Polarization of the hard bremsstrahlung of the relativistic electrons in a crystal
Results of the polarization measurements of high energy bremsstrahlung in crystals are presented. For analysis of the photon polarization the asymmetry of the yields of the single p-meson photo-production on proton was used. The asymmetry of the yields of products of p-meson photo-production on the...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2007
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| Cite this: | Polarization of the hard bremsstrahlung of the relativistic electrons in a crystal / S.V. Kasian, V.L. Morokhovskii // Вопросы атомной науки и техники. — 2007. — № 5. — С. 64-68. — Бібліогр.: 13 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860128247134552064 |
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| author | Kasian, S.V. Morokhovskii, V.L. |
| author_facet | Kasian, S.V. Morokhovskii, V.L. |
| citation_txt | Polarization of the hard bremsstrahlung of the relativistic electrons in a crystal / S.V. Kasian, V.L. Morokhovskii // Вопросы атомной науки и техники. — 2007. — № 5. — С. 64-68. — Бібліогр.: 13 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | Results of the polarization measurements of high energy bremsstrahlung in crystals are presented. For analysis of the photon polarization the asymmetry of the yields of the single p-meson photo-production on proton was used. The asymmetry of the yields of products of p-meson photo-production on the liquid-hydrogen target are presented for bremsstrahlung photons with energy Eγ = 700 MeV generated by electrons with energy Eₑ₋ = 800 MeV in the Si-crystal targets with thickness 120 µm and 30 µm. The properties of the high energy bremsstrahlung in crystals for the cases of electron beam orientations under the small angles respectively to the crystal axis (111) and plane (110) are investigated.
Приведено дані вимірювання поляризації високоенергетичного гальмового випромінювання релятивістських электронів в кристалах. Для аналізу поляризації фотонів використана асимметрія виходу фотонародження p-мезонів на протоні. Приведено асиметрії виходів фотонародження p-мезонів гальмовими фотонами з енергією Eγ = 700 МеВ, які генеруються електронами з енегією Eₑ₋ = 800 МеВ в кристалічних мішенях Si з товщиною 120 та 30 мкм. Досліджено властивості високоенергетичного гальмового випромінювання в кристалах у випадках, коли пучок електронів ориєнтований під малим кутом відносно вісі кристалу (111) та площини кристалу (110).
Приведены результаты измерения поляризации высокоэнергетичного тормозного излучения релятивистских электронов в кристаллах. Для анализа поляризации фотонов использована асимметрия выхода фоторождения p-мезонов на протоне. Приведены асимметрии выходов фоторождения p-мезонов тормозными фотонами с енергией Eγ = 700 МэВ, генерируемых электронами с энегией Eₑ₋ = 800 МэВ в кристаллических мишенях Si с толщинами 120 и 30 мкм. Исследованы свойства высокоенергетичного тормозного излучения в кристаллах в случаях, когда пучок электронов ориентирован под малым углом относительно оси кристалла (111) и плоскости кристалла (110).
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POLARIZATION OF THE HARD BREMSSTRAHLUNG OF
THE RELATIVISTIC ELECTRONS IN A CRYSTAL
S.V. Kasian, V.L. Morokhovskii∗
National Science Center ”Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine
(Received April 24, 2007)
Results of the polarization measurements of high energy bremsstrahlung in crystals are presented. For analysis of
the photon polarization the asymmetry of the yields of the single π-meson photo-production on proton was used.
The asymmetry of the yields of products of π-meson photo-production on the liquid-hydrogen target are presented
for bremsstrahlung photons with energy Eγ = 700 MeV generated by electrons with energy Ee− = 800 MeV in the
Si-crystal targets with thickness 120 µm and 30 µm. The properties of the high energy bremsstrahlung in crystals for
the cases of electron beam orientations under the small angles respectively to the crystal axis 〈111〉 and plane (110)
are investigated.
PACS: 25.20.Lj, 29.27.Hj, 41.75.Ht
1. INTRODUCTION
As follows from the theory of coherent
bremsstrahlung in the first Born approximation [1]
the highest photon polarization can be obtained for
the lowest photon energies, because minimum mo-
mentum transfer to the nucleus δ (δ ≈ mc2
2E0
x
1−x , where
x = h̄ω
E0
is the re-lative quantum energy) much less
than the period of the reciprocal lattice bi = 2π
ai
. In
this case the recoil momentum ~q of the nuclei are
restricted to a very thin disk-shape region perpen-
dicular to ~p0 called ”pancake” by Uberall, the lower
and sharp boundary being a distance δ away from
the origin. Such kinematic conditions allow to create
such crystal orientation respectively to the electron
momentum ~p0, when only one point of the reciprocal
lattice will be inside the ”pancake”, and only one
quanted recoil momentum ~q = ~g is possible. Selected
direction of the recoil momentum is the reason of the
bremsstrahlung polarization with high degree.
The intensity and polarization in the coherent
maxima fall down rapidly if x → 1. If x → 1, then
δ becomes of order or larger than period of the recip-
rocal lattice b. Very large number of the reciprocal
lattice points hits the ”pancake”, so the spectrum of
the recoil momenta becomes practically continuous,
and coherent part of the bremsstrahlung intensity be-
comes negligibly small. In the case x ∼ 1 the length
of the photon creation δ becomes less than lattice pe-
riod and therefore only one atom can be inside the
sone of the photon creation [1],[2], so the construc-
tive interference of the bremsstrahlung amplitudes
from different atoms is absent. The polarization of
bremsstrahlung with high relative energy accordingly
to the Diambrini’s theory must be negligibly small.
However it’s known, that if high energy electron
beam directed under the small angle respectively the
atomic rows or planes of crystal target, then the an-
gular distributions of the multiply scattered electrons
characterized by azimuthal asymmetry [3]. Naturally
to assume that in the analogous conditions we can
obtain the high energy bremsstrahlung with not van-
ished polarization. It can be stipulated by the distor-
tion of the wave function of the initial electron state
due to interaction with string or plane potential. The
aim of this experiment is to verify this hypotheses.
2. EXPERIMENTAL SETUP AND
PROCEDURE
The experiment has been performed on the Kharkov
2 GeV linear accelerator. The experimental setup is
shown on the Fig.1.
Fig.1. The experimental setup: 1-beam line of
the 2 GeV electron accelerator; 2,5-magnets of
parallel beam transfer; 3,6-quadrupolar lenses;
4,10-collimators monochromators; 7,11,14-electron
monitors; 8-goniometer and crystal target; 9,13-
cleaning magnets; 12-photon collimators; 15-Faraday
cup; 17- magnetic spectrometer SP-103; 18-target
chamber; 19-quantometer; 20- magnetic spectrom-
eter SP-02; 21- lead-shealding; 22- liquid hydrogen
target
∗Corresponding author. E-mail address: victor@kipt.kharkov.ua
64 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2007, N5.
Series: Nuclear Physics Investigations (48), p.64-68.
Electron beam with energy 800 MeV and a spec-
tral spread of order of 4E/E ≈ 1% after the system
of parallel beam- transfer (pos.2-5) was focused by
the quadrupolar lenses (pos.6) on the Si-crystal tar-
get (pos.8).
Electron beam on the target has the axial sym-
metrical distribution with middle cross section of or-
der of ≈ 6mm and middle divergence of order of
≈ 2 · 10−4 rad. The beam distribution was controlled
by scintillator screen¡ which can be placed directly in
front of the crystal. Crystal targets were placed into
the three-axes goniometer, which provided orienta-
tion of the crystal axes respectively to the electron
beam direction with precision of order of 5 · 10−5 rad.
Silicon crystal targets have the form of foils with di-
ametrical dimensions are about the four times larger
than the beam spot dimensions and have the thick-
nesses t1 = 120 µm and t2 = 30 µm. The platitude
of the crystal target coincides with (111) crystallo-
graphic plane. Crystals were orientated by using the
method, which was described in details in the [4].
Electron beam was deflected by the magnet (pos.9)
after passing through the crystal and after crossing
the secondary electron monitor (pos.11), which was
used for the beam current controlling during the ex-
periment, was dumped in the shielding.
The bremsstrahlung from the crystal target was
selected with the help of two couples of collimators
(pos.12) in the forward direction. The angle of col-
limation was θk = 1/(2γ), where γ is the electron
Lorentz factor. Photon beam after the second clean-
ing magnet was directed to the liquid-hydrogen tar-
get with the thickness of 200 mm. The photon beam
has the transverse dimensions 10× 10 mm2 on the
liquid-hydrogen target. After the hydrogen target
the photon beam intensity was controlled by thin ion-
ization chamber (pos.19) and finally by quantometer
(pos.19). Ionization chamber and quantometer are
also used for the control of the crystal orientation.
Photo-producing of the single π-meson on the pro-
ton is the result of the interaction of the high energy
photons with liquid-hydrogen target:
γp → π0p′, γp → π+n. (1)
The yields of the products of these reactions: pro-
tons p′ and mesons π+ were measured by magnetic
spectrometer equipped with telescope of scintillator
detectors and threshold Cherenkov gas detector [5].
Magnetic spectrometer [6] has angular acceptance
4Ω = 8.2 · 10−3 sterad and momentum acceptance
4p/p ≈ 0.1. Telescope of scintillator detectors was
built of three plastic scintillators in the form of rect-
angular plates with dimensions: (10×175×130) mm3,
(20 × 175 × 150)mm3, (20 × 200 × 150)mm3. For
connections with photomultipliers the organic glass
light-conductor was used. For excluding the electron-
positron background the threshold Cherenkov gas de-
tector was used. It was constructed in the form of
steel box (200×150×600) mm3 with 4 mm steel win-
dows and filled by CO2-gas with pressure 6− 20 Pa.
The photo-multiplier supplied with special optic
system was used for registration the Cherenkov ra-
diation. Construction and parameters of this device
were described in details in [5]. The identification of
the products of the photo production, i.e. π+-mesons
and protons were realized by registration the coin-
cidence of signals in the three scintillations of tele-
scope under the condition of anti-coincidence with
signal from Cherenkov gas detector, which was placed
behind the telescope. Such scheme allows to reli-
able registration of the products of photo-production
with elimination of the background from relativistic
electrons. Parameters of the scintillations, the high
voltage on the photomultipliers, the levels of thresh-
olds of pulse discriminators were chosen in such a
way that the products of photoproducing were regis-
trated with efficiency about 100%. Anti-coincidence
with signals from Cherenkov detector allows us to
exclude 99% of the electron background. Analogous
equipment was successfully used earlier in the expe-
riments, where coherent bremsstrahlung polarization
was measured [7]. Spectrometer was tuned up on the
momentum of 539 MeV/c and angle of registration
θL = 49.3◦ respectively to the photon beam direction
in the horizontal plane. As a result we have regis-
tered π+-mesons and protons, which were produced
by photons with energies 700± 35 MeV . The cross
sections of the photo-production have maxima at the
energy 700 MeV . This condition is the best for using
reactions (1) as an analyzer of the photon polariza-
tion. The reactions of the photo-production (1) in
such conditions have the analyzing abi-lity for pho-
ton polarization Σ ≈ 0.7, [8], where analyzing ability
determines by the value of asymmetry
Σ =
dσ⊥ − dσ‖
dσ⊥ + dσ‖
, (2)
and dσ⊥, dσ‖ are cross sections of photo-
production of p or π+ by polarized photons in the
plane perpendicular or parallel to the plane of reac-
tion. For the chosen photon energy Σ has the same
values as for protons, so for π+-mesons. The experi-
mental value of the photon beam polarization can be
defined as
P =
1
Σ
· N⊥ −N‖
N⊥ + N‖
, (3)
where N⊥, N‖ are the sum yields of p and π+-
mesons in the planes, which are ⊥ and ‖ to the plane
of reaction, respectively. The second multiplier in (3)
is the asymmetry of the yields of products of photo-
production, which we measured in our experiment.
For the aim of excluding the systematic errors the
measurements of yields N⊥ and N‖ were performed
as a series of measurements with many times chang-
ing orientation of the crystal plane respectively to the
horizontal plane.
65
3. EXPERIMENTAL RESULTS
1. The asymmetry of the yields of products of π-
meson photo-production on the liquid-hydrogen tar-
get
Σ′ =
N⊥ −N‖
N⊥ + N‖
was measured for bremsstrahlung photons with en-
ergy Eγ = 700 MeV generated by electrons with en-
ergy Ee− = 800 MeV in the Si-crystal targets with
thickness 120 µm and 30 µm. The electron beam
was directed in the crystal plane (110) under the
angle θ = 35 mrad respectively to the crystal axis
〈111〉. We performed the yields measurement by
many times changing plane (110) orientation parallel
and perpendicular to the plane of reaction. Such
crystal orientations are shown on the Fig.2.
Fig.2. The crystal orientations, which were used.
The first picture shows the crystal plane (110)
parallel to the plane of photo-production; the second
picture shows the position of the plane (110) perpen-
dicular to the plane of photo-production
Analogous results of measurements were performed
earlier for the Si crystal target with thickness 120 µm
and presented in the work [9], [10], [11]. Here we im-
prove the previous result [9], [10], [11] by excluding
some systematic errors caused by errors of the crystal
orientations and unstability of the electron beam pa-
rameters. Besides we presented the new result for the
crystal target with thickness of 30µm. Experimental
results are presented in the Table 1.
Table 1.
Crystal thickness 30 µm 120 µm
Asymmetry Σ′ 0.04 0.05
The authenticity 0.95 0.95
The confiding interval ±0.02 ±0.04
2. The asymmetry yields Σ′ of products of π-
meson photo-production on the liquid-hydrogen tar-
get measured for bremsstrahlung photons with en-
ergy Eγ = 700 MeV generated by electrons with
energy 800MeV in the Si crystal target with
thickness 120 µm for the cases of electron beam
orientations under the different angles respec-
tively to the crystal axis 〈111〉 in the arbitrary
plane, which was far from any crystal plane.
Fig.3. The yield of the products of π-meson
photo-producing in arbitrary units as a function of
the angle φ between photon beam direction and
< 111 > crystal axes (The yield equal unit
corresponds to the angle φ = 10−1 rad). The line
with points ◦ corresponds to the measurement of the
angle φ in the plane of reaction. The line with
points • corresponds to the measurement of the
angle φ in the plane, which is perpendicular to the
plane of reaction
The crystal orientations were chosen by the follow-
ing way. The yield of photo-producing depends on
the crystal orientation, i.e. depends from the an-
gle φ created by crystal axis 〈111〉 and the electron
beam direction. Such dependence correlates with
the dependence of the bremsstrahlung intensity from
angle φ. It’s shown on the Fig.3. The asymmetry
was measured in 5 points, which are designed by
φi (i = 1; 2; 3; 4; 5). The angle φ5 = 10−1 rad cor-
responds to the case of large angle φ, when the
yield of the products of π-meson photo-producing
becomes constant. We should pay attention to the
reason of the minimum in the point φ3 = 0.9 mrad
of the orientation dependence which is shown on
Fig.3. This crystal orientation characterized by the
maximum asymmetry of the angular distribution of
scattered electrons and radiated photons, which is
caused by coherent scattering on the atomic strings.
Orientations φ1 = 0 mrad and φ5 = 0.9 mrad char-
acterized by the symmetrical angular distributions
as for scattered electrons, so for radiated photons.
Our results of measurements of the asymmetry Σ′
for different angles φi are presented in the Table 2.
Table 2.
Crystal orientation φ1 φ2 φ3 φ4
Angle φ (mrad) 0 0.5 0.9 1.1
Asymmetry Σ′ 0.02 0.04 0.08 −0.08
The authenticity 0.95 0.95 0.95 0.95
The confiding
interval ±0.06 ±0.06 ±0.07 ±0.1
One can see, that significant asymmetry observed
only at the orientation angle φ = 0.9 mrad, which
corresponds to the minimum of the yield dependence
on Fig.2. and it is Σ′ = 0.08± 0.07.
66
4. CONCLUSIONS
Summing up the results of our measurements of
asymmetry of the π-meson photo-production on pro-
tons by bremsstrahlung with relative photon energy
x → 1, which was created by relativistic electrons in
crystal targets, we have the reason to draw the fol-
lowing conclusions.
1. If relativistic electron momentum was directed
respectively the crystal axes or plane under the an-
gles, which was essentially larger than the angle of
the multiple electron scattering in a crystal target,
then the asymmetry of the π-meson photo-production
on protons by high energy bremsstrahlung was not
observed. Under conditions of our experiment the
theory of the coherent bremsstrahlung in the first
Born approximation can be applied. The theoreti-
cal value of the bremsstrahlung polarization for the
photons with energy 700MeV created by electrons
with energy 800 MeV in the Si-crystal is of order of
P ∼ 10−8. The experimental errors overheads this
value, and the asymmetry of the π-meson photo-
production was not revealed.
2. In the cases when momentum of the relativistic
electron forms small angle with crystal axes or plane
the asymmetry of the π-meson photo-production on
protons by high energy bremsstrahlung comes to
light. In these cases the experimental errors are less
than the observed asymmetry. So the polarization of
the high energy bremsstrahlung in this case is much
larger than the value predicted in the frame of the
first Born approximation. It’s necessary to accentu-
ate that the largest asymmetry of the π-meson photo-
production was observed in the case when the max-
imum asymmetry exists in the angular distribution
of the multiply scattered high energy electrons in a
crystal. Such correlation points out on the necessity
of development more general theory of the coherent
bremsstrahlung.
3. The sign of the asymmetry of the π-meson
photo-production Σ′ ” + ” means that the plane of
photon polarization is perpendicular to the plane of
the reaction of the π-meson photo-production [8]. For
the first case of the crystal orientation, which was
described above in subsection 3 the plane of photon
polarization coincides with the crystal plane, which
is shown on the Fig.2. In the axial case described
in the subsection 3 in the second part, the plane of
the photon polarization is perpendicular to the plane,
which is created by the electron beam direction and
the crystal axis.
4. For obtaining real spectra of photon energy
and polarization it’s necessary to take into account
the multiple scattering of relativistic electrons in the
crystal matter. If electron momentum and atomic
row or plane form the angle θ much larger than
middle square angle of multiple scattering, then the
spectra averaging over the electron momentum di-
vergence, stipulated by multiple scattering [12] is or-
dinary used. In the opposite case if angle θ is smaller
than middle square angle of multiple scattering, we
must take into account real angular distribution of
multiple electron scattering in a crystal target. Ap-
parently the most convenient solution of this problem
is to obtain the bremsstrahlung cross section in the
high-energy approximation [13] and calculate spec-
tra of photon energy and polarization. In this case
the potential may be presented as a single atomic
potential in the region of small impact parameters
plus averaged string or plane potential in the region
of large impact parameters.
ACKNOWLEDGEMENT
Authors would like to thank V.I. Kasilov and
K.S. Kohnyuk for the help in carrying out the mea-
surements.
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ПОЛЯРИЗАЦИЯ ЖЕСТКОГО ТОРМОЗНОГО ИЗЛУЧЕНИЯ
РЕЛЯТИВИСТСКИХ ЭЛЕКТРОНОВ В КРИСТАЛЛЕ
С.В. Касьян, В.Л. Мороховский
Приведены результаты измерения поляризации высокоэнергетичного тормозного излучения реляти-
вистских электронов в кристаллах. Для анализа поляризации фотонов использована асимметрия вы-
хода фоторождения π-мезонов на протоне. Приведены асимметрии выходов фоторождения π-мезонов
тормозными фотонами с енергией Eγ = 700 МэВ, генерируемых электронами с энегией Ee− = 800 МэВ
в кристаллических мишенях Si с толщинами 120 и 30 мкм. Исследованы свойства высокоенергетично-
го тормозного излучения в кристаллах в случаях, когда пучок электронов ориентирован под малым
углом относительно оси кристалла 〈111〉 и плоскости кристалла (110).
ПОЛЯРИЗАЦIЯ ЖОРСТКОГО ГАЛЬМОВОГО ВИПРОМIНЮВАННЯ
РЕЛЯТИВIСТСЬКИХ ЕЛЕКТРОНIВ В КРИСТАЛI
С.В. Кас’ян, В.Л. Мороховський
Приведено данi вимiрювання поляризацiї високоенергетичного гальмового випромiнювання реля-
тивiстських электронiв в кристалах. Для аналiзу поляризацiї фотонiв використана асимметрiя виходу
фотонародження π-мезонiв на протонi. Приведено асиметрiї виходiв фотонародження π-мезонiв галь-
мовими фотонами з енергiєю Eγ = 700 МеВ, якi генеруються електронами з енегiєю Ee− = 800 МеВ
в кристалiчних мiшенях Si з товщиною 120 та 30 мкм. Дослiджено властивостi високоенергетичного
гальмового випромiнювання в кристалах у випадках, коли пучок електронiв ориєнтований пiд малим
кутом вiдносно вiсi кристалу 〈111〉 та площини кристалу (110).
68
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| id | nasplib_isofts_kiev_ua-123456789-110168 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T17:43:05Z |
| publishDate | 2007 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Kasian, S.V. Morokhovskii, V.L. 2016-12-31T07:07:40Z 2016-12-31T07:07:40Z 2007 Polarization of the hard bremsstrahlung of the relativistic electrons in a crystal / S.V. Kasian, V.L. Morokhovskii // Вопросы атомной науки и техники. — 2007. — № 5. — С. 64-68. — Бібліогр.: 13 назв. — англ. 1562-6016 PACS: 25.20.Lj, 29.27.Hj, 41.75.Ht https://nasplib.isofts.kiev.ua/handle/123456789/110168 Results of the polarization measurements of high energy bremsstrahlung in crystals are presented. For analysis of the photon polarization the asymmetry of the yields of the single p-meson photo-production on proton was used. The asymmetry of the yields of products of p-meson photo-production on the liquid-hydrogen target are presented for bremsstrahlung photons with energy Eγ = 700 MeV generated by electrons with energy Eₑ₋ = 800 MeV in the Si-crystal targets with thickness 120 µm and 30 µm. The properties of the high energy bremsstrahlung in crystals for the cases of electron beam orientations under the small angles respectively to the crystal axis (111) and plane (110) are investigated. Приведено дані вимірювання поляризації високоенергетичного гальмового випромінювання релятивістських электронів в кристалах. Для аналізу поляризації фотонів використана асимметрія виходу фотонародження p-мезонів на протоні. Приведено асиметрії виходів фотонародження p-мезонів гальмовими фотонами з енергією Eγ = 700 МеВ, які генеруються електронами з енегією Eₑ₋ = 800 МеВ в кристалічних мішенях Si з товщиною 120 та 30 мкм. Досліджено властивості високоенергетичного гальмового випромінювання в кристалах у випадках, коли пучок електронів ориєнтований під малим кутом відносно вісі кристалу (111) та площини кристалу (110). Приведены результаты измерения поляризации высокоэнергетичного тормозного излучения релятивистских электронов в кристаллах. Для анализа поляризации фотонов использована асимметрия выхода фоторождения p-мезонов на протоне. Приведены асимметрии выходов фоторождения p-мезонов тормозными фотонами с енергией Eγ = 700 МэВ, генерируемых электронами с энегией Eₑ₋ = 800 МэВ в кристаллических мишенях Si с толщинами 120 и 30 мкм. Исследованы свойства высокоенергетичного тормозного излучения в кристаллах в случаях, когда пучок электронов ориентирован под малым углом относительно оси кристалла (111) и плоскости кристалла (110). Authors would like to thank V.I. Kasilov and K.S. Kohnyuk for the help in carrying out the measurements. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Ядернo-физические методы и обработка данных Polarization of the hard bremsstrahlung of the relativistic electrons in a crystal Поляризація жорсткого гальмового випромінювання релятивістських електронів в кристалі Поляризация жесткого тормозного излучения релятивистских электронов в кристалле Article published earlier |
| spellingShingle | Polarization of the hard bremsstrahlung of the relativistic electrons in a crystal Kasian, S.V. Morokhovskii, V.L. Ядернo-физические методы и обработка данных |
| title | Polarization of the hard bremsstrahlung of the relativistic electrons in a crystal |
| title_alt | Поляризація жорсткого гальмового випромінювання релятивістських електронів в кристалі Поляризация жесткого тормозного излучения релятивистских электронов в кристалле |
| title_full | Polarization of the hard bremsstrahlung of the relativistic electrons in a crystal |
| title_fullStr | Polarization of the hard bremsstrahlung of the relativistic electrons in a crystal |
| title_full_unstemmed | Polarization of the hard bremsstrahlung of the relativistic electrons in a crystal |
| title_short | Polarization of the hard bremsstrahlung of the relativistic electrons in a crystal |
| title_sort | polarization of the hard bremsstrahlung of the relativistic electrons in a crystal |
| topic | Ядернo-физические методы и обработка данных |
| topic_facet | Ядернo-физические методы и обработка данных |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110168 |
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