Fission of heavy nuclei by linearly polarized photons
Analysing power Σ data from photofission of ²³²Th, ²³³U, ²³5U, ²³⁶U, ²³⁸U at the region of giant resonance have been measured using linearly polarized photons. The polarized photons were obtained by plane channelling of electrons in a silicon single crystal. The analysing power Σ dependence of the m...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2002
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| Цитувати: | Fission of heavy nuclei by linearly polarized photons / V.M. Khvastunov, V.V. Denyak, S.V. Kas’yan, V.P. Likhachev, S.A. Paschuk // Вопросы атомной науки и техники. — 2002. — № 2. — С. 25-29. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860010361182224384 |
|---|---|
| author | Khvastunov, V.M. Denyak, V.V. Kas’yan, S.V. Likhachev, V.P. Paschuk, S.A. |
| author_facet | Khvastunov, V.M. Denyak, V.V. Kas’yan, S.V. Likhachev, V.P. Paschuk, S.A. |
| citation_txt | Fission of heavy nuclei by linearly polarized photons / V.M. Khvastunov, V.V. Denyak, S.V. Kas’yan, V.P. Likhachev, S.A. Paschuk // Вопросы атомной науки и техники. — 2002. — № 2. — С. 25-29. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | Analysing power Σ data from photofission of ²³²Th, ²³³U, ²³5U, ²³⁶U, ²³⁸U at the region of giant resonance have been measured using linearly polarized photons. The polarized photons were obtained by plane channelling of electrons in a silicon single crystal. The analysing power Σ dependence of the mass number of even-even nucleus has been discovered. Comparison of the analysing power Σ values with the data from other experiments with both polarized and unpolarized photon beams was made. It is shown that the analysing power Σ values agree with the modern knowledge of E1 transitions but cannot be explain by domination any one of them. It is supposed that analysing power Σ is very sensitive to different relative inner and outer fission barrier heights and this affects on Σ values for even-even nuclei with the same Z.
|
| first_indexed | 2025-12-07T16:41:35Z |
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FISSION OF HEAVY NUCLEI BY LINEARLY POLARIZED PHOTONS
V.M. Khvastunova, V.V. Denyaka*, S.V. Kas’yana, V.P. Likhachevb, S.A. Paschukc
a - National Scientific Center "Kharkov Institute of Physics and Technology", Kharkov, Ukraine
e-mail: denyak@kipt.kharkov.ua
b - University of San Paulo, San Paulo, Brazil
c - Federal Center of Technological Education, CEFET-PR, Curitiba, PR, CEP 80230-901,
Brazil
Analysing power Σ data from photofission of 232Th, 233U, 235U, 236U, 238U at the region of giant resonance have
been measured using linearly polarized photons. The polarized photons were obtained by plane channelling of
electrons in a silicon single crystal. The analysing power Σ dependence of the mass number of even-even nucleus has
been discovered. Comparison of the analysing power Σ values with the data from other experiments with both
polarized and unpolarized photon beams was made. It is shown that the analysing power Σ values agree with the
modern knowledge of E1 transitions but cannot be explain by domination any one of them. It is supposed that
analysing power Σ is very sensitive to different relative inner and outer fission barrier heights and this affects on Σ
values for even-even nuclei with the same Z.
PACS: 25.85.Jg, 27.90.+b, 24.70.+s
1. INTRODUCTION
The investigation of fission of heavy nuclei by real
photons is a convenient method for determining the spin
and parity of collective nuclear states. Measurement of
the angular distributions of fission fragments reveals the
multipole structure of the process. In the vicinity of the
fission barrier, the multipole structure is determined
mainly by dipole (electric E1 and magnetic M1)
transitions and, to a considerably lesser extent, by
quadrupole (E2 and M2) transitions [1]. Such a small set
of total moments of photons interacting with nuclei
yields a restricted number of excited collective states,
particularly for even-even nuclei This makes it possible
to determine spin and parity of these states.
A new trend in the research of the fission process is
the application of polarized photon beams. This opens
new possibilities for investigation of the mechanism of
fission process and for studying the structure of excited
states. It permits one to understand the fission cross
section dependence of the direction of the photon
polarization vector and to measure the analysing power
Σ of photofission. The Σ, a new observable that is
possible to measure in experiments using polarized
photon beam, is the second (following the cross section
at unpolarized photons) independent characteristic of
fission. It also contains information about the spin
structure of excited collective states.
The application of polarized photon beams in studies
of nuclear fission is at its very beginning. First such
investigations were carried out in Giessen [2,3] and
Kharkov [4,5]. In these works the analysing power of
232Th and 236U fission was measured.
In this paper, we represent the results of
measurements of Σ in the fission of 232Th, 233U, 235U,
236U, 238U nuclei by polarised photons in the energy
range Eγ~5-20 MeV. Using modern theoretical concepts
as a basis, we compare our experimental results with
data from [2,3] and with the results of investigations of
fission induced by unpolarized photons.
2. EXPERIMENTAL CONDITIONS
The experiment was carried out at the LINAC-2000
Kharkov Institute of Physics and Technology. Linearly
polarized photons were obtained by transmitting
electrons with the energy Ee=1200 MeV through the
silicon single crystal under the conditions approaching
channeling in the (110) plane. The intensity and the
polarization degree (Pγ) of the photon beam was
determined with a deuterium gas polarimeter, by
measuring the proton yield from the reaction γ+d=p+n at
an angle Θ=90o with respect to the photon beam. An
experimental targets of thickness 500 µg/cm2(232Th),
115 µg/cm2(233U), 225 µg/cm2(235U), 186 µg/cm2(236U),
233 µg/cm2(238U) were deposited onto a nickel or an
aluminum substrates of thickness 10 µm. The thickness
nonhomogeneity of the targets is not more than 3%.
Isotope enrichments were natural for 232Th and 238U and
98% for 233U, 235U and 236U.
Fission fragments were detected at an angle Θ=90o
with respect to the photon beam by 100 µm-thick
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2002, № 2.
Series: Nuclear Physics Investigations (40), p. 25-29. 25
Semiconductor Surfacebarrier Detector (SSD).
Amplitude spectra of the yield of protons emitted in the
reaction γ+d=p+n and fragments formed in the fission
were measured simultaneously for each of the three
positions of the silicon single crystal: for the photon
polarization vector parallel (N) and perpendicular (N⊥)
to the reaction plane and for disoriented crystal (No).
Protons detected in our experiment assumed to be
produced by the direct photodisintegration of the
deuteron, and the photon energy Eγ was determined in
accordance with this hypothesis. The experimental data
for the ratio
2
N
oN
N⊥Ι Ι +=β (1)
show the radiation intensity from the oriented crystal
comparing the radiation intensity from the disoriented
crystal. The relative photon yield increases sharply with
energy decreasing (from about 1.5 at Eγ=20 MeV to 5.6
at 5 MeV)[5].
An enrichment of the spectrum of the photons
emitted from the oriented crystal takes place at energies
up to 20 MeV, which falls within the region of the giant
resonance. To eliminate the effect of photons with
energies above 20 MeV, we subtracted the yield of
reaction products measured for disoriented single crystal
from the yield obtained for the oriented crystal. That is,
the result was obtained only for the coherent part (β-1)N
γ
br of the photon spectrum (Nγ
br is the spectrum of
photons emitted from the disoriented crystal, i.e.
bremsstrahlung spectrum).
The degree of polarization of the photon beam in the
coherent part of the spectrum was defined as
1
cc
cc
pnd
c
NN
NNP
⊥Ι Ι
⊥Ι Ι
→γ
γ +
−
Σ
= (2)
where Nc
,⊥=N,⊥-No The value of Σγd→pn was taken from
[6].
The photon polarization for coherent part of the
spectrum is nearly constant in the energy range Eγ=5.4-
20 MeV, with an averaged value Pγ
c=0.77+0.17.
The coherent part (β-1)Nγ
br of the photon spectrum
was used to form a convolution with the photofission
cross section (σ) from [7]. This convolution shows that
we have measured the yield of fragments produced at
the energies of the giant dipole resonance.
3. EXPERIMENTAL RESULTS AND
DISCUSSION
3.1 AMPLITUDE SPECTRA AND MEASURED
AZIMUTHAL ASYMMETRY OF FISSION
FRAGMENTS YIELD
Under above experimental conditions, yields of
fragments produced in the photofission of 232Th, 233U,
235U, 236U and 238U were measured for three orientations
of the silicon single crystal. Fig. 1 illustrates the
amplitude spectra of fragments yield in 232Th and 236U
fission. For clarity, curves are drawn through the
experimental points. Fig. 1 shows that the yield of
fission fragments for the oriented single crystal (N and
N⊥) is considerably larger than that for the disoriented
one (No) and that the spectrum of N and N⊥ differ one
from another as a result of change in orientation of the
photon polarization vector.
Fig. 1. Amplitude spectra of photofission fragments
yields: (■) and (•) are the yields for photon
polarization vector parallel (N) and perpendicular (N
⊥) to the reaction plane and (▲) - for disoriented silicon
crystal (No)
The experimentally measured azymuthal asymmetry
ε in the yield of fission fragments at Θ=90o for the
coherent part of the photon spectrum was determined
using the formula:
cc
cc
c
NN
NNP
⊥Ι Ι
⊥Ι Ι
γ +
−=Σ=ε (3)
3.2 THEORETIC FORMULAS
The theoretic formalism developed in [2,8] shows
that the analysing power in fission induced by polarized
photons may be compared with the coefficients of the
angular distribution of fission fragments for unpolarized
photons. Previous investigations of the fission of the
nuclei being discussed showed the dominant role of E1
transitions in the energy region of giant dipole
resonance. The contribution of the E2 and M1
components is significantly smaller then the E1
contribution.
In the dipole approximation, the analysing power in
fission has the form
Σ(90o)=ω.b/(a + b) (4)
and the cross section
dσ/dΩ(Θ)=a+b.sin2(Θ) (5)
26
where ω=1 for electric and ω=-1 for magnetic
transitions.
The coefficients a and b may be expressed through σ
(Jπ,K) – the cross section of the excitation of the
collective state with fixed quantum numbers: J, the spin
of a compound nucleus; π, its parity; and K, the
projection of J onto the symmetry axis of the nucleus.
For electric excitation:
a=3/2.σ(1-,±1) (6)
b=3/4.σ(1-,0)-3/4.σ(1-,±1) (7)
In the case of any one state excitation only the
analysing power have the value not dependent of the
excitation energy
Σ(1-,0)=1, (8)
Σ(1-,±1)=-1. (9)
3.3 ANALYSING POWER Σ OF 232Th
Fig. 2 presents the existing experimental data for the
Σ of fission together with Σ values obtained from known
values of a and b under the assumption that fission is
governed by the dipole transition alone.
Fig. 2. The analysing power Σ of 232Th photofission
as a function of the maximum energy Eγ
max of the photon
spectrum: (×) - bremsstrahlung photons [10];
(•) - electrons, virtual photons [11]; (ο) - positrons,
virtual photons [11]; (■) - bremsstrahlung polarised
photons [2]; (▲) - polarised photons obtained at
channelling (our work)
These measurements were performed with a
bremsstrahlung spectrum, and not with monochromatic
photons. For this reason, the energy at which
measurements were made ranges from photofission
barrier (5.8 MeV) to the maximum photon energy used
in the experiments, and the experimental values are
located at the maximum photon energy. Our Σ value is
given in Fig. 2 at Eγ=18 MeV.
Of all the data obtained in experiments with an
unpolarized photon beam, only the part that covers our
energy range most completely is used for constructing
Fig. 2. It also shows the data on electron- and positron
induced fission of 232Th nucleus [11] at 16 MeV, along
with the data obtained in experiments with a polarized
bremsstrahlung photon beam at maximum energies of 10
and 12 MeV [2]. It should be noted that additional data
obtained using a polarized bremsstrahlung photon beam
in the energy range 10-12 MeV [3] (and not presented in
Fig. 2) shows good agreement with the results
represented in [2].
It can be seen from Fig.2 that, in spite of the
difference in photon spectra (bremsstrahlung photons,
virtual photons obtained using electron and positron
beams, and the coherent part of the photon spectrum
formed during channeling), the analysing power Σ
values are in a rather good agreement one with another
at the energy Eγ=15-20 MeV. Thus, in the energy range
under study, the quadrupole excitation does not manifest
itself in the analysing power Σ of fission (which is a new
observable of the process) within the experimental error.
Comparison of our results with the data obtained in
[2] by direct measurement of the Σ reveals a
considerable discrepancy in the values determined by
these two methods. This can be attributed to the fact that
different ranges of photon energies were used in the two
studies. It was shown in [10,12] that the coefficient b
decreases from unity to zero (the angular distribution of
fragments becomes increasingly isotropic) with
increasing Eγ; hence, the Σ also tends to zero with
increasing Eγ.
It can be seen from the formula (4) that the sign of Σ
in the case of dipole excitation is opposite for electric
and magnetic transitions. The positive Σ value obtained
by us shows that the energy range under study is
dominated by the electric dipole transition.
3.4 ANALYSING POWER Σ OF 236U
Fig. 3 shows the value of Σ for 236U obtained by us,
results of work [3], and values of Σ calculated from
coefficients a and b [11] as a function of maximum
photon energy (Eγ
max). Value of the analysing power Σ
from [3] was obtained by using the value of photon
beam polarization from work [2]. Our result is shown
for Eγ
max=18 MeV.
Fig. 3. The analysing power Σ of 236U photofission
as a function of the maximum energy Eγ
max of the photon
spectrum: (•) - work [13], (■) - work [3], (▲)- our
work
One can see from Fig. 3 that neither the (1-, 0) state
nor the (1-, ±1) state dominates in the region of the giant
resonance. Asymmetry of fission, reported in work [3]
agrees with our result only in sign, but is significantly
bigger. This may be so, because the (1-, 0) state
27
dominates at the small energy. The contribution of the
(1-,±1) state become bigger with Eγ
max increasing and
correspondingly the coefficient b decreases (the angular
distribution becomes more isotropic) that leads to Σ
decreasing. Most close to our energy region are results
of work [10], where the value of b/a decreases and tends
to zero with Eγ
max increasing and, therefore, the Σ also
will tend to zero according to expression (4). The value
of analysing power Σ obtained by us agrees with the Σ
behavior from results of work [10]. It is necessary to
mention that our result, nevertheless, differs from zero.
It means that angular distribution should not be isotropic
for the giant resonance region.
3.5 ANALYSING POWER Σ OF 238U
Fig. 4 shows the results for 238U of our measurements
and values of Σ obtained from the coefficients a and b
for different Eγ
max and E1 transition assumptions. All
experimental data for Eγ
max>12 MeV existing now are
shown here except the results of work [13] for Eγ
max=12.01 and 14.02 MeV, which coincide with the data
shown in Fig.4 within the limits of experimental error.
The value from work [14] for Eγ
max=20 MeV is moved to
0.3 MeV for picture clarity. Our result is shown at Eγ
max=18 MeV.
Fig. 4. The analysing power Σ of 238U photofission
as a function of the maximum energy Eγ
max of the photon
spectrum: (•) - works [10,17], (■) – work [18], (▼) –
work [14], (▲) - our work
As for 236U the measured value of Σ differs
significantly from Σ of any of dipole fission channels (1-
, 0) or (1-,±1).
From comparison between our measurements and the
results obtained by calculation from coefficients a and b
it is seen that they coincide very good in spite of the fact
that the measurements were made by different research
groups with the photon spectrum that differs from ours.
It means that the manifestation of E2 transition is not
observed in the new observable (analysing power Σ).
3.6 ANALYZING POWER Σ OF 233U AND 235U
The theoretic formulas from [2,8] are not valid for
these nuclei. It is not possible to write such simple
equation for the angular distribution at unpolarized
photons and the analyzing power at polarised photons
comparison as for even-even nuclei. The main reason of
this is the nonzero spin and therefor a big number of
spin projections (K).
But from general reasons the Σ should be close to
zero. For these nuclei with spin 5/2+ (233U) and 7/2-
(235U) even the E1 excitation gives the big number of
intermediate states with different (Jπ, K). It is
improbable that such big number of excited states gives
the Σ value, which differs from zero.
Our results ((-1.17±1.07) 10-2 for 233U and (-6.23±
3.76) 10-2 for 235U) confirm these assumptions.
3.7 MASS NUMBER DEPENDENCE OF THE
ANALYZING POWER OF EVEN-EVEN NUCLEI
The values of Σ for even-even nuclei 232Th, 236U, 238U
measured by us differ significantly one from another.
The Σ obtained in our experiments is shown in Fig. 5a as
a function of mass number (A). One can see that
analyzing power decrease with mass increasing.
Fig. 5. Mass number dependence of the analyzing
power Σ. a) our work. b) from works [9,15] for Eγ
max=7 MeV
For all three elements Σ values agree well with the Σ
calculated from a and b coefficients on the basis of E1
assumption. Therefore, it is interesting to compare our
analyzing power mass number dependence with the
analyzing power mass number dependence calculated
from these coefficients near the barrier, where the
experimental errors are significantly smaller than at Eγ
max~20 MeV and there are the experimental results for
bigger number of elements. To eliminate the systematic
errors of different experiments it is necessary to
compare the results of coefficients a and b
measurements obtained by one experimental group.
Fig.5b shows Σ mass number dependence calculated
28
from the results of work [10,15] for Eγ
max=7 MeV. If for
this Eγ
max the experimental result was absent, the
necessary data were obtained by the linear interpolation
of results for nearest Eγ
max. It is seen from Fig. 5b that
the calculated Σ has clear dependence on the charge of
the nucleus (Z) and it is practically constant while the
number of neutrons (N) is changed for nuclei with the
same Z. Such dependence is the result of the well known
effect of the angular distribution of fission products
“anomaly”, which reflect the arbitrary value of inner and
external fission barrier dependence on Z (see for
example [16]).
Accuracy of Σ values obtained by us is significantly
higher than the accuracy of calculated results in the
same region of Eγ
max. The difference of Σ values for 236U
and 238U is more than three standard deviations and the
probability that this difference has an accidental
character is small. The existence of analyzing power
dependence not only on Z but also on N means that
either there is the contribution of another (not E1)
multipole, or such kind of measurements is very
sensitive to different relative inner and outer fission
barrier heights and this effect is observed in our
experiments for the nuclei with the same Z.
4. CONCLUSION
The measurements of the cross section analyzing
power Σ of 232Th, 236U and 238U in the giant dipole
resonance region carried out by us show the sensitivity
of the fission cross section to the polarization vector
direction. The obtained values of the Σ can not be
explain by domination of either channels (1-, 0) or (1-,±
1) but agrees with the modern knowledge of E1
domination in this energy region.
The analyzing power Σ dependence on the nucleus
mass is observed. Such dependence cannot be explained
on the basis of E1 transition and by existing now results
of the experiments with unpolarized photons. So, it will
be very interesting to carry out the systematic
investigation of even-even nuclei analyzing power mass
number dependence especially near the barrier.
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29
PACS: 25.85.Jg, 27.90.+b, 24.70.+s
|
| id | nasplib_isofts_kiev_ua-123456789-80107 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:41:35Z |
| publishDate | 2002 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Khvastunov, V.M. Denyak, V.V. Kas’yan, S.V. Likhachev, V.P. Paschuk, S.A. 2015-04-11T19:31:31Z 2015-04-11T19:31:31Z 2002 Fission of heavy nuclei by linearly polarized photons / V.M. Khvastunov, V.V. Denyak, S.V. Kas’yan, V.P. Likhachev, S.A. Paschuk // Вопросы атомной науки и техники. — 2002. — № 2. — С. 25-29. — Бібліогр.: 18 назв. — англ. 1562-6016 PACS: 25.85.Jg, 27.90.+b, 24.70.+s https://nasplib.isofts.kiev.ua/handle/123456789/80107 Analysing power Σ data from photofission of ²³²Th, ²³³U, ²³5U, ²³⁶U, ²³⁸U at the region of giant resonance have been measured using linearly polarized photons. The polarized photons were obtained by plane channelling of electrons in a silicon single crystal. The analysing power Σ dependence of the mass number of even-even nucleus has been discovered. Comparison of the analysing power Σ values with the data from other experiments with both polarized and unpolarized photon beams was made. It is shown that the analysing power Σ values agree with the modern knowledge of E1 transitions but cannot be explain by domination any one of them. It is supposed that analysing power Σ is very sensitive to different relative inner and outer fission barrier heights and this affects on Σ values for even-even nuclei with the same Z. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Nuclear reactions Fission of heavy nuclei by linearly polarized photons Деление тяжёлых ядер линейно поляризованными фотонами Article published earlier |
| spellingShingle | Fission of heavy nuclei by linearly polarized photons Khvastunov, V.M. Denyak, V.V. Kas’yan, S.V. Likhachev, V.P. Paschuk, S.A. Nuclear reactions |
| title | Fission of heavy nuclei by linearly polarized photons |
| title_alt | Деление тяжёлых ядер линейно поляризованными фотонами |
| title_full | Fission of heavy nuclei by linearly polarized photons |
| title_fullStr | Fission of heavy nuclei by linearly polarized photons |
| title_full_unstemmed | Fission of heavy nuclei by linearly polarized photons |
| title_short | Fission of heavy nuclei by linearly polarized photons |
| title_sort | fission of heavy nuclei by linearly polarized photons |
| topic | Nuclear reactions |
| topic_facet | Nuclear reactions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/80107 |
| work_keys_str_mv | AT khvastunovvm fissionofheavynucleibylinearlypolarizedphotons AT denyakvv fissionofheavynucleibylinearlypolarizedphotons AT kasyansv fissionofheavynucleibylinearlypolarizedphotons AT likhachevvp fissionofheavynucleibylinearlypolarizedphotons AT paschuksa fissionofheavynucleibylinearlypolarizedphotons AT khvastunovvm delenietâželyhâderlineinopolârizovannymifotonami AT denyakvv delenietâželyhâderlineinopolârizovannymifotonami AT kasyansv delenietâželyhâderlineinopolârizovannymifotonami AT likhachevvp delenietâželyhâderlineinopolârizovannymifotonami AT paschuksa delenietâželyhâderlineinopolârizovannymifotonami |