About the possibility to measure the circular polarization of high-energy photon in reaction γ + e⁻ → e⁺ + e⁻ + e⁻
Two possibilities of the measuring high-energy photon circular polarization by means of the process γ + e⁻ → e⁺ + e⁻ + e⁻ are investigated. The first one is connected with the measurement of polarization asymmetry of the cross section when the initial electron beam is longitudinally polarized. The s...
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| Zitieren: | About the possibility to measure the circular polarization of high-energy photon in reaction γ + e⁻ → e⁺ + e⁻ + e⁻ / G.I. Gakh, M.I. Konchatnij, I.S. Levandovsky, N.P. Merenkov // Вопросы атомной науки и техники. — 2012. — № 1. — С. 97-101. — Бібліогр.: 9 назв. — англ. |
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| author | Gakh, G.I. Konchatnij, M.I. Levandovsky, I.S. Merenkov, N.P. |
| author_facet | Gakh, G.I. Konchatnij, M.I. Levandovsky, I.S. Merenkov, N.P. |
| citation_txt | About the possibility to measure the circular polarization of high-energy photon in reaction γ + e⁻ → e⁺ + e⁻ + e⁻ / G.I. Gakh, M.I. Konchatnij, I.S. Levandovsky, N.P. Merenkov // Вопросы атомной науки и техники. — 2012. — № 1. — С. 97-101. — Бібліогр.: 9 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | Two possibilities of the measuring high-energy photon circular polarization by means of the process γ + e⁻ → e⁺ + e⁻ + e⁻ are investigated. The first one is connected with the measurement of polarization asymmetry of the cross section when the initial electron beam is longitudinally polarized. The second possibility related with the measurement of the created-positron (or electron) polarization. Just this polarization does not decrease when the photon energy grows up and can be used for effective determination of the photon circular polarization degree.
Проанализированы две возможности определения степени циркулярной поляризации высокоэнергетического фотона в процессе γ + e⁻ → e⁺ + e⁻ + e⁻. Первая связана с измерением поляризационной асимметрии сечения, когда начальный пучок электронов обладает продольной поляризацией. Вторая – с измерением поляризации образованного позитрона (или электрона). Показано, что в последнем случае поляризация не убывает с ростом энергии фотона и может быть использована для эффективного определения степени его циркулярной поляризации.
Проаналізовано дві можливості визначити ступінь циркулярної поляризації фотона високої енергії у реакції γ + e⁻ → e⁺ + e⁻ + e⁻. Перша пов'язана із вимірюванням асиметрії перерізу, коли початковий пучок електронів має поздовжню поляризацію. Друга -- із вимірюванням поляризації утворюваного позитрона (чи електрона). Виявлено, що в останньому випадку поляризація не зменшується з ростом енергії фотона і може бути використана для ефективного визначення його циркулярної поляризації.
|
| first_indexed | 2025-12-07T13:35:39Z |
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| fulltext |
ABOUT THE POSSIBILITY TO MEASURE THE CIRCULAR
POLARIZATION OF HIGH-ENERGY PHOTON IN
REACTION γ + e− → e+ + e− + e−
G.I. Gakh 1, M.I. Konchatnij 1, I.S. Levandovsky 2, N.P. Merenkov 1∗
1National Science Center “Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine
2Karazin Kharkov National University, 61077, Kharkov, Ukraine
(Received October 27, 2011)
Two possibilities of the measuring high-energy photon circular polarization by means of the process γ + e− →
e+ + e− + e− are investigated. The first one is connected with the measurement of polarization asymmetry of the
cross section when the initial electron beam is longitudinally polarized. The second possibility related with the
measurement of the created-positron (or electron) polarization. Just this polarization does not decrease when the
photon energy grows up and can be used for effective determination of the photon circular polarization degree.
PACS: 12.20.Ds, 13.40.-f, 13.88.+e
1. INTRODUCTION
It is well known that the azimuthal asymmetry in the
process of triplet production
γ(k) + e−(p) → e−(k1) + e+(k2) + e−(p1) (1)
by the high-energy polarized photons on the atomic
electrons can be used to measure the photon lin-
ear polarization degree (see review [1] and references
therein). This single-spin effect lies on theoretical
footing of polarimeters where the different angular
and energy distributions are used [2].
The circular photon polarization in the region of
small and intermediate energies can be probed by
the effects due to double-spin correlation in Compton
scattering. For example, in Ref. [3] the corresponding
possibility is considered, connected with the Comp-
ton cross-section asymmetry at scattering of photon
on polarized electrons. In principle, one can also
measure the polarization of the recoil electron. The
double-spin effects may be used to create polarized
electron beams using the laser photons [4].
At high energies of photons the use of Compton
scattering is not efficient because the Compton cross-
section decreases with the growth of an energy. If the
photon energy is large, the cross-section of the pair
production becomes larger than the Compton scat-
tering one. To estimate the respective energy one
can use the asymptotic formulas for the total cross-
sections [5]:
σC ≈ 2πr2
0
x
ln x , σpair ≈ 28αr2
0
9
ln x , (2)
x =
s
m2
, s = (k + p)2 , α =
1
137
,
where r0 is the classical radius of electron and m is
the electron mass. In the rest system of the initial
electron (s ≈ 2ωm) the photon energy ω has to be
larger than about 80m. Thus, to measure the circular
polarization of photons with the energies more than
100m it is advantageous to use the process (1) rather
than Compton scattering.
The cosmic rays can contain very high-energy
photon component, and analysis of their polarization
is very important to understand the remarkable fea-
tures of the cosmologically distant gamma ray bursts.
In the case of the circular polarization of the pho-
ton, the cross-section of the process (1) is sensitive
to it if either the initial electron is polarized or the
polarization of the created electron (positron) is mea-
sured. Below we consider both respective experimen-
tal setups which can be realized in the scattering of
the photons on unpolarized atomic electron or in the
collision of photons with the beams of polarized elec-
trons.
In our calculation, at the high energies, we take
into account only so-called Borselino diagrams [6]
which correspond to the one-photon exchange in the
t-channel between the target electron and created
electron-positron pair.
2. DIFFERENTIAL CROSS-SECTION
The high-energy differential cross-section of the
process (1) in the case of polarized photon and longi-
tudinally polarized initial electron beam can be writ-
ten in the form:
dσ =
e6
2(2π)5sq4
V μνBμνdΦ , (3)
∗Corresponding author E-mail address: merenkov@kipt.kharkov.ua
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2012, N 1.
Series: Nuclear Physics Investigations (57), p. 97-101.
97
dΦ =
d3k1
2E1
d3k2
2E2
d3p1
2ε1
δ(k + p − p1 − k1 − k2) ,
where s = (k + p)2 is squared total energy in the re-
action c.m.s. and ε1 is the energy of electron with
4-momentum p1. The tensor Bμν is defined by the
electron current jμ:
Bμν = jμj∗ν , jμ = ū(p1)γμu(p) , (4)
and in the case of polarized initial electron:
Bμν =
1
2
Tr(p̂1 + m)γμ(p̂ + m)(1 − γ5Ŝ)γν ,
where Sμ is its polarization 4-vector. Taking the trace
over the spinor indices we have
Bμν = q2gμν + (2pp1)μν − 2im(μνqS) , (5)
where the following notation is used: (ab)μν = aμbν +
aνbμ, (μνqS) = εμνλρqλSρ, ε1230 = 1 .
The tensor Vμν is defined by the electromagnetic
current Jμ:
Vμν = JμJ∗
ν , Jμ = ū(k1)
[
γλ
k̂1 − k̂ + m
−2(kk1)
γμ+ (6)
+γμ
k̂ − k̂2 + m
−2(kk2)
γλ
]
v(k2)Aλ ,
where 4-vector Aλ can be chosen as a column
Aλ =
(
e1λ
e2λ
)
(7)
in the photon spin space. For the photon polarization
4-vectors we choose
e1λ =
1
N
[
χ1k2λ − χ2k1λ
]
, e2λ =
1
N
(λkk1k2) , (8)
e2
1 = e2
2 = −1 , (e1k) = (e2k) = (e1e2) = 0 ,
where the following short notation is used:
N2 =
[
2χ1χ2χ − m2(χ2
1 + χ2
2)
]
,
χ1 = (kk1) , χ2 = (kk2) , χ = (k1k2) .
If the photon is polarized and the polarization of
created electron is measured, one has:
Vμν = Tr(k̂1 + m)
1
2
(1 − γ5Ŝ1)
[
γλ
k̂1 − k̂ + m
−2(kk1)
γμ+
+γμ
k̂ − k̂2 + m
−2(kk2)
γλ
]
(k̂2 − m)
[
γν
k̂1 − k̂ + m
−2(kk1)
γρ+
+γρ
k̂ − k̂2 + m
−2(kk2)
γν
]
λρ = Tμνλρ
λρ . (9)
Here S1 is the 4-vector of created electron and
λρ is
the spin density matrix of the polarized photon:
λρ =
1
2
A+
λ (I + �ξ�σ)Aρ , (10)
where �σ represents the Pauli matrices and 3-vector
�ξ = (ξ1 , ξ2 , ξ3 ) has the photon Stock’s parameters
as its components. If polarization of the created elec-
tron is not measured one has to eliminate (1−γ5Ŝ1)/2
in the r.h.s. of Eq. (9).
When calculating the non-decreasing (with the
energy growth) contribution into the unpolarized
part of the cross-section one ought to account
for terms proportional to s2 in the contraction
Tμνλρ(e1λe1ρ + e2λe2ρ)Bμν , which arise due to scalar
products (k1p), (k2p), and (kp) . Then we have:
Tμνλρ(e1λe1ρ + e2λe2ρ)Bμν = −16
[ 4m2
χ1χ2
(k1p)(k2p)+
(k1p)2
( q2
χ1χ2
−2m2
χ2
2
)
+(k2p)2
( q2
χ1χ2
−2m2
χ2
1
)]
. (11)
To calculate the high-energy cross-section of the
process (1) it is convenient to introduce so-called
Sudakov’s variables [7]. These variables define an
expansion of the final 4-momenta on the longitudi-
nal and transversal components relative to the 4-
momenta of the initial particles. For the process (1)
k2 = αp′ + βk + k⊥ , q = αqp
′ + βqk + q⊥ , (12)
p′ = p − m2
s
k , s = 2(kp), p′2 = 0,
d4k2 =
s
2
dαdβd2k⊥, d4q =
s
2
dαqdβqd
2q⊥ ,
where 4-vectors k⊥ and q⊥ are the space-like ones, so
k2
⊥ = −k2, q2
⊥ = −q2, and k and q are two-dimension
Euclidian vectors.
The phase space of the final particles can be writ-
ten as
dΦ =
1
4sβ(1 − β)
dβd2kd2q . (13)
The variable β is the photon energy fraction that is
carried out by the positron β = E2/ω. In terms of
the Sudakov’s variables, the independent invariants
are expressed as follows:
χ1 =
m2 + (k + q)2
2(1 − β)
, χ2 =
m2 + k2
2β
, q2 = −q2.
(14)
Using Eq. (11) we easily obtain the well-known result
for unpolarized differential cross-section
dσ =
2α3
π2q4
[
2m2β(1 − β)
( 1
m2 + (k + q)2
− (15)
1
m2 + k2
)2
+
q2[1 − 2β(1 − β)]
[m2 + (k + q)2][m2 + k2]
]
dβd2kd2q .
This form of the differential cross-section allows the
integration over the positron perpendicular momen-
tum where the upper limit of integration can be sup-
posed to equal to infinity. For chosen accuracy [8]:
dσ =
2α3
πq4
{[
1−2β(1−β)
]
Ψ1 +2β(1−β)Ψ2
}
dβd2q ,
Ψ1 =
1
x
ln
x + 1
x − 1
, Ψ2 = 1 − 2m2
q2
Ψ1, (16)
98
x =
√
1 +
4m2
q2
.
For the pair creation in the process (1) by the
high-energy photon and the relativistic initial elec-
tron with the energy E >> m at back-to-back colli-
sion, the scattered electron can be detected, in prin-
ciple, by means of the circular detector which sums
all events with θmin < θ < θmax, where the scatter-
ing electron angle θ = |q|/E. In this experimental
setup the differential cross-section (16) ought to be
integrated over the detector aperture. For analytical
integration it is convenient to introduce new variable
q2/m2 = 4 sh2 z , so that:
Ψ1 = 2z cth z, Ψ2 = 1 − z
sh z ch z
,
dq2
q4
=
ch zdz
2m2 sh3 z
and the integration of the Eq. (16) with respect to
azimuth angle and new variable z leads to following
positron spectrum for the unpolarized case:
dσ
dβ
= 2αr2
0
{
A(z0)−A(z1)+β(1−β)
[
B(z0)−B(z1)
]}
,
(17)
where z0 and z1 are the minimal and maximal values
of z and functions A(z) and B(z) are
A(z) = 2z cth z − 2 ln(2 sh z) , (18)
B(z) =
2
3 sh2 z
− 2z cth z − 2
3
z cth3 z +
8
3
ln(2 sh z).
When writing the latter formulae we fixed the
integration constant in such a way that both
A(z), B(z) → 0 if z → ∞. This choice is specified by
behavior of the cross-section (16) at large |q2/m2|.
The total cross-section in such experimental setup
can be derived by elementary integration over the
positron energy fraction:
σ=2αr2
0
[
C(z0)−C(z1)
]
, C(z)=A(z)+
B(z)
6
. (19)
Note, that in the pair production by the photon
on the stationary target with arbitrary mass M the
quantity q2 is connected with mass M and energy W
of the recoil particle in the laboratory system:
q2 = 2M(W − M) , W =
√
M2 + l2 ,
where l is the absolute value of the recoil momentum.
It means that in the case of the atomic electron target
l = m sh(2z) , (M = m), and for the very heavy target
l = 2m sh(z), (M >> m). For the stationary target
it is possible to investigate such experimental setup
when detector records all events with l > l0 , l0 ∼ m.
In this case we can formally suppose the upper limit
of integration in Eq. (16) to be equal to infinity. To
write the corresponding results it is enough to elimi-
nate A(z1), B(z1) and C(z1) in Eqs. (17) and (19).
On the other hand, one can study the angular
distribution of the recoil electrons. It is easy to see
that in this case the angle ϑ between the photon
3-momentum k and the recoil electron one p1 is de-
fined by the relation [9] sin2 ϑ = 4m2/(4m2 + q2). It
means that large q2 correspond to small recoil angles
ϑ and and vice-versa. In this case sh z = ctg ϑ.
3. CROSS-SECTION ASYMMETRY AND
CREATED ELECTRON POLARIZATION
To evaluate either asymmetry of the cross-section or
the created electron polarization one has to calculate
the part of cross-section that depends on polarization
states either of the initial electron or of the created
one. For this goal it is convenient to use the covari-
ant form of the electron polarization 4-vectors which
enter in Eqs. (5) and (9):
S =
(pk)p − m2k
m(pk)
, S1 =
(kk1)k1 − m2k
m(kk1)
. (20)
It means that in the rest frame of the initial electron
S = (0,−k/|k|), and in the rest frame of the created
one S1 = (0,−k/|k|).
The asymmetry of the cross-section in considered
process is defined by the ratio:
A = −iξ2
Tμνλρ(e1λe2ρ − e1ρe2λ)B(a)
μν dΦ
Tμνλρ(e1λe1ρ + e2λe2ρ)B
(s)
μν dΦ
, (21)
where B
(s)
μν and B
(a)
μν are the symmetric and antisym-
metric parts of the tensor Bμν , respectively. The di-
rect calculation for the numerator gives
8ξ2(μνqp)
{[
m2
( 1
χ2
1
+
1
χ2
2
)
− q2
2χ1χ2
]
(μνkq)−
− (μνk1q)
χ1
− (μνk2q)
χ2
}
. (22)
Because at the used accuracy (μνqp)(μνkq) =
q2s, (μνqp)(μνk1q) = q2(1 − β)s, (μνqp)(μνk2q) =
q2βs, the respective electron polarization dependent
part of the differential cross-section dσ2 is:
dσ2 = − 2α3ξ2
sq2π2
{
2m2
[ 1 − β
β[(k + q)2 + m2]2
+ (23)
β
(1 − β)[k2 + m2]2
]
+
q2
[(k + q)2 + m2][k2 + m2]
− 1 − β
β[(k + q)2 + m2]
− β
(1 − β)[k2 + m2]
}
dβd2kd2q .
Note that if the initial electron is polarized in its rest
frame opposite to the direction of recoil electron 3-
momentum, one has to divide the r.h.s. of Eq. (23)
by
√
1 + 4m2/q2.
The ratio dσ2/dσ, which define the cross-section
asymmetry is of the order q2/s, i.e. it is parame-
terically small. On the other hand, dσ2 increases
near the edges of the positron spectrum due to terms
containing 1/β and 1/(1 − β). This effect is absent
in polarization-independent part of the cross-section.
Integration of these terms over β leads to large loga-
rithmic contribution ln(ω/m) ≈ (1/2) ln(s/m2). Nev-
ertheless, the method to determine the photon circu-
lar polarization based on the measured cross-section
99
asymmetry in process (1) cannot be efficient at high
energies because of above mentioned smallness of the
ratio dσ2/dσ.
Consider now another possibility based on the
measurement of the created electron polarization. In
this case we have to calculate:
P = −iξ2
T
(pol)
μνλρ(e1λe2ρ − e1ρe2λ)B(s)
μν dΦ
Tμνλρ(e1λe1ρ + e2λe2ρ)B
(s)
μν dΦ
, (24)
where T
(pol)
μνλρ is part of the tensor Tμνλρ (see Eq. (9))
that depends on the created electron polarization 4-
vector S1. The numerator in the r.h.s. of Eq. (24) can
be written as follows:
16mξ2
{[ (k2p)
χ1
− (k1p)
χ2
]
×
[χ1 + χ2
χ1χ2
[
(k2p)(kS1) + χ1(pS1)
]
− (kp)(k2S1)
χ2
+
q2(χ2 − χ1)(kp)(pS1)
2χ1χ2
2
]}
. (25)
The necessary scalar products read:
2m(pS1) = s
[
1 − β − m2/χ1
]
,
m(kS1) = χ1, m(k2S1) = (k1k2) − m2χ2/χ1),
and expression in the braces in the r.h.s. of Eq. (25)
becomes very simple:
s2q2
8χ2
[1 − 2β
χ1
− m2
χ1
( 1
χ1
− 1
χ2
)]
.
Now the integration with respect to the positron
perpendicular momentum leads to the part of the dif-
ferential cross-section which depends on the photon
circular polarization degree:
dσ2 =
2α3ξ2(1 − 2β)
q4x2
[
Ψ2 − Ψ1
]
dβdq2. (26)
The created electron polarization along direction
−k/|k| is defined by the relation:
P = P (β,q2, ξ2) = 2dσ2/dσ,
so that
P =
ξ2(1 − 2β)
(
Ψ2 − Ψ1
)
x2
[
(1 − 2β(1 − β))Ψ1 + 2β(1 − β)Ψ2
] . (27)
The corresponding distribution is antisymmetric rel-
ative to change β → 1 − β and can vary inside wide
interval. It means that the created electron polar-
ization is very sensitive to the high energy photon
circular polarization. For ξ2 = 1 it is shown in Fig. 1.
If the recoil electrons are recorded by narrow cir-
cular detector we have to integrate over the detector
aperture as described above. This procedure results:
P (β, ξ2) = ξ2P (β),
P (β) =
(1 − 2β)
[
D(z0) − D(z1)
]
A(z0) − A(z1) + β(1 − β)
[
B(z0) − B(z1)
] ,
D(z) = 2z[th(z) − cth(2z)]. (28)
If the whole recoil momenta with l > l0 are recorded
then polarization P (β) can be derived with the same
rules as it is described at the end of Sec. 2, namely one
has to eliminate A(z1), B(z1) and D(z1) in Eq. (28)
and use l0 = 2m sh(z0). If the angular distribution of
the recoil electron is measured than one has to use
sh z = ctg ϑ. In Fig. 2 and 3 we give function P (β) as
defined by Eq. (28) for different experimental setups.
Fig. 1. Double distribution for the created electron
polarization calculated by means Eq. (27) for ξ2 = 1
0.2 0.4 0.6 0.8 1.0 Β
�0.5
0.5
P�Β�
0.2 0.4 0.6 0.8 1.0 Β
�0.6
�0.4
�0.2
0.2
0.4
0.6
P�Β�
Fig. 2. Function P (β) at different values of the
minimal recorded recoil electron momentum. The up-
per curve corresponds to back-to-back collision with
detector aperture 1o < θ < 6o. The lower curves cor-
respond to production on atomic electrons: the solid
to l0 = 1.1 m, the dashed to l0 = 2.1 m, the dotted to
l0 = 17.1 m
100
0.2 0.4 0.6 0.8 1.0 Β
�0.4
�0.2
0.2
0.4
P�Β�
Fig. 3. Function P (β) at different values of the
minimal scattering angles of the recoil electron at
fixed value of the maximal one: θmax = 63.6o. The
solid line corresponds to θmin = 5o, the dashed – to
θmin = 30o, and the dotted –to θmin = 60o
4. CONCLUSIONS
The double spin correlations in the process (1) al-
low to probe the high-energy photon circular polar-
ization. In the region |q2| ≥ δm2, where δ is of the
order one, the pair production on the longitudinally
polarized electron beam cannot give efficient measure
for the circular polarization of the high-energy pho-
tons and the created electron polarization is large and
does not decrease with the photon energy. Therefore
the latter can be used, in principle, to determine the
circular polarization degree of high-energy photon.
References
1. V.F. Boldyshev, E.A. Vinokurov, N.P. Meren-
kov, Yu.P. Peresun’ko. A method for measure-
ment of the photon beam linear polarization
by means of of recoil electrons asymmetry in
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| id | nasplib_isofts_kiev_ua-123456789-107004 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T13:35:39Z |
| publishDate | 2012 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Gakh, G.I. Konchatnij, M.I. Levandovsky, I.S. Merenkov, N.P. 2016-10-10T20:23:23Z 2016-10-10T20:23:23Z 2012 About the possibility to measure the circular polarization of high-energy photon in reaction γ + e⁻ → e⁺ + e⁻ + e⁻ / G.I. Gakh, M.I. Konchatnij, I.S. Levandovsky, N.P. Merenkov // Вопросы атомной науки и техники. — 2012. — № 1. — С. 97-101. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 12.20.Ds, 13.40.-f, 13.88.+e https://nasplib.isofts.kiev.ua/handle/123456789/107004 Two possibilities of the measuring high-energy photon circular polarization by means of the process γ + e⁻ → e⁺ + e⁻ + e⁻ are investigated. The first one is connected with the measurement of polarization asymmetry of the cross section when the initial electron beam is longitudinally polarized. The second possibility related with the measurement of the created-positron (or electron) polarization. Just this polarization does not decrease when the photon energy grows up and can be used for effective determination of the photon circular polarization degree. Проанализированы две возможности определения степени циркулярной поляризации высокоэнергетического фотона в процессе γ + e⁻ → e⁺ + e⁻ + e⁻. Первая связана с измерением поляризационной асимметрии сечения, когда начальный пучок электронов обладает продольной поляризацией. Вторая – с измерением поляризации образованного позитрона (или электрона). Показано, что в последнем случае поляризация не убывает с ростом энергии фотона и может быть использована для эффективного определения степени его циркулярной поляризации. Проаналізовано дві можливості визначити ступінь циркулярної поляризації фотона високої енергії у реакції γ + e⁻ → e⁺ + e⁻ + e⁻. Перша пов'язана із вимірюванням асиметрії перерізу, коли початковий пучок електронів має поздовжню поляризацію. Друга -- із вимірюванням поляризації утворюваного позитрона (чи електрона). Виявлено, що в останньому випадку поляризація не зменшується з ростом енергії фотона і може бути використана для ефективного визначення його циркулярної поляризації. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Section B. QED Processes at High Energies About the possibility to measure the circular polarization of high-energy photon in reaction γ + e⁻ → e⁺ + e⁻ + e⁻ О возможности измерения циркулярной поляризации фотона высокой энергии в реакции γ + e⁻ → e⁺ + e⁻ + e⁻ Про можливість вимірювання ступені циркулярної поляризації фотона високої енергії у реакції γ + e⁻ → e⁺ + e⁻ + e⁻ Article published earlier |
| spellingShingle | About the possibility to measure the circular polarization of high-energy photon in reaction γ + e⁻ → e⁺ + e⁻ + e⁻ Gakh, G.I. Konchatnij, M.I. Levandovsky, I.S. Merenkov, N.P. Section B. QED Processes at High Energies |
| title | About the possibility to measure the circular polarization of high-energy photon in reaction γ + e⁻ → e⁺ + e⁻ + e⁻ |
| title_alt | О возможности измерения циркулярной поляризации фотона высокой энергии в реакции γ + e⁻ → e⁺ + e⁻ + e⁻ Про можливість вимірювання ступені циркулярної поляризації фотона високої енергії у реакції γ + e⁻ → e⁺ + e⁻ + e⁻ |
| title_full | About the possibility to measure the circular polarization of high-energy photon in reaction γ + e⁻ → e⁺ + e⁻ + e⁻ |
| title_fullStr | About the possibility to measure the circular polarization of high-energy photon in reaction γ + e⁻ → e⁺ + e⁻ + e⁻ |
| title_full_unstemmed | About the possibility to measure the circular polarization of high-energy photon in reaction γ + e⁻ → e⁺ + e⁻ + e⁻ |
| title_short | About the possibility to measure the circular polarization of high-energy photon in reaction γ + e⁻ → e⁺ + e⁻ + e⁻ |
| title_sort | about the possibility to measure the circular polarization of high-energy photon in reaction γ + e⁻ → e⁺ + e⁻ + e⁻ |
| topic | Section B. QED Processes at High Energies |
| topic_facet | Section B. QED Processes at High Energies |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/107004 |
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