Critical parameters of channeling

Basic methods for calculating critical channeling parameters that play a decisive role in the problem of dechanneling of ions are reviewed. The analytic expressions derived for the threshold energy of channeling, the critical transverse energy, and the closest approach distance between particles and atomic chains or planes forming the channels, as well as critical angles of axial and planar channeling, are valid in a wide range of particle energies. The dependence of critical parameters of channeling on the temperature of crystals is analyzed.     

Combined channeling study of α-LiIO3 crystal in an electrostatic field

The combined channeling backscattering and channeling nuclear reaction analysis of the α-LiIO₃ monocrystal in an electrostatic field has been performed by proton beam at different energies to identify the behaviour of Li and I ions in the crystal. The thickness of the crystal was about 2 mm and has been cut perpendicular to C-direction. The channeling parameters like half angular width and minimum yield of 〈001〉 axial channeling have been measured precisely and the channeling behaviour of different ions in the crystal has been observed and measured quantitatively first time. The ionic d.c. conductivity can be calculated from the surface peak of the aligned channeling spectrum directly.     

Proton channeling studies in thin crystals with a supercollimated beam

Abstract

A supercollimated beam of 4 MeV H^? ions with an angular spread of 1.5 × 10^?3 degrees, a diameter of 25 μ and a current of 10 picoamps was used to study the axial and planar channeling characteristics of single crystal silicon samples ranging in thickness from 0.5 to 1.0 μ. Since the angular spread of the beam is much smaller than most of the gross angular phenomena associated with channeling, it is possible to study the detailed characteristics of both planar and axial channeling with greater precision than before. Preliminary results indicate that this technique will allow a direct study of interatomic or continuum potential distributions and will also be useful for studying nuclear multiple scattering as a function of the tranverse energy of channeled particles relative to atomic rows and planar directions.     

Angular distributions of channeled pions and protons up to 250 GeV/c

Channeling phenomena are observed for positive particles of momentum up to 250 GeV/c in a germanium crystal. The polar angular distributions of the channeled particles are compared with theoretical predictions based on a diffusion model. The results indicate that at high particle energy there may be additional mechanisms besides those operative at low energy leading to dechanneling of the particles. In spite of this, channeling effects are observed for particles incident at up to several times the critical angle, in contrast with the results from low energy channeling. Statistical equilibrium in the azimuthal angular distribution has also been observed at all measured beam momenta to about twice the calculated channeling critical angle. The breakdown of statistical equilibrium for the 2 cm crystal used occurs at an incident angle 2–3 times smaller than predicted theoretically.     

Dynamical chaos and stochastic mechanism of high-energy negatively charged particle deflection by bent crystals

Deflection of high-energy negatively charged particles in straight and bent crystals through multiple scattering by crystal atomic strings was considered for the case in which the initial angle between the particle momentum and one of the main crystallographic axes was approximately four critical angles of axial channeling. It was shown that in a bent crystal with a small crystal thickness, when the crystal bend was less than the beam incidence angle, the beam deflected in the direction opposite to the direction of the crystal bend. At larger crystal thicknesses, the large part of the beam starts to deflect in the direction of the crystal bend. In addition, there is a group of particles that follow the crystal axis bend in the angular region of approximately the critical angle of axial channeling with respect to the current direction of the crystal axis. It was shown that in all of these deflection processes, the periodicity of the location of atomic strings in the crystal does not influence the angular distributions of scattered particles. This fact is connected with the effect of dynamical chaos in particle motion in the periodical field of bent crystal atomic strings. It was also shown that observed in a recent CERN experiment effect of beam deflection, when the angle between the initial particle momentum and the crystal axis was approximately four critical angles of axial channeling, is due to peculiarities of the stochastic multiple scattering of particles by bent crystal atomic strings. These peculiarities are connected with the effect of dynamical chaos in particle motion in crystals.     

Spectral method in axial channeling theory

The energy quantization of transverse particle motion in continuous potentials of atomic chains and planes can occur when fast charged particles travel in crystals. In the proposed paper, the energy levels of electrons moving in the mode of axial channeling in a system of parallel atomic chains have been found (Si crystal [110] chains have been used as an example). The energy eigenvalues were determined numerically using the so-called spectral method, which shows itself to good advantage in the problem of the plane channeling of charged particles in crystals.     

ABNORMAL ENERGY DEPENDENCE OF AXIAL MINIMUM CHANNELING YIELDS IN GexSi1-x/Si(100) STRAINED

An energy dependence of the axial minimum channeling yield in Ge_xSi_1-x/Si(100) Strained-layer superlattice is observed in the energy range of impinging He⁺ ione from 1.2 to 3.0 MeV. For [100] axial channeling, the measurements ere in agreement with what have been known in a single crystal. However, for [110] axial channeling, it is found that the minimum channeling yields increase markedly with the increase of He⁺ ion energy, which is contrary to the general channeling behaviors in a single crystal. A tentative model is suggested to explain this aberrance.     

Channeling and electromagnetic radiation of relativistic charged particles in metal-organic frameworks

We have developed the theory of electromagnetic interaction of relativistic charged particles with metal-organic frameworks (MOFs). The electrostatic potential and electron number density distribution in MOFs were calculated using the most accurate data for the atomic form factors. Peculiarities of axial channeling of fast charged particles and various types of electromagnetic radiation from relativistic particles has been discussed.     

Modification of the theory of diffracted channeling radiation for axial electron and positron channeling

A new type of combinational channeling radiation induced by subbarrier (interband) transitions for the transverse motion of relativistic electrons (positrons) is studied. It is known as diffracted channeling radiation (DCR). The formula describing the DCR angular distribution in the case of axial channeling is obtained by taking into account the band structure of energy levels for the transverse motion of electrons (positrons). It is shown that, in the two-wave approximation of the wave function A(r) of virtual photons, the DCR matrix elements in the dipole approximation for axial and plane channeling coincide formally (with the dimension of the problem taken into account). However, the formulas for DCR angular distributions in the cases of axial and plane channeling differ considerably.     

Deflection of a 100-MeV positron beam by repeated reflections in thin crystals

The phenomenon of the deflection of a charged particle beam due to channeling in a bent crystal is thoroughly investigated and successfully applied for the extraction of the beam in high-energy accelerators, at the energies of about 10 GeV and higher. However, a big practical interest lies in the task of bending and extracting charged particles with energies below 1 GeV, for example, for the production of ultrastable beams of low emittance for medical and biological applications. That is why a novel crystal technique, namely thin straight crystal targets, is investigated in this article, using crystals as elements for extraction and collimation of the circulating beam in a ring accelerator. The advantages of reflection in straight crystals in comparison with bent crystal channeling consist in the small length of straight crystals along the beam that reduces the amount of nuclear interactions and improves the background. Experimental results were obtained for the bending of a 100 MeV positron beam with using five sequential straight crystals.     

A qualitative description of the transverse motion of axial channeled particles in thin crystals

The qualitative features of the angular distribution of particles emergent from thin ～ 1μ, uniform single crystals of silicon and germanium for incidence at small angles to axial directions are discussed in terms of the continuum picture of particle channeling. Blocking of axially channeled particles in the transverse plane is demonstrated. Implications and possibilities arising from observation of non-equilibrium of the transverse momentum vector are discussed. The use of the radial spreading of the angular distribution to investigate the average inter-atomic potential distribution in the plane transverse to the axial direction is explored and perturbations due to multiple scattering in surface films or inside the crystal and to beam divergence are qualitatively considered.     

Measurement of average electron densities in Si and Ge using MeV δ-rays produced by channelled high-energy projectiles

For the first time, average electron densities in silicon and germanium were measured using the channeling effect for 5 and 12 GeV/c protons, π⁺ and π^?. In the investigation, the yield of MeV electrons emitted through the back of the target was measured. Such gd-ray yields are proportional to the local electron density averaged along the path of the projectile in the target. For well-aligned, positive particles, the electron yield is reduced to around 15% of normal yield for germanium and 25% for silicon, whereas negatively charged, channeled projectiles give an increase in yield by a a factor of three compared to normal yield. The experimental results have been compared to yield curves calculated using the Lindhard channeling model in connection with special potential models, and very good agreement is obtained for positive particles when the electron density in the middle of the channels is obtained by summing the contributions from many neighbouring strings. For positive projectiles, this channeling method is most sensitive far away from the strings, where other techniques are weak. The results for negative, channeled particles agree fairly well with simplified theoretical calculations, neglecting dechanneling and the lack of equilibrium in angular momenta in the transverse plane.     

Ion-channeling analysis for epitaxial YBa2Cu3Ox superconducting thin films by laser deposition

Rutherford backscattering/channeling has been applied to study structures of as-deposited epitaxial YBa₂Cu₃O_x thin films prepared on {100}SrTiO₃ by laser deposition. The epitaxial growth has been proved by a planar channeling experiment and transmission electron microscopy. An axial angular yield profile for barium along the c-axis has ideal characters of compensating shoulders and of a flat region at the bottom of the channeling dip. The thermal vibration amplitude, which has been determined from a half-angle of the axial angular yield profile by using Gemmell's channeling model for polyatomic crystals, is compared to those from diffraction experiments.     

A study of small impact parameter ion channeling effects in thin crystals

We have recorded channeling patterns produced by 1–2 MeV protons aligned with ?1 1 1? axes in 55 nm thick silicon crystals which exhibit characteristic angular structure for deflection angles up to and beyond the axial critical angle, ψ _a . Such large angular deflections are produced by ions incident on atomic strings with small impact parameters, resulting in trajectories which pass through several radial rings of atomic strings before exiting the thin crystal. Each ring may focus, steer or scatter the channeled ions in the transverse direction and the resulting characteristic angular structure beyond 0.6ψ _a at different depths can be related to peaks and troughs in the nuclear encounter probability. Such “radial focusing” underlies other axial channeling phenomena in thin crystals including planar channeling of small impact parameter trajectories, peaks around the azimuthal distribution at small tilts and large shoulders in the nuclear encounter probability at tilts beyond ψ _a .     

ABNORMAL ENERGY DEPENDENCE OF AXIAL MINIMUM CHANNELING YIELDS IN GexSi1-x/Si(100) STRAINED

An energy dependence of the axial minimum channeling yield in Ge_xSi_1-x/Si(100) Strained-layer superlattice is observed in the energy range of impinging He⁺ ione from 1.2 to 3.0 MeV. For [100] axial channeling, the measurements ere in agreement with what have been known in a single crystal. However, for [110] axial channeling, it is found that the minimum channeling yields increase markedly with the increase of He⁺ ion energy, which is contrary to the general channeling behaviors in a single crystal. A tentative model is suggested to explain this aberrance.     

Channeling in single-wall nanotubes: Possible applications

The relevant potentials are calculated and used to investigate the trajectories and various characteristics of axial channeling of high-energy positively charged particles in the recently discovered single-wall nanotubes (SWNTs). The application of SWNTs in high-energy physics, specifically, in future colliders, is discussed, in view of the fact that the dechanneling length in SWNTs is much longer than in single crystals. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 5, 304–307 (10 September 1997)     

Chaotic behavior of channeling particles

Channeling describes the collimated motion of energetic charged particles along the lattice plane or axis in a crystal. The energetic particles are steered through the channels formed by strings of atomic constituents in the lattice. In the case of planar channeling, the motion of a charged particle between the atomic planes can be periodic or quasiperiodic, such as a simple oscillatory motion in the transverse direction. In practice, however, the periodic motion of the channeling particles can be accompanied by an irregular, chaotic behavior. In this paper, the Moliere potential, which is considered as a good analytical approximation for the interaction of channeling particles with the rows of atoms in the lattice, is used to simulate the channeling behavior of positively charged particles in a tungsten (100) crystal plane. By appropriate selection of channeling parameters, such as the projectile energy E(0) and incident angle psi(0), the transition of channeling particles from regular to chaotic motion is demonstrated. It is argued that the fine structures that appear in the angular scan channeling experiments are due to the particles' chaotic motion.     

Diffracted channeling radiation for axial electron channeling

It is shown that, in contrast to diffracted channeling radiation (DCR) in the case of planar channeling, transitions of type 2 → 1, 3 → 2, 4 → 3, and so on make the main contribution to DCR in the case of axial channeling along an isolated axis. The angular DCR distributions for channeling of electrons with the energy corresponding to the Lorentz factor γ = 100 are calculated for an isolated axis using the Coulomb-type potential.     

Energy losses of electrons in oriented crystals

Abstract

Within the framework of the multistring model of axial channeling of electrons the method for calculating the losses to radiation in channeling is proposed. The physical model includes the multiple scattering, the beam and target characteristics. The simulated results are compared with the experimental data.