arXiv subjects
Publications and source records attributed to N. F. Shul'ga.
The differential scattering cross section for the problem of charged ultrarelativistic particles motion near a flat beam of charged ultrarelativistic particles was obtained. The problem is considered in the eikonal approximation in the representation of the beam by a continuous potential.
The differential scattering cross section for charged relativistic particles moving parallel close to the crystalline plane of atoms was obtained. The rainbow scattering effect in the approximation of continuous potential was demonstrated. The problem was considered on the basis of the eikonal approximation of quantum electrodynamics.
The study addresses the quantum spreading of a localized stationary flow of high energy particles. Results demonstrate that as particle energy increases, the spreading speed of the particle wave packet diminishes rapidly. Concurrently, increasing the energies stabilizes the initially localized packet, preserving its transverse form in a vacuum over extended distances. This allows substantial simplifications when using various approximate methods to calculate the wave function in an external field.
An investigation on stochastic deflection of high-energy charged particles in a bent crystal was carried out. In particular, we investigated the deflection efficiency under axial confinement of both positively and negatively charged particles as a function of the crystal orientation, the choice of the bending plane, and of the charge sign. Analytic estimations and numerical simulations were compared with dedicated experiments at the H4 secondary beam line of SPS North Area, with 120 GeV/$c$ electrons and positrons. In the work presented in this article, the optimal orientations of the plane of bending of the crystal, which allow deflecting the largest number of charged particles using a bent crystal in axial orientation, were found.
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 [110] direction of the silicon crystal, in the case when the classical motion was completely chaotic. The case of channeling along [100] direction is of special interest because the classical motion here can be both regular and chaotic for the same energy depending on the initial conditions. The semiclassical energy level density (as well as its part that corresponds to the regular motion domains in the phase space) is computed for the 10 GeV channeling electrons and positrons. 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) distributions.
On the basis of the eikonal approximation of quantum scattering theory, the problem of fast charged particles scattering in a thin crystal when particles fall along one its plane of atoms and in a thin layer of amorphous matter is considered. It is shown that the scattering cross section in this problem, for parameters, which are beyond the scope of application of the Born perturbation theory, differs significantly from the corresponding result of the Born approximation. In this case, the scattering in the transverse to the plane direction is determined mainly by a continuous plane potential, which is widely used in the theory of the channeling phenomenon. The scattering of a particle in the longitudinal direction has features of scattering in a two-dimensional amorphous medium with inhomogeneous density of atoms. The concept of a continuous potential of the crystal plane of atoms in the considered approach appears automatically.
The process of scattering of fast charged particles in thin crystals is considered in the transitional range of thicknesses, between those at which the channeling phenomenon is not developed and those at which it is realized. The possibility is shown of application of the methods of geometrical optics for description of the scattering process. The dependence is studied of the total scattering cross-section of ultrarelativistic positrons on target thickness in this range of crystal thicknesses. In the case of ultrarelativistic particles channeling the possibility is shown of the existence of an effect analogical to the Ramsauer-Townsend effect of conversion into zero of the total scattering cross-section at some values of crystal thickness. The important role is outlined of the Morse-Maslov index that enters into the wave function expression in the geometrical optics method.
The scattering of fast charged particles in a thin crystalline undulator is considered under conditions when all particles of the beam undergo above-barrier motion with respect to the bent crystalline atomic planes. The consideration is based on the analysis of the particles motion in the continuous potential field of the bent crystal atomic planes and on the simulation of the scattering process taking into account the influence of incoherent effects in scattering on the particles motion. The possibility of manifestation of the effect of multiple volume reflection from bent crystalline atomic planes both for positively and negatively charged particles is shown. The possibility of the beam profiles significant change by means of a small size crystalline undulator is demonstrated.
When a high-energy electrons move in a crystal along one of the crystallographic planes the phenomenon of planar channeling is possible, in which the particles move in channels formed by the continuous potential of crystalline planes. Such particle motion in a crystal is conserved for most particles even for weak bending of crystalline planes of atoms. In [1-3] the process of channeled electrons radiation in such a device was considered. It was shown that the radiation spectrum of particles in the crystal in this case contains maxima associated with the period of oscillation of the channeled particles in the channel and with the period of the crystal planes bending. In [4] the radiation process in a crystalline undulator with large bending amplitude of the crystal planes was considered. In this case the trajectories of particles that are crossing the crystal planes are close to rectilinear. This allowed consider the radiation process in the first approximation in the interaction of particles with the crystal field analytically. In that paper the possibility of manifesting coherent and interference effects in radiation leading to high radiation intensity was demonstrated. Taking into account the incoherent effects in the particle scattering leads to particle mutual transitions from the sub-barrier to the above-barrier states and vice versa. Analysis of the radiation process in this case can be carried out on the basis of numerical simulation method for this process. In this paper such method is developed on the basis of the proposed in [5] method of the radiation process simulation in a direct crystal. We present some results of simulation of 1 and 10 GeV electron radiation in crystalline undulator at different values of the plane bending amplitudes. The calculations are performed in the dipole approximation of radiation theory with taking into account the recoil effect in radiation.
In this paper we revisit the idea of measuring the magnetic dipole moments of the charm baryons and, in particular, of charmed Lambda by studying the spin precession induced by the strong effective magnetic field inside the channels of a bent crystal. We present a detailed sensitivity study showing the feasibility of such an experiment at the LHC in the coming years.
The motion of fast electrons through the crystal during axial channeling could be regular and chaotic. The dynamical chaos in quantum systems manifests itself in both statistical properties of energy spectra and morphology of wave functions of the individual stationary states. In this report, we investigate the axial channeling of high and low energy electrons and positrons near [100] direction of a silicon crystal. This case is particularly interesting because of the fact that the chaotic motion domain occupies only a small part of the phase space for the channeling electrons whereas the motion of the channeling positrons is substantially chaotic for the almost all initial conditions. The energy levels of transverse motion, as well as the wave functions of the stationary states, have been computed numerically by the method presented at previous RREPS. Note that the potential of the elementary cell in (100) plane of silicon crystal possesses the symmetry of the square. The group theory methods had been used for classification of the computed eigenfunctions and identification of the non-degenerate and doubly degenerate energy levels. The channeling radiation spectrum for the low energy electrons has been also computed.
The radiation arising under uniform motion of non-relativistic charged particle by (or through) perfectly conducting sphere is considered. The rigorous results are obtained using the method of images known from electrostatics.
Existence of different types of interference in the spectrum of radiation emitted by a doubly hard scattered electron is demonstrated. The spectrum develops oscillations in two regions: the hard, where the oscillations depend on the electron Lorentz factor, and the soft, where the oscillations depend on the electron scattering angles. This interference pattern owes to the presence of jetlike radiation configurations, formed by a piecewise-rectilinearly moving electron and the accompanying photon. The corresponding nondipole decomposition relation is derived. Notions describing proper field formation and interference, and presumably being applicable more generally, are discussed in detail.
Quantum theory is proposed of high energy electrons scattering in ultrathin crystals. This theory is based upon a special representation of the scattering amplitude in the form of the integral over the surface surrounding the crystal, and on the spectral method of determination of the wave function. The comparison is performed of quantum and classical differential scattering cross-sections in the transitional range of crystal thicknesses, from those at which the channeling phenomenon is not developed up to those at which it is realized. It is shown that in this thickness range the quantum scattering cross-section, unlike the classical one, contains sharp peaks corresponding to some specific scattering angles, that is connected with the diffraction of the incident plane wave onto the periodically distributed crystal atomic strings. It is shown that the value of the scattering cross-section in the peaks varies periodically with the change of the target thickness. We note that this must lead to a new interference effect in radiation that is connected with the rearrangement of incident wave packet in transitional area of crystal thicknesses.
An investigation on stochastic deflection of high-energy negatively charged particles in a bent crystal was carried out. On the basis of analytical calculation and numerical simulation it was shown that it exists a maximum angle at which most of the beam is deflected. The existence of a maximum, which is taken in the correspondence of the optimal radius of curvature, is a novelty with respect to the case of positively charged particles, for which the deflection angle can be freely increased by increasing the crystal length. This difference has to be ascribed to the stronger contribution of incoherent scattering affecting the dynamics of negative particles that move closer to atomic nuclei and electrons. We therefore identified the ideal parameters for the exploitation of axial confinement for negatively charged particle beam manipulation in future high-energy accelerators, e.g., ILC or muon colliders.
The reports collected in these proceedings have been presented in the third French-Ukrainian workshop on the instrumentation developments for high-energy physics held at LAL, Orsay on October 15-16. The workshop was conducted in the scope of the IDEATE International Associated Laboratory (LIA). Joint developments between French and Ukrainian laboratories and universities as well as new proposals have been discussed. The main topics of the papers presented in the Proceedings are developments for accelerator and beam monitoring, detector developments, joint developments for large-scale high-energy and astroparticle physics projects, medical applications.
The stationary wave functions of fast electrons axially channeling in the silicon crystal near [110] direction have been found numerically for integrable and non-integrable cases, for which the classical motion is regular and chaotic, respectively. The nodal structure of the wave functions in the quasi-classical region, where the energy levels density is high, is agreed with quantum chaos theory predictions.
Classical and quantum properties of scattering of charged particles in ultrathin crystals are considered. A comparison is made of these two ways of study of scattering process. In the classical consideration we remark the appearance of sharp maxima that is referred to the manifestation of the rainbow scattering phenomenon and in quantum case we show the sharp maxima that arise from the interference of single electrons on numerous crystal planes, that can be expressed in the terms of reciprocal lattice vectors. We show that for some parameters quantum predictions substantially differ from the classical ones. Estimated is the influence of the beam divergence on the possibility of experimental observation of the studied effects.