Angular distributions of gamma-radiation of 1.2 GeV electrons in silicon monocrystals of great thickness
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2001
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| Cite this: | Angular distributions of gamma-radiation of 1.2 GeV electrons in silicon monocrystals of great thickness / G.L. Bochek, S.P. Fomin, V.I. Kulibaba, V.P. Lapko, N.I. Maslov, B.I. Shramenko, N.F. Shul’ga // Вопросы атомной науки и техники. — 2001. — № 5. — С. 211-213. — Бібліогр.: 5 назв. — англ. |
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Bochek, G.L. Fomin, S.P. Kulibaba, V.I. Lapko, V.P. Maslov, N.I. Shramenko, B.I. Shul’ga, N.F. 2015-03-24T18:53:48Z 2015-03-24T18:53:48Z 2001 Angular distributions of gamma-radiation of 1.2 GeV electrons in silicon monocrystals of great thickness / G.L. Bochek, S.P. Fomin, V.I. Kulibaba, V.P. Lapko, N.I. Maslov, B.I. Shramenko, N.F. Shul’ga // Вопросы атомной науки и техники. — 2001. — № 5. — С. 211-213. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS numbers: 29.25.-t https://nasplib.isofts.kiev.ua/handle/123456789/79033 en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Angular distributions of gamma-radiation of 1.2 GeV electrons in silicon monocrystals of great thickness Спектрально-угловые распределения гамма-излучения электронов с энергией 1,2 ГэВ в монокристаллах Si большой толщины Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Angular distributions of gamma-radiation of 1.2 GeV electrons in silicon monocrystals of great thickness |
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Angular distributions of gamma-radiation of 1.2 GeV electrons in silicon monocrystals of great thickness Bochek, G.L. Fomin, S.P. Kulibaba, V.I. Lapko, V.P. Maslov, N.I. Shramenko, B.I. Shul’ga, N.F. |
| title_short |
Angular distributions of gamma-radiation of 1.2 GeV electrons in silicon monocrystals of great thickness |
| title_full |
Angular distributions of gamma-radiation of 1.2 GeV electrons in silicon monocrystals of great thickness |
| title_fullStr |
Angular distributions of gamma-radiation of 1.2 GeV electrons in silicon monocrystals of great thickness |
| title_full_unstemmed |
Angular distributions of gamma-radiation of 1.2 GeV electrons in silicon monocrystals of great thickness |
| title_sort |
angular distributions of gamma-radiation of 1.2 gev electrons in silicon monocrystals of great thickness |
| author |
Bochek, G.L. Fomin, S.P. Kulibaba, V.I. Lapko, V.P. Maslov, N.I. Shramenko, B.I. Shul’ga, N.F. |
| author_facet |
Bochek, G.L. Fomin, S.P. Kulibaba, V.I. Lapko, V.P. Maslov, N.I. Shramenko, B.I. Shul’ga, N.F. |
| publishDate |
2001 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Article |
| title_alt |
Спектрально-угловые распределения гамма-излучения электронов с энергией 1,2 ГэВ в монокристаллах Si большой толщины |
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1562-6016 |
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https://nasplib.isofts.kiev.ua/handle/123456789/79033 |
| citation_txt |
Angular distributions of gamma-radiation of 1.2 GeV electrons in silicon monocrystals of great thickness / G.L. Bochek, S.P. Fomin, V.I. Kulibaba, V.P. Lapko, N.I. Maslov, B.I. Shramenko, N.F. Shul’ga // Вопросы атомной науки и техники. — 2001. — № 5. — С. 211-213. — Бібліогр.: 5 назв. — англ. |
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ANGULAR DISTRIBUTIONS OF GAMMA-RADIATION
OF 1.2 GEV ELECTRONS IN SILICON MONOCRYSTALS
OF GREAT THICKNESS
G.L. Bochek, S.P. Fomin, V.I. Kulibaba, V.P. Lapko, N.I. Maslov,
B.I. Shramenko, N.F. Shul’ga
NSC KIPT, Kharkov Ukraine
PACS number: 29.25.-t
In the motion of relativistic electrons at a small an-
gle to one of the crystallographic axes, coherence and
interference effects manifest themselves in the radiation,
owing to which the gamma-radiation intensity of parti-
cles in the crystal may far exceed the intensity of radia-
tion in amorphous medium. These effects can be used as
the basis for creation of intense radiation sources with a
high spectral-angular density of radiation.
The intensity of electron radiation in the crystal is
known to be proportional to the target thickness. There-
fore, to create gamma-sources, it is advantageous to use
thick crystals. However, with an increasing target thick-
ness the average square of the angle of multiple electron
scattering by atoms also increases, and this results in
broadening of the angular distribution of gamma-quanta
emitted, and also in the attenuation of the coherence ef-
fect of electron radiation in the crystal. Besides, in thick
crystals the radiation yield can be appreciably influ-
enced by electron energy losses and by the absorption of
emitted gamma-quanta.
The present paper is concerned with investigating
spectral-angular distributions of 1 GeV electron radia-
tion in thick single crystals. The main attention is here
focused on the analysis of influence of the above-men-
tioned factors on the radiation, and to the determination
of the optimum crystalline target thickness from the
viewpoint of elucidating the conditions, at which the
maximum spectral-angular gamma-radiation density
magnitude is attained.
Let us consider the radiation with the relativistic
electron beam incident on the crystal along one of its
crystallographic axes. In thick crystals the greater part
of beam particles executes an infinite above-barrier mo-
tion with respect to crystal atom strings lying parallel to
the crystallographic axis. Therefore, to the first approxi-
mation one can assume that this group of particles
makes the decisive contribution to the radiation. In its
above-barrier motion the electron sequentially collides
with different strings of atoms. If the motion occurs at
angles to the crystallographic axis, ψ, of about several
critical angle values of axial channeling, ψc, the scatter-
ing and radiation of the particle from different atom
strings can be considered independent [1]. In this case,
the spectral-angular radiation distribution will be deter-
mined, first of all, by the special features of electron ra-
diation in the field of a single atom row string.
As a result of incoherent multiple scattering of the
particle by crystal atoms, the particles are redistributed
in the angles ψ. If the average scattering angle values
exceed the characteristic value of the angle of relativis-
tic electron radiation υk ~ γ-1, then the formation of
spectral-angular distribution of radiation is significantly
influenced by multiple scattering of the particle in the
crystal.
With due regard for the multiple scattering, the aver-
age spectral-angular radiation density can be written as
,
),(
)(
2
2
,
2
2
dod
bEd
bdtfddtn
dod
Ed R
T
o ω
ψ
ψψ
ω ∫∫ ⋅> =< (1)
where n is the density of atom strings in the plane or-
thogonal to the crystal axis, and d2ER(ψ,b)/dωdo is the
spectral-angular radiation density of the electron on the
crystal atom string, which is determined by the angle ψ
and the impact parameter of the string b (the corre-
sponding formulae for this quantity are given in ref.
[1]).
The d2ER(ψ,b)/dωdo value was calculated in the
framework of the modified theory of coherent radiation
that takes into account the distortion of the electron tra-
jectory as the electron moves in the field of a single
atomic string [5]. The calculations were made in the
dipole approximation, neglecting the recoil during radi-
ation. The use of this theory to describe the electron ra-
diation in the light-element crystals of relatively moder-
ate thickness has provided good qualitative and quanti-
tative agreement with the previously obtained data [4,
5].
The experiments performed previously at NSC KIPT
on scattering of relativistic electrons in oriented crystals
have shown that in thick crystals with the electron beam
incidence along the crystallographic axis, the function
of particle distribution in the angles f(ψ,t) has practical-
ly the same Gaussian form as is the case in the amor-
phous medium, with the only difference that the average
square values of the multiple scattering angle somewhat
differ from similar values for the amorphous target. This
difference is due to electron beam redistribution in the
angles under the action of the average field of the atom-
ic string at particle entry into the crystal.
In the passage of electrons through a rather thick
crystal (T ~ LR, where LR is the radiation length) the
electron energy losses must be taken into account.
These losses by ~1 GeV electrons in the crystal mainly
go through the radiation losses given by the equation
)( 2 β εα εε +−=
dt
dLR , (2)
where the constants α and β are determined by the radi-
ation losses for coherent and incoherent bremsstrahlung
in the crystal (α ≈ 0.73 (GeV)-1, β = 1).
Solving this equation we obtain the average particle
energy as a function of depth t of particle penetration
211
into the crystal, ε(t). The gamma-quanta radiated in a
thick crystal can be absorbed in the same crystal due to
secondary electrodynamic processes such as pair pro-
duction, Compton scattering, etc. The effect of gamma-
quanta absorption in the crystal can be taken into ac-
count by multiplying the spectral density
οω dd
Ed R
2
by the
factor )L/)tT(exp( a−− , where La is the characteristic
absorption length (La ≈ 2LR for gamma-quanta in the en-
ergy range from 10 to 100 MeV), with a subsequent in-
tegration over t in expression (1).
The above-presented model of calculations was used
in the analysis of experimental data on the spectral-an-
gular distributions of electron gamma-radiation in thick
crystals. The experiment was conducted at NSC KIPT
using the 2 GeV electron linac. The 1.2 GeV electron
beam was incident on silicon crystals of various thick-
nesses along the <111> axis. The original technique
GROM, previously developed at NSC KIPT and based
on the Compton scattering effect [2], was used to mea-
sure spectral-angular distributions of the radiation. The
measurements have shown that the maximum of the
spectral density of 1.2 GeV electron radiation in thick
silicon crystals lies in the region of gamma-quantum en-
ergies ω = 10 - 15 MeV.
Fig. 1.
Fig. 1 shows the measured angular distributions of
gamma-radiation with ω = 15 MeV for the <111> axis-
oriented silicon crystals of thickness T = 15 mm (cir-
cles), T = 30 mm (triangles) and T = 63 mm (squares)
[3]. Fig. 1 also gives the corresponding calculated re-
sults for the angular distributions of gamma-radiation
with ω = 15 MeV produced in silicon crystals of thick-
nesses 15 mm (. . . ), 30 mm (- - -) and 63 mm (- ⋅ -)
(curves 1, 2, 3, respectively). The dashed curve shows
the calculated radiation angular distributions for the
T = 63 mm silicon crystal without taking into account
the electron energy losses and the gamma-quanta ab-
sorption in the crystal. The comparison of this curve
with curve 3 shows that the mentioned factors exert an
essential effect on the radiation yield from thick crystals
and must be taken into account.
Within the experimental errors, the results of mea-
surements for disoriented crystals (amorphous targets)
of the same thicknesses agree very closely between
themselves (black circles) and with the theoretical cal-
culations (dash-dotted curves). This agreement is ex-
plained by the fact that an increase in the quantity of
gamma-quanta emitted with a growing target thickness
is practically compensated by the effect of their absorp-
tion. The present results indicate that, compared to the
disoriented crystal even thick (about a few cm) oriented
crystals exhibit a significant (nearly 20-fold) increase in
the yield of “forward” gamma-quanta with the energy
ω = 15 MeV. The halfwidth of angular distributions of
these gamma-quanta in a thick crystal appears approxi-
mately equal to ∆θ ≈ mc2/E, this being essentially nar-
rower than in the amorphous target.
The comparison between theoretical and experimen-
tal data shows their fair agreement, and this gives evi-
dence for the validity of the proposed model. A certain
discrepancy between the data at θ=0 is probably due to
a complicated dynamics of the electrons moving in the
vicinity of the crystallographic axis; this calls for an ad-
ditional analysis and, before all, a more careful consid-
eration of the absorption of 10 to 20 MeV gamma-quan-
ta in single crystals.
T , mm
random
∆ ω = 1 0 ∼ 2 0 MeV
Fig. 2.
The results obtained here suggest the conclusion
about the optimum crystal thickness for attaining the
maximum spectral-angular radiation density. Figure 2
shows the yield of gamma-quanta of energies ranging
between 10 and 20 MeV as a function of the crystal
thickness, the gamma-quanta being concentrated in the
cone with an opening ∆θ ≈ mc2/E along the direction of
212
the incident electron beam. For comparison, the same
figure shows the results for the amorphous target (dash-
dotted curve). These data give evidence that the opti-
mum crystal thickness for obtaining the maximum spec-
tral-angular radiation density is approximately equal to
15-30 mm, this being in agreement with the previous
data on the total energy losses of gamma-radiation in
single crystals of various thicknesses [4].
It must be also noted that the angular distributions of
15-20 MeV gamma-radiation show a “dip” in the for-
ward direction, that has previously been observed in a
1.5 mm thick silicon single crystal [5].
REFERENCES
1. A.I.Akhiezer and N.F.Shul’ga. High energy elec-
trodynamics in matter. Amsterdam: Gordon and
Breach Publishers, 1996.
2. D.I.Adeishvili et al. // Prib. Tekhn. Ehksp. 1991,
v. 2, p. 62-65.
3. G.L.Bochek et al. // Theses of reports for the XXVII
International Conference on Physics of Charged
Particle Interaction with Crystals, (in Russian).
MGU publ., 1997, p. 75.
4. A.P.Antipenko et al. // NIM, 1990, v. B48,
p. 291-295.
5. A.P.Antipenko et al. // Phys. Lett. 1991, v. A158,
p. 176-180.
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 213-213.
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