Quantum and classical effects at scattering of high energy charged particles in thin crystals

The present work reviews the results concerning quantum scattering theory of ultrarelativistic electrons in ultrathin crystals and itscomparison with analogous classical results. It deals with an intermediate range of thicknesses, large enough for that the particlemotion could not be considered as rectilinear but small enough for that the channeling regime of motion was not established. Thequantum theory is based both upon the representation of the scattering amplitude as an integral over the surface surrounding thetarget, and on the so-called operator method of determination of the wave function as a solution of a Schro..dinger-like equation.The latter method implies a wide use of the Fourier technique, both in calculation of each next step in the wave packet evolution,and in moving from the spatial coordinates to the angular ones. The authors compare the quantum differential scattering cross-sec-tions with the classical ones in the considered range of crystal thicknesses and show their resemblances, distinctions and the evo-lution of these distinctions with the change of the particle energy. The simplest variant of quantum scattering theory based uponthe eikonal approximation of quantum mechanics is considered. In the paper the quantum differential scattering cross-section wascalculated and its affinity with the classical one was demonstrated. In the preparation of these lecture notes the material of the paper[4] was used

Landau-Pomeranchuk-Migdal effect for finite-size targets

A rigorous evaluation of the Landau-Pomeranchuk-Migdal effect for finite-size targets is performed within the path integral approach previously developed in ref. [4]. The bremsstrahlung rate in QED is expressed through a solution of a two-dimensional Schr\"odinger equation with an imaginary potential. The boundary condition for this solution is formulated in terms of a product of the light-cone electron--photon wave function and the dipole cross section for scattering of $e^{+}e^{-}$ pair off an atom. Numerical calculations are performed for homogeneous and structured targets. Our predictions for the homogeneous target agree well with the photon spectrum measured recently at SLAC with 25 GeV electrons. The spectra obtained for the structured two segment targets exhibit the interference minima and maxima.Comment: 8 pages, LaTeX, 3 figure

Regular and chaotic motion domains in the channeling electron's phase space and mean level density for its transverse motion energy

The motion of charged particles in a crystal in the axial channeling regime can be both regular and chaotic. The chaos in quantum case manifests itself in the statistical properties of the energy levels set. These properties have been studied previously for the electrons channeling along direction of the silicon crystal, in the case when the classical motion was completely chaotic. It is demonstrated that the level spacing distribution for both electrons and positrons can be better described by Berry-Robnik distribution than by both Wigner (completely chaotic case) or Poisson (completely regular case) distribution

Bremsstrahlung Suppression due to the LPM and Dielectric Effects in a Variety of Materials

The cross section for bremsstrahlung from highly relativistic particles is suppressed due to interference caused by multiple scattering in dense media, and due to photon interactions with the electrons in all materials. We present here a detailed study of bremsstrahlung production of 200 keV to 500 MeV photons from 8 and 25 GeV electrons traversing a variety of target materials. For most targets, we observe the expected suppressions to a good accuracy. We observe that finite thickness effects are important for thin targets.Comment: 52 pages, 13 figures (incorporated in the revtex LaTeX file

Energy dependence of the efficiency of high-energy negatively charged particle beam deflection by planar channeling in a bent crystal

The study of planar channeling of high-energy negatively charged particles in bent crystals was carried out. The value of the critical radius of planar channeling in the Doyle–Turner approximation for the atomic potential is determined. The dependence of the maximum angle at which a given fraction of beam particles could be deflected by means of planar channeling in a bent crystal on the particle energy was found. We identified the ideal parameters for the exploitation of planar channeling for negatively charged particle beam deflection by planar channeling in a bent crystal at current and future high-energy accelerators, e.g., SLAC, MAMI, ILC or muon colliders

Formation region effects in transition radiation, bremsstrahlung, and ionization loss of ultrarelativistic electrons

The processes of transition radiation and bremsstrahlung by an ultrarelativistic electron as well as the effect of transition radiation influence upon the electron ionization loss in thin layer of substance are theoretically investigated in the case when radiation formation region has macroscopically large size. Special attention is drawn to transition radiation (TR) generated during the traversal of thin metallic plate by the electron previously deflected from its initial direction of motion. In this case TR characteristics are calculated for realistic (circular) shape of the electron deflection trajectory. The difference of such characteristics under certain conditions from the ones obtained previously with the use of approximation of anglelike shape of the electron trajectory (instant deflection) is shown. The problem of measurement of bremsstrahlung characteristics in the prewave zone is investigated. The expressions defining the measured radiation distribution for arbitrary values of the size and the position of the detector used for radiation registration are derived. The problem of TR influence upon the electron ionization loss in thin plate and in a system of two plates is discussed. The proposal for experimental investigation of such effect is formulated

On the possibility of extracting part of a beam of negatively charged particles from an accelerator using a bent crystal

Abstract The efficiency of deflection of high-energy negatively charged particles by a bent crystal using planar channeling and stochastic deflection mechanism is compared. The comparison is carried out on the example of antiprotons with kinetic energy from 1 to 14 GeV, which will be achievable on accelerators of the Facility for Antiproton and Ion Research. The comparison showed that both deflection mechanisms make it possible to deflect a part of the antiproton beam in the specified energy range by angles of the order of several hundred microradians, which significantly exceed the critical angle of planar channeling. At the same time, the stochastic deflection mechanism makes it possible to deflect particles at much larger angles than planar channeling