.1 6.21± 0.04
Σ-asymmetry in the data presented in Fig.1 has
been obtained in the conditions where it is not
influenced by the contribution of fission via the
quadrupole excitation. In the range of energy from
5 to 6MeV of Σ-asymmetry it is close to +1. It
specifies that the contribution only through dipolar
excitation is shown and within errors the contribu-
tion of other multipolarities isn’t observed. In the
range of energy from 5 to 6.04MeV of Σ-asymmetry
it is close to +1. It specifies that the contribu-
tion only through dipole excitation is shown and
within errors the contribution of other channels of
fission isn’t observed. However, the contribution of
quadrupole fission becomes noticeable in this energy
range. In reference [12] angular distribution have
been obtained for 238U fission fragments at six en-
ergies 6.25, 6.61, 7.14, 7.44, 7.75, 8.50MeV near the
fission barrier. It has been stressed there that these
distributions show the shift of the maximum towards
45◦. Such a behavior of the angular distribution
of fission fragments is very different from its be-
havior at higher energies. We have processed the
data of [13]. In paper [12], the experimental data
were presented in the figures. In paper [11], ex-
pression (1) was made to fit to those data, and nu-
merical values of the coefficients a, b, c were deter-
mined. Using the numerical values of c from ref.
[11], we have obtained the contribution of the term
V (θ) = c sin2(2θ) in Eq.(1), which is determined by
the quadrupole fission contribution alone, for all six
energies, at which the measurements in ref. [12] were
performed. As an example, in Fig.2 the experimen-
tal data of [12] are shown for the electron energy
7.14MeV . Also shown in this figure is the contri-
bution of the quadrupole term V (θ) calculated by us
as well as the values of W (θ) with V (θ) subtracted.
Fig.2. Angular distribution of fragments W (θ)
from 238U fission by electrons with the energy
7.14MeV . Black squares are values W (θ) from data
[13]. Black circles are contributions of the coefficient
V (θ) = c · sin2(2θ)
It can be seen from Fig.2 that the peak on
the angular distribution of fission fragments located
around 45◦ is not visible after the subtraction of the
quadrupole contribution. For the rest five energies,
peak is also not seen because the deviation from the
smooth change of the angular distribution of fission
fragments stays within the experimental error bars.
Thus, it has been determined that the appearance of
the peak is connected with the contribution of the
quadrupole fission. It should be noted that the mag-
nitude of the quadrupole contribution is not signifi-
cant as it is seen from Fig.2. This may be the rea-
son why this contribution does not have a significant
influence on the behavior of Σ-asymmetry in Fig.1.
Despite that the contribution of the quadrupole fis-
sion in this energy range has a noticeable influence
on the angular distribution of fission fragments.
3. CONCLUSIONS
Using the values of energy dependence of Σ-
asymmetry obtained from the data on angular dis-
tribution of fission fragments, the numerical value
of 238U fission threshold in (1−, 1) dipole channel,
(6.04±0.06)MeV , has been determined. It has been
determined that the peak, which is observed around
45◦ on the angular distribution of 238U fragments
25
near the fission threshold [12], results from the con-
tribution to the fission of the quadrupole excitation.
References
1. H.Uberall. Electron scattering from complex nu-
clei, parts A, B. New York: ”Academic Press”,
1971.
2. V.Bellini et al. // Lett. Nuovo Cim. 1979, v.26,
p.173.
3. R.Ratzek et al. Atoms and Nuclei //Z. Phys.
A308, 1982, v.63.
4. Yu.V.Vladimirov, V.V.Denyak, I.G. Evseev, et
al. //Problems of Atomic Science and Technol-
ogy. Series ”Nuclear Physics (theory and experi-
ment)”, N8(8), Moscow, 1989, p.89-91.
5. V.M.Khvastunov, V.V.Denyak, I.G. Evseev, et
al.// Physics of Atomic Nuclei. 1994, v.57,
p.1858-1862.
6. V. M.Khvastunov, V.V.Denyak //Physics of
Atomic Nuclei. 2001, v.64, p.1269.
7. V.V.Denyak, V.M.Khvastunov, S.A. Paschuk,
H.R. Schelin //Eur. Phys. J. A . 2013, p.49-51.
8. F. Steiper et al. //Nucl. Phys. 1993, v.A563,
p.283.
9. N.S.Rabotnov, et al. //Sov. J. Nucl. Phys. 1970,
v.11, p.508.
10. A.Manfredini et al. //Nucl. Phys. 1969, v.A123,
p.664.
11. V.V.Varlamov, V.V. Surgutanov,
Yu.M.Tsypenyuk, A.P.Chernyaev. Photonuclear
data. Fission of heavy nuclei. Moscow: ”Moscow
State University Publishing”, 1983, 212 p.
12. J.D.T.ArrudaNeto, S.B.Herdade,
B.S. Bhandari, I.C.Nascimento //Phys. Rev.
1978, v.C18, p.863.
ÄÅËÅÍÈß 238U Ó ÏÎÐÎÃÀ
Â.Ì.Õâàñòóíîâ, Â.È.Êàñèëîâ. Ñ.Ñ.Êî÷åòîâ, À.À.Õîìè÷
Îïðåäåëåí ïîðîã â äèïîëüíîì êàíàëå äåëåíèÿ ñ ïðîåêöèåé ñïèíà J = 1 íà îñü ñèììåòðèè ÿäðà èç äàí-
íûõ óãëîâîãî ðàñïðåäåëåíèÿ îñêîëêîâ äåëåíèÿ. Ïîêàçàíî, ÷òî ïèê, íàáëþäàåìûé â ñå÷åíèè äåëåíèÿ
238U îêîëî ïîðîãà, îáóñëîâëåí âêëàäîì â äåëåíèå ïðè êâàäðóïîëüíîì âîçáóæäåíèè.
ÄIËÅÍÍß 238U ÁIËß ÏÎÐÎÃÓ
Â.Ì.Õâàñòóíîâ, Â.É.Êàñiëîâ. Ñ.Ñ.Êî÷åòîâ, À.À.Õîìè÷
Çíàéäåíî ïîðiã ó äèïîëüíîìó êàíàëi äiëåíèÿ ç ïðîåêöi¹þ ñïiíà J = 1 íà âiñü ñèìåòði¨ ÿäðà iç äàíèõ
êóòîâîãî ðîçïîäiëó îñêîëêiâ äiëåíèÿ. Ïîêàçàíî, ùî ïiê, ÿêèé ñïîñòåðiãà¹òüñÿ â ïåðåðiçi äiëåííÿ 238U
áiëÿ ïîðîãó, çóìîâëåíèé âêëàäîì ó äiëåííÿ ïðè êâàäðóïîëüíîìó çáóäæåííi.
26
|