Theoretical and experimental investigations of the Landau-Pomeranchuk-Migdal effect in amorphous and crystalline matter
The brief review of theoretical investigations carried out in NSC KIPT on the problem of multiple scattering effect on radiation of high energy particles in matter is presented. The comparison of results of the theory with experimental data obtained recently on accelerators of SLAC and CERN at the s...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2003
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| Cite this: | Theoretical and experimental investigations of the Landau-Pomeranchuk-Migdal effect in amorphous and crystalline matter / N.F. Shul'ga, S.P. Fomin // Вопросы атомной науки и техники. — 2003. — № 2. — С. 11-18. — Бібліогр.: 47 назв. — англ. |
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| author | Shul'ga, N.F. Fomin, S.P. |
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| citation_txt | Theoretical and experimental investigations of the Landau-Pomeranchuk-Migdal effect in amorphous and crystalline matter / N.F. Shul'ga, S.P. Fomin // Вопросы атомной науки и техники. — 2003. — № 2. — С. 11-18. — Бібліогр.: 47 назв. — англ. |
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| description | The brief review of theoretical investigations carried out in NSC KIPT on the problem of multiple scattering effect on radiation of high energy particles in matter is presented. The comparison of results of the theory with experimental data obtained recently on accelerators of SLAC and CERN at the study of the Landau-Pomeranchuk-Migdal effect in amorphous and crystalline matter is carried out.
Дано стислий огляд теоретичних досліджень з проблеми впливу багатократного розсіяння на випромінювання частинок високих енергій у речовині, які виконувалися в ННЦ ХФТІ. Проведено порівняння результатів теорії з експериментальними даними, отриманими нещодавно на прискорювачах SLAC і CERN при дослідженні ефекту Ландау-Померанчука-Мигдала в аморфних і кристалічних середовищах.
Дан краткий обзор теоретических исследований по проблеме влияния многократного рассеяния на излучение частиц высоких энергий в веществе, выполненных в ННЦ ХФТИ. Проведено сравнение результатов теории с экспериментальными данными, полученными недавно на ускорителях SLAC и CERN при исследовании эффекта Ландау-Померанчука-Мигдала в аморфных и кристаллических средах.
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THEORETICAL AND EXPERIMENTAL INVESTIGATIONS
OF THE LANDAU-POMERANCHUK-MIGDAL EFFECT
IN AMORPHOUS AND CRYSTALLINE MATTER
N.F. Shul'ga, S.P. Fomin
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
e-mail: sfomin@kipt.kharkov.ua
The brief review of theoretical investigations carried out in NSC KIPT on the problem of multiple scattering
effect on radiation of high energy particles in matter is presented. The comparison of results of the theory with
experimental data obtained recently on accelerators of SLAC and CERN at the study of the Landau-Pomeranchuk-
Migdal effect in amorphous and crystalline matter is carried out.
PACS: 11.80.Fv; 13.40.-f; 41.60.-m
1. INTRODUCTION
The successful splitting of the lithium nucleus in
UFTI (now NSC KIPT) in 1932 became a stimulus for
further broad theoretical and experimental
investigations in the field of nuclear physics and physics
of accelerators. Researches in these directions are
carried on practically during all the time of UFTI
existence. Creation of the electron accelerator with the
energy up to 2000 MeV in UFTI in 1965 opened new
possibilities for investigations in the field of nuclear
physics, connected with the research of electro- and
photonuclear reactions in this range of the energies. For
realization of the researches of photonuclear reactions
the beams of monochromatic and polarized gamma-
quanta are required. One of perspective methods of such
beams production was designed in UFTI in 1960s. This
method is based on the process of coherent radiation of
ultra relativistic electrons in aligned crystals. Now this
method is utilized at many accelerating centers of the
world for production of monochromatic and polarized
gamma-quanta beams.
The theoretical and experimental investigations of
interaction processes of relativistic electrons with crys-
tals carried out in UFTI at the beginning of the 1970s
have led to not only interesting but sometimes even
paradoxical results. Thus, in particular, it appeared, that
at a small angle of particle incidences on a crystal
relative to one of its crystallographic axes the radiation
by electrons and positrons essentially differs, in spite of
the fact that the radiating particles are ultra relativistic.
The existing by then theory of coherent radiation of
ultra relativistic electrons in a crystal was grounded on
the first Born approximation of a quantum
electrodynamics. Within the framework of this theory
the cross-section of bremsstrahlung does not depend on
a sign of a particle charge, so, electrons and positrons
should radiate equally. It was revealed also, that the
angular distributions of particles scattered by aligned
crystal essentially differ from angular distributions of
particles in an amorphous medium.
What was also paradoxically is the following. The
analysis of applicability conditions of the Born approxi-
mation for describing of particle radiation in a crystal,
carried out in 1970s, showed, that this approximation
fails fast with the decrease of particle incidence angle
relative to a crystal axis. Thus, it turned out that
practically all experiments on check of predictions of
the Born theory of coherent radiation were carried out
under the conditions, when the applicability conditions
of the Born approximation for describing of particle
interaction with crystal are not fulfilled. And in some
cases the good consent between the experiment and the
theory was reached in the domain, where the theory
does not work. All this required a detail research of
interaction processes of high energy particles with
crystals under the conditions, when the Born
perturbation theory is inapplicable. The state of
theoretical and experimental researches and the main
results obtained in KIPT in this field between late 1960s
and 1998 is observed in Refs. [1,2].
The detailed research of processes of high energy
particle interaction with aligned crystals out of the
domain of applicability of the Born perturbation theory
also stimulate a number of other directions of study of
particle interaction with intensive external fields and
unregulated (amorphous) media. One of such directions
of investigations falls into the Landau-Pomeranchuk-
Migdal effect (LPM effect) that is the multiple
scattering effect on radiation of ultra high energy
electrons in amorphous medium [3-5]. In spite of the
fact that this effect was predicted at the beginning of
1950s the new interest to the LPM effect has arisen at
the end of 1970s. It was caused by the following. In
Refs. [6-9] it was shown, that in crystals the multiple
scattering of particles in some cases could essentially
exceed the scattering in an amorphous target of the
same thickness. It means, that in a crystal there should
be an analog of the LPM effect, moreover it should
appear at lower energies of electrons and in a broader
spectral range of radiation.
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2003, № 2.
Series: Nuclear Physics Investigations (41), p. 11-18. 11
Besides that, the searches of methods, permitting to
describe interaction of high energy particles with crys-
tals outside of the domain of applicability of the Born
perturbation theory, led to the methods, which opened
possibilities for a new view on the problem of the LPM
effect and searching common regularities between
processes of particles interaction with crystal and
amorphous medium.
The new interest to the LPM effect, which has been
observed lately, is connected to the development of a
new generation of accelerators of super high energies.
The reason is the following. The multiple scattering
effect on radiation increases squared with electron
energy increasing. It leads to a considerable distortion
of the standard Bethe-Heitler’s spectrum of
bremsstrahlung and electron-positron pair production,
and, hence, the development of electromagnetic
cascades in substance at high energies will be
influenced essentially. Therefore it is necessary to take
into account the LPM effect when designing detectors
and radiation protection for ultra high energy
accelerators and also in cosmic rays physics. Because of
this, the special experimental investigation of the LPM
effect was carried out recently in SLAC (experiment E-
146) Refs. [10-13]. This experiment confirms the main
predictions of the Migdal’s theory of the LPM effect for
relatively thick targets; it also shows a number of
problems for describing radiation in a thin target case.
This initiated a number of new theoretical works on this
problem [14-22].
In the present paper we shall consider briefly some
results obtained in NSC KIPT when studying the LPM
effect and close effects.
2. THE LANDAU-POMERANCHUK-
MIGDAL EFFECT
The process of radiation of a relativistic electron
develops in a large spatial region along the direction of
particle motion, which is called the coherence length of
radiation process. This length grows fast with particle
energy ε increasing and with decreasing of emitted
photon energy ω [4,5]:
'
2
2
cl m
ε ε
ω
= , (2.1)
where m is the electron mass and ε´= ε - ω. If in limits
of this region an electron interacts with one atom of a
medium, the cross-section of bremsstrahlung is deter-
mined by the Bethe-Heitler formula [4,5,23]
2 6 2
2 2
4 21 ln
3 9
BHd Z e mR
d m
σ ε ε ε
ω ω ε ε ε
′ ′ ′ = + − +
, (2.2)
where Z|e| is the charge of atomic nuclear and R is the
screening radius of atomic potential.
Moving in an amorphous medium electron
sequentially interacts with different atoms of a medium,
and these collisions can be considered as random. If the
electron in limits of coherence length of radiation pro-
cess collides only with one atom, then the interference
of radiation from electron interaction with other atoms
of a medium is unessential. Thus the radiation spectral
density is determined by the formula [4,5]
2 2
2 2
2 1
3 2
BH
Rad
dE L
d L
ε ω
ω ε ε
′
= + +
, (2.3)
where LRad is the radiation length,
1 2 6 2(4 / ) lnRadL Z e n m mR− = (2.4)
and n is the density of atoms in a medium.
Landau and Pomeranchuk showed in Ref. [3], that if
in limits of coherence length of radiation process an
electron interacts with a large number of atoms, the
multiple scattering of particle on these atoms could
conduce to suppression of bremsstrahlung in an
amorphous medium. The effect of suppression of
radiation arises, when the mean square angle of multiple
scattering of a particle on atoms of a medium in limits
of coherence length of the radiation process exceeds
square of a characteristic angle of radiation of a
relativistic electron θγ
2 ~ m 2/ε 2. This result was obtained
on the basis of the classical theory of electron radiation.
However, the formula for a spectral density of electron
radiation in substance, obtained by Landau and
Pomeranchuk, has only evaluative character. The reason
is that at the development of this formula the terms of
the same order of smallness, as left ones were discarded.
(This circumstance was noted in Refs. [9,14].)
The quantitative theory of the multiple scattering
effect on an electron radiation in an amorphous medium
was offered by Migdal in Ref. [24]. This theory was
based on the application of the kinetic equation method
to the given task. Migdal obtained the following
formula for a spectrum of electron radiation in an
amorphous medium at ω << ε
( )
0
M
dE dE Ф s
d dω ω
=
, (2.5)
where (dE/dω)0 is the spectrum of radiation without
taking into account the multiple scattering influence on
radiation (this value with a logarithmic accuracy
coincides appropriate result of Bethe and Heitler (2.3))
and ФМ(s) is the function, obtained by Migdal, and
which describes the influence of multiple scattering on
radiation
( ) 2 2
0
24 sin 2
4
sx
MФ s s dx cth x e sx π∞
− = −
∫ . (2.6)
The parameter s is determined by the expression
1
2 2 LPM
s ω
ω
= , (2.7)
where
2 4 2
4
16 ln ( )LPM
Z e n mR
m
π εω = . (2.8)
12
The value ωLPM determines the range of gamma
quanta energies, starting with which the multiple
scattering influences radiation spectrum essentially.
Owing to Migdal’s important contribution to the
theory of the given effect now it is called the Landau-
Pomeranchuk-Migdal effect.
The function of Migdal is close to a unit at s ≥ 1, i.e.
at ω ≥ ωLPM. The spectrum of radiation in this case
coincides with the corresponding result of Bethe and
Heitler.
If s << 1,
( ) 6Ф s s≈ . (2.9)
The intensity of radiation in this case is much less,
than the corresponding result of Bethe and Heitler.
The theory of the LPM effect has afterwards got its
development in a number of works. In particular, on the
basis of the method of density matrix the recoil effect at
radiation was taken into account, the influence of
polarization of a medium and boundaries of the target
on radiation of photons and a number of other effects at
high energy electrons and photons interaction with an
amorphous medium were taken into account (see
monographs and reviews [4,5,25,26] and references in
them). All these researches are based on the application
to the given task either the method of kinetic equation or
the density matrix method.
3. THE LPM EFFECT IN AMORPHOUS
MEDIA AND IN CRYSTAL
At the end of the 1970s there was a new interest to
investigation of the LPM effect. It was stipulated by the
analysis of processes of relativistic electrons interaction
with crystals. There were several reasons for this. Let's
point out only some of them.
Firstly, the analysis of applicability conditions of the
Born theory results of coherent radiation of electrons in
a crystal, carried out in the 1970s, has shown, that the
condition of applicability of a Born approximation in
the given task is destroys quickly with increase of
energy and with decrease of the angle of particle falling
on a crystal related to one of the crystal axes [5,6,9].
Thus, to describe the interaction of an electron with a
crystal it was required to advance methods permitting to
go beyond the frameworks of the Born perturbation
theory. Such methods were developed on the basis of
the classical theory of radiation, as well as the eikonal
and quasi-classical approximation of a quantum
electrodynamics. It indicated a possibility to consider
the processes of particle radiation in crystals and in
amorphous media from uniform positions (on the basis
of identical methods) and to reveal common regularities
and distinctive features between the processes of
radiation of particles in these cases.
Secondly, the analysis of the process of scattering of
charged particles in a crystal showed, that in case of
special orientations of the latter, there can be set up the
conditions, when the average value of scattering angles
of particles will considerably exceed the corresponding
value of scattering angles in an amorphous medium
[8,9]. It indicated new possibilities for investigation of
the LPM effect at interaction of particles with crystals.
Research in this direction has led to the following
results.
4. RADIATION IN A THIN LAYER OF
SUBSTANCE
The analysis of the radiation process of a relativistic
electron in a thin layer of substance has shown, that at
rather high energies of electrons and small energies of
radiated photons the following condition can be carried
out [7,9]
cl L> > , (4.1)
e.g. the coherence length of radiation is greater, than the
target thickness L. The process of radiation in this case
was explicitly studied in [7,15-17,26]. It was shown,
that at realization of the condition (4.1) the radiation
spectral density is determined by the expression
( )2 2
2 2
2
2 2 1( , ) n 1 1
1
dE e d f L l
d
ξϑ ϑ ξ ξ
ω π ξ ξ
+= + + −
+
∫ ,(4.2)
where ξ = γθ /2, θ is the scattering angle of particles by
the target and f(θ,L) is the distribution function of
particles on angles θ.
The formula (4.2) shows that at realization of the
condition (4.1) the radiation spectral density is
determined only by the scattering angle of a particle and
does not depend on details of its trajectory in a target.
Therefore, the formula (4.2) can be used when studying
radiation of particles, both in crystalline, and amorphous
targets. The difference between processes of radiation in
these cases will be determined only by distribution
function of scattered particles on angles.
The formula (4.2) has simple asymptotes at small
and large values of a mean square angle of multiple
scattering of particles by the target 2ϑ :
2
2 2 2 2
2
2 2 2 2
2 , 1;
3
2 ln( ) , 1.
e
dE
d e
γ ϑ γ ϑ
π
ω
γ ϑ γ ϑ
π
< <≈
> >
(4.3)
In the amorphous target the value 2ϑ is
proportional to the thickness L. Thus, if 2 2 1γ ϑ < < , the
formula (4.3) passes into the corresponding result of
Bethe and Heitler (2.3). If 2 2 1γ ϑ > > , then according to
(4.3), the linear dependence of dE/dω from L is replaced
by a weaker logarithmic one. It means, that at
realization of the condition 2 2 1γ ϑ > > the effect of
suppression of radiation as contrasted to the
corresponding result of Bethe and Heitler takes place.
Modification of character of electron radiation in a
thin layer of substance happens under the same
conditions, as in case of the LPM effect. However, the
radiation spectral densities (2.5) and (4.3), essentially
differ (different are the dependencies from L, ε and ω).
It is connected that the formula (4.3) is valid at
realization of the condition lc >> L, whereas the formula
(2.5), describing the LPM effect is valid at lc << L.
The similar effects are also possible at electron
radiation in a crystal. However, in a crystal there can be
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2000, №2.
Серия: Ядерно-физические исследования (36), с. 3-6.
13
carried out the conditions, at which the mean square
value of multiple scattering angles will be considerably
larger, than in an amorphous target. Thus, if 2 2 1γ ϑ < < ,
the formula (4.3) turns into the corresponding result of
the theory of coherent radiation of relativistic electrons
in a field of atomic strings of a crystal. At realization of
the condition 2 2 1γ ϑ > > , accordingly to (4.3), there
appears an effect of suppression of coherent radiation.
Thus, modification of the character of electron radiation
in a crystal can take place much faster, than in the
amorphous target.
5. QUANTUM THEORY
The results of the classical theory of radiation in thin
layers of substance were generalized afterwards in the
case, when the effect of quantum recoil at radiation is
essential [5,17,27]. Such research was carried out on the
basis of the theorem of a factorization of cross-section
of high energy electron radiation in an external field,
according to which the cross-section of radiation could
be represents as a product of radiation probability and
elastic scattering cross-section of a particle in this field.
Thus, the only cross-section of elastic scattering
depends on the external field. This theorem is valid, if
the coherence length of the radiation process is big as
contrasted to the longitudinal size of the spatial region,
in which the external field influences on a particle.
At rather high of electron energy this condition can
be always carried out at its interaction with a thin layer
of substance. Thus, all layer of substance is considered
as uniform object, with which the electron interacts. The
scattering of a particle is considered in an eikonal
approximation of the quantum theory of scattering.
This approach allowed considering not only the
process of radiation, but also such processes as a photo-
and electro-production of electron-positron pairs at high
energies in a thin layer of substance [9,17,27,28]. Thus,
it was shown that for all these processes when the
thickness of the target increases, the linear dependence
of their cross-sections from the target thickness is
replaced by a weaker logarithmic one. Modification of
the character of these processes happens at realization of
the same conditions, as in the case of the LPM effect.
Such effect takes place at particles interaction with both
an amorphous and crystalline targets.
When studying the process of scattering of high
energy electrons in a thin layer of an amorphous
substance in the eikonal approximation of the quantum
theory of scattering the following result was also
obtained [9,17,27,28]. It was shown, that the averaging
of quantum cross-section of scattering by positions of
atoms in the target leads to the angular distribution of
scattered particles, which exactly coincides with the
Bethe-Molierè distribution obtained as a result of the
solution of kinetic equation for the angular distribution
function of particles in a medium. In other words, the
study of the scattering of fast particles in an amorphous
medium on the basis of an eikonal approximation of the
quantum theory of scattering and on the basis of the
method of the kinetic equation leads to identical results
for the angular distribution function of particles.
6. THE FUNCTIONAL INTEGRATION
METHOD
In Refs. [6,9] at studying the process of coherent
radiation of relativistic electrons in a crystal outside the
domain of applicability of the Born perturbation theory,
were investigated the possibilities to develop the
method of description of relativistic electrons radiation
in substance, proposed by Landau and Pomeranchuk
[3]. This method was based on the classical theory of
radiation of electrons in substance. Thus, the inaccuracy
of the Ref. [3] was corrected, and there was obtained a
common formula (see formula (2.4) of Ref. [9]) for the
spectral density of radiation of a relativistic electron
moving in an external field on the given trajectory. Both
the field of a crystal lattice and the field of an aggregate
of atoms of an amorphous medium can be considered as
an external field. In the latter case the trajectory of a
particle in a medium is random, therefore the radiation
spectral density should be averaged by random
trajectories of an electron in substance. Thus, it was
noted, that the radiation density, being a subject to an
average, represents a functional, which has the Gaussian
form. The random process, to which the multiple
scattering of an electron in an amorphous medium is
connected, can be considered as the Gaussian process. It
meant, that for realization of the averaging procedure
the method of functional integration (also known as the
method of integration over trajectories) could be
utilized.
The implementation of this method in the task of
description of the LPM effect was realized in [29-31].
Thus, on the basis of the method of functional
integration it became possible to reproduce completely
the main result of the Migdal theory. It opened new
possibilities in describing the interaction of high energy
particles with substance.
This method was also applied to the task on the
influence of multiple scattering of high energy electrons
on atomic strings of a crystal on the process of their
coherent radiation in a crystal [29,31]. Thus, it was
shown, that the multiple scattering of electrons in a
crystal at high energies leads to suppression of the
process of their coherent radiation. This effect is similar
to the LPM effect in an amorphous medium. However,
in a crystal, contrary to an amorphous medium, the
coherent radiation is suppressed, and the conditions of
the effect appearance could be fulfilled much earlier,
than in an amorphous medium. It happens because the
average value of angles of multiple scattering of elec-
trons on atomic strings of a crystal could considerably
exceed the average value of angles of multiple
scattering of particles in an amorphous medium.
The substantiation of using of a method of a
functional integration in the task about radiation of an
electron in a crystal was based on dynamic chaos
phenomenon at motion of a particle in periodic field of
atomic strings of a crystal [32-34].
14
Afterwards on the basis of the functional integration
method the spectral-angular distribution of bremsstrah-
lung of a high energy electron in an amorphous medium
was researched [35]; the influence of polarization of a
medium on radiation and the recoil effect at radiation
were taken into account [5,36,37]; the process of
electron-positron pair production in amorphous and
crystalline mediums was surveyed [5,36]; the influence
of multiple scattering on energy losses by fast charged
particles in substance was investigated [5,38]. Recently
in Ref. [39] there was shown a possibility of utilization
of the method of functional integration in the task on the
influence of multiple scattering of relativistic electrons
in a crystal on the process of their parametric X-
radiation as well.
7. EXPERIMENTAL RESEARCHES OF
THE LPM EFFECT
The first experiments on detection of the LPM effect
were conducted using of cosmic rays [40,41] and
secondary electron beams with the energy of 40 GeV on
the protons accelerator of IHEP (Protvino, Russia) [42].
Because of the insufficient statistics of measurements
these experiments could only deal with qualitative
confirmation of the LPM effect existence.
The detail experimental research of the LPM effect
was carried out only recently, 40 years after its predic-
tion. This experiment was carried out in 1993-95 on
SLAC accelerator at the electron energies 8 and 25 GeV
[10-13]. In this experiment there were measured the
spectra of bremsstrahlung in the region of small
energies of gamma-quanta (from 200 keV up to
500 MeV) for targets produced from different materials
(from carbon to uranium) and in a rather wide interval
of target thickness (from 0.1 % up to 6 % of radiation
lengths).
The measurements were carried out with a rather
high accuracy that allowed realizing a quantitative
comparison of experimental data with theoretical calcu-
lations, and to research different mechanisms of
medium influence on the process of bremsstrahlung of
electrons in substance. Some results of the experiment
and the comparison of experimental data with
theoretical calculations are presented in Figs. 1-3.
Fig. 1. Radiation spectra of 25 GeV electrons in the
uranium target of thickness 3% LRad in the range of
photon energies from 200 keV to 500 MeV
Fig. 2. The same as in Fig. 1, for the golden target of
thickness 0.7% LRad
Fig. 3. The same as in Fig. 2, for 8 GeV electrons
The solid curves in these figures correspond to the
results of calculations under the Migdal’s formula
Eq. (2.5), histograms are the results of the Monte-Carlo
simulation of radiation spectrum in Refs. [12,13],
straight lines are the results of calculations under the
Eq. (4.2).
The experimental data obtained in SLAC have
shown not only a good consent with predictions of the
Migdal theory for rather thick targets, but also a
considerable discrepancy with the latter in the case of
targets of relatively small thickness. The experiment
carried out in SLAC boosted further development of the
theory of multiple scattering influence on bremsstrah-
lung of relativistic electrons in substance permitting to
take into account the finiteness of the target sizes and its
structure [14,16-22,43]. The analysis of the results of
this experiment showed, that, alongside with confir-
mation of the LPM effect, the effect of suppression of
bremsstrahlung of high energy electrons in a thin layer
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2000, №2.
Серия: Ядерно-физические исследования (36), с. 3-6.
15
of substance was also confirmed. This effect was
pointed out in Refs. [7,44].
In the 1980s detailed research of the process of
radiation of electrons and positrons with energies from
several GeV up to several tens GeV in the aligned
crystals were carried out. Such researches were
conducted on accelerators SLAC (Stanford), KIPT
(Kharkov), YerPI (Yerevan), TPI (Tomsk), IHEP
(Protvino), CERN (Geneva). The main attention in these
experiments was paid to the research of radiation
properties of particles moving under the conditions of
planar and axial channeling and above-barrier motion
relative to the crystalline planes of atoms and atomic
strings of a crystal. In some experiments the spectra of
radiation at disorientation of a crystal on some values of
a critical angle of an axial channeling were obtained.
One of the purposes of these experiments was to
research the influence of multiple scattering of particles
in crystals on the process of their coherent radiation. Of
special interest is the experiment [45], in which the
attempt to detect the effect of suppression of coherent
radiation similar to the LPM effect was undertaken. The
experiment was carried out on electron beams with the
energy 10 GeV and positrons with the energy 10 and
20 GeV at disorientation of an axis <110> of a silicon
crystal on angles up to ten critical angles of an axial
channeling ψc [45]. Some results of this experiment and
the corresponding theoretical curves are presented in
Figs. 4,5.
The ration of radiation spectral density in a crystal to
the corresponding value in an amorphous medium is put
on the axis of ordinates. The experimental data are
obtained by averaging the spectrum of radiation over
azimuthal angles as related to the axis <110> (see
Fig. 17 in Ref. [45]).
The results of the experiment show that in the
region of high energies of radiated gamma-quanta
(ω > 200 MeV) the spectra of radiation slightly depend
on the energy of a gamma-quantum. The value of
emis-
Fig. 4. The radiation spectra of electrons with
energy 10 GeV arriving at a silicon crystal at small
angles ψ to the axis <110>: the dots correspond to
experimental data from Ref. [45]; the solid lines show
the results of calculations from Ref. [46]. The intervals
of angles ψ, for which the measurements were carried
out, are shown in the figure: a) ψ = (2 - 2.5)ψc and
b) ψ = (2.5 - 3)ψc
Fig. 5. The same as in Fig. 4, for 20 GeV positrons
a) ψ = (2 - 4)ψc and b) ψ = (4 - 6)ψc
sion intensity in this range of frequencies coincides with
the corresponding result of the theory of coherent
radiation of relativistic electrons in a crystal obtained in
an approximation of random collisions of a particle with
atomic strings. In the range of relatively small energies
of emitted quanta (ω < 200 MeV) the effect of suppres-
sion of coherent radiation takes place, and theoretical
predictions in this range of frequencies are also in a
rather good consent with the experiment [46].
This effect of suppression of coherent radiation is
similar to the LPM effect of suppression of bremsstrah-
lung in an amorphous medium. The experiment also
shows, that in a crystal the effect of suppression of
coherent radiation occurs much earlier than in an
amorphous medium (in the case of amorphous targets of
16
carbon and aluminum, as shown in the experiment [12]
for 25 GeV electrons the LPM effect arises in the region
of gamma quanta energies about several tens MeV).
In conclusion we shall note, that the multiple
scattering of electrons on atomic strings of a crystal can
also lead to suppression of coherent radiation at electron
energies of about several hundreds MeV, when the
condition of dipole radiation of particles in a crystal is
satisfied, i.e. at realization of the condition 2 2ϑ γ −<
[26,31,47]. However, the mechanism of this effect
emergence differs from the mechanism of the LPM
effect. The given effect has not been experimentally
investigated yet.
ACKNOWLEDGMENTS
The work was partially supported by the Science and
Technology Center in Ukraine (project №1746).
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18
N.F. Shul'ga, S.P. Fomin
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
3. the LPM effect in amorphous media and in crystal
4. Radiation in a thin layer of substance
5. Quantum theory
6. the functional integration Method
7. Experimental researches of the LPM effect
acknowledgmentS
REFERENCES
|
| id | nasplib_isofts_kiev_ua-123456789-110603 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T15:24:11Z |
| publishDate | 2003 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Shul'ga, N.F. Fomin, S.P. 2017-01-05T18:26:13Z 2017-01-05T18:26:13Z 2003 Theoretical and experimental investigations of the Landau-Pomeranchuk-Migdal effect in amorphous and crystalline matter / N.F. Shul'ga, S.P. Fomin // Вопросы атомной науки и техники. — 2003. — № 2. — С. 11-18. — Бібліогр.: 47 назв. — англ. 1562-6016 PACS: 11.80.Fv; 13.40.-f; 41.60.-m https://nasplib.isofts.kiev.ua/handle/123456789/110603 The brief review of theoretical investigations carried out in NSC KIPT on the problem of multiple scattering effect on radiation of high energy particles in matter is presented. The comparison of results of the theory with experimental data obtained recently on accelerators of SLAC and CERN at the study of the Landau-Pomeranchuk-Migdal effect in amorphous and crystalline matter is carried out. Дано стислий огляд теоретичних досліджень з проблеми впливу багатократного розсіяння на випромінювання частинок високих енергій у речовині, які виконувалися в ННЦ ХФТІ. Проведено порівняння результатів теорії з експериментальними даними, отриманими нещодавно на прискорювачах SLAC і CERN при дослідженні ефекту Ландау-Померанчука-Мигдала в аморфних і кристалічних середовищах. Дан краткий обзор теоретических исследований по проблеме влияния многократного рассеяния на излучение частиц высоких энергий в веществе, выполненных в ННЦ ХФТИ. Проведено сравнение результатов теории с экспериментальными данными, полученными недавно на ускорителях SLAC и CERN при исследовании эффекта Ландау-Померанчука-Мигдала в аморфных и кристаллических средах. The work was partially supported by the Science and Technology Center in Ukraine (project №1746). en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Articles presented on the jubilee scientific conference dedicated to the 70th anniversary of the atomic nucleus disintegration (Kharkov , 10 October 2002 ) Theoretical and experimental investigations of the Landau-Pomeranchuk-Migdal effect in amorphous and crystalline matter Теоретичні та експериментальні дослідження ефекту Ландау-Померанчука-Мігдала в аморфних і кристалічних середовищах Теоретические и экспериментальные исследования эффекта Ландау-Померанчука-Мигдала в аморфных и кристаллических средах Article published earlier |
| spellingShingle | Theoretical and experimental investigations of the Landau-Pomeranchuk-Migdal effect in amorphous and crystalline matter Shul'ga, N.F. Fomin, S.P. Articles presented on the jubilee scientific conference dedicated to the 70th anniversary of the atomic nucleus disintegration (Kharkov , 10 October 2002 ) |
| title | Theoretical and experimental investigations of the Landau-Pomeranchuk-Migdal effect in amorphous and crystalline matter |
| title_alt | Теоретичні та експериментальні дослідження ефекту Ландау-Померанчука-Мігдала в аморфних і кристалічних середовищах Теоретические и экспериментальные исследования эффекта Ландау-Померанчука-Мигдала в аморфных и кристаллических средах |
| title_full | Theoretical and experimental investigations of the Landau-Pomeranchuk-Migdal effect in amorphous and crystalline matter |
| title_fullStr | Theoretical and experimental investigations of the Landau-Pomeranchuk-Migdal effect in amorphous and crystalline matter |
| title_full_unstemmed | Theoretical and experimental investigations of the Landau-Pomeranchuk-Migdal effect in amorphous and crystalline matter |
| title_short | Theoretical and experimental investigations of the Landau-Pomeranchuk-Migdal effect in amorphous and crystalline matter |
| title_sort | theoretical and experimental investigations of the landau-pomeranchuk-migdal effect in amorphous and crystalline matter |
| topic | Articles presented on the jubilee scientific conference dedicated to the 70th anniversary of the atomic nucleus disintegration (Kharkov , 10 October 2002 ) |
| topic_facet | Articles presented on the jubilee scientific conference dedicated to the 70th anniversary of the atomic nucleus disintegration (Kharkov , 10 October 2002 ) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110603 |
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