Rosette motion and string scattering of 20 MeV electrons in MgO single crystals

Analytical estimates and computer simulations were undertaken to perceive the motion of negative particles through a lattice structure, the interaction being classical binary scattering. Three distinct modes of particle motion along atomic strings were found depending on the magnitude of the transverse energy and the angular momentum L of the particle with regard to the string axis. At small and large L increased scattering on the strings as compared with random penetration dominates. At medium L and negative transverse energy (bound state particles in the attractive potential) a rosette motion along the string occurs. In this case small impact parameters to the string atoms are avoided and thus an increased penetrability of the negative particles results. The influence of thermal lattice vibrations on these motions was studied.

Experimentally, the negative particle motion modes manifested themselves in the penetration profiles of 20 MeV electrons through an 8 μm MgO single crystal.     

The Extraction of Neutron Target Cross Sections from Reactions on Deuterium

The theory of scattering and production reactions on deuterium is developed with a view to the extraction of neutron target amplitudes from analysis of deuterium experiments. Corrections to the spectator model due to the following effects are examined: target particle binding corrections to the Impulse Approximation; (ii) the Pauli principle in charge exchange reactions; (iii) internal or „Fermi”︁ motion of the target particles; (iv) multiple scattering and final state interactions. The closure approximation and the general analysis of single-arm spectrometer experiments are discussed. The connection at high energies and small momentum transfers between the general Watson Theory and the Glauber model is established, and the results of calculations of deuterium corrections for pion and rho photoproduction at high energies are reviewed. “Fresnel” and recoil corrections to Glauber theory are examined. An approximation scheme suitable to the analysis of high energy wide angle coincidence or bubble chamber experiments is developed. A special examination is made of the breakdown of the impulse approximation in the 3-3 resonance region, and of the applicability of lowest order binding and in multiple scattering corrections in this sensitive kinematical region.     

Deuteron electrodisintegration at high energy and momentum transfer

Inelastic electron-deuteron scattering has been calculated at backward angles for energy transfers up to 50 MeV and momentum transfers up to 60 fm^?2. Exchange currents from the pion, vector mesons and mixed ?πγ and ωπγ were taken into account. The effect of the meson-nucleon form factor is studied, and various approximations of the mesonic currents are discussed. Baryon resonance configurations in the wave function have been used to calculate the Δ-resonance currents. We show that the effect from meson-nucleon form factors, the ?πγ, ωπγ and Δ currents cancels almost exactly against the vector meson contribution at low momentum transfer. Thus the pure pionic current defines a reasonable choice. In the high momentum region this approximation breaks down.     

Eikonal expansion

An eikonal expansion of the potential scattering T matrix is evaluated, without approximation, through third order in the inverse momentum. Based on the results, their correspondence with the WKB approximation and a new statement of the unitarity constraint, we propose a sequence of four approximations to the exact impact parameter (Fourier-Bessel) representation of the scattering matrix. The sequence consists of the Glauber approximation and three systematic corrections to the Glauber approximation. The corrections are analytic functions of the impact parameter for Yukawa and Gaussian potentials; they vanish for a Coulomb potential.The sequence of eikonal amplitudes is convergent at high energy and is clearly established for small momentum transfer. Validity for all momentum transfer is conjectured based on systematic cancellation, explicitly verified through third order in the expansion, of momentum transfer dependence in the eikonal impact parameter representation. Such cancellation is shown to occur in the explicit construction of the eikonal expansion of the second Born amplitude for a Yukawa potential.Numerical tests of the sequence of eikonal amplitudes show systematic increase of the angular range of validity by comparison with partial wave results for continuous potentials; the theory is not convergent for discontinuous potentials.The WKB phase shift formula is shown to produce a systematic connection with eikonal expansion results. From this we deduce a generating function for the eikonal phase corrections of arbitrary order and also conjecture a sum of the eikonal expansion valid in the limit of high energy and arbitrary potential strength.     

Focusing of high-energy particles in the electrostatic field of a homogeneously charged sphere and the effective momentum approximation

The impact of the strongly attractive electromagnetic field of heavy nuclei on electrons in quasi-elastic (e, e') scattering is often accounted for by the effective momentum approximation. This method is a plane wave Born approximation which takes the twofold effect of the attractive nucleus on initial- and final-state electrons into account, namely the modification of the electron momentum in the vicinity of the nucleus, and the focusing of electrons towards the nuclear region leading to an enhancement of the corresponding wave function amplitudes. The focusing effect due to the attractive Coulomb field of a homogeneously charged sphere on a classical ensemble of charged particles incident on the field is calculated in the highly relativistic limit and compared to results obtained from exact solutions of the Dirac equation. The result is relevant for the theoretical foundation of the effective momentum approximation and describes the high-energy behavior of the amplitude of continuum Dirac waves in the potential of a homogeneously charged sphere. Our findings indicate that the effective momentum approximation is a useful approximation for the calculation of Coulomb corrections in (e, e') scattering off heavy nuclei for sufficiently high electron energies and momentum transfer.     

Fermi systems with strong forward scattering

We review the theory of interacting Fermi systems whose low-energy physics is dominated by forward scattering, that is scattering processes generated by effective interactions with small momentum transfers. These systems include Fermi liquids as well as several important non-Fermi-liquid phases: one-dimensional Luttinger liquids, systems with long-range interactions, and fermions coupled to a gauge field. We report results for the critical dimensions separating different 'universality classes' and discuss the behaviour of physical quantities such as the momentum distribution function, the single-particle propagator and low-energy response functions in each class. The renormalization group for Fermi systems will be reviewed and applied as a link between microscopic models and effective lowenergy theories. Particular attention is paid to conservation laws, which constrain any effective low-energy theory of interacting Fermi systems. In scattering processes with small momentum transfers the velocity of each scattering particle is (almost) conserved. This asymptotic conservation law leads to non-trivial cancellations of Feynman diagrams and other simplifications, making thus possible a non-perturbative treatment of forward scattering via Ward identities or bosonization techniques.     

Glauber amplitude for ionization of helium by electron impact

The high-energy Glauber approximation is used to derive the formula for scattering amplitude for ionization of helium atom by electron impact. The scattering amplitude is expressed as a one dimensional integral involving MeijerG-functions. This may further be expressed in a closed form as simple sums of Meijer functions by writing down the series expansion for Bessel and Meijer functions. Further, the asymptotic behaviour of these amplitudes is examined for both large and small momentum transfers.     

Anomalous Diffusion Equations with Multiplicative Acceleration

A generalization of the model of Lévy walks with traps is considered. The main difference between the model under consideration and the already existing models is the introduction of multiplicative particle acceleration at collisions. The introduction of acceleration transfers the consideration of walks to coordinate–momentum phase space, which allows both the spatial distribution of particles and their spectrum to be obtained. The kinetic equations in coordinate–momentum phase space have been derived for the case of walks with two possible states. This system of equations in a special case is shown to be reduced to ordinary Lévy walks. This system of kinetic equations admits of integration over the spatial variable, which transfers the consideration only to momentum space and allows the spectrum to be calculated. An exact solution of the kinetic equations can be obtained in terms of the Laplace–Mellin transform. The inverse transform can be performed only for the asymptotic solutions. The calculated spectra are compared with the results of Monte Carlo simulations, which confirm the validity of the derived asymptotics.     

Classical binary-encounter collision theory for electron-impact ionization of ions

We calculated electron-ion impact ionization using classical binary-encounter collision theory. A differential cross section per unit energy and momentum transfer is derived for two-electron scattering. We obtain the total ionization cross section by integrating this differential cross section over the appropriate energy and momentum transfer and the bound electron-velocity distribution. To simplify the computation, we calculated the bound electron-velocity distribution in the Thomas-Fermi approximation. Comparison with other theoretical calculations shows that our results agree within 50% with the best quantum qpproximations. Our cross sections and rate coefficients, which are sufficiently accurate for many practical applications, are expressed in computationally simple form.     

Neutron scattering from a substitutional mass defect

The dynamic structure factor is calculated for a low concentration of light mass scatterers substituted in a cubic crystal matrix. A new numerical method for the exact calculation is demonstrated. We derive a local density of states for the low momentum transfer limit, and derive the shifts and widths of the oscillator peaks in the high momentum transfer limit. We discuss the limitations of an approximation which decouples the defect from the lattice.     

Exponentially small scattering amplitude in high energy potential scattering

The high energy scattering amplitude of spherical symmetric potentials, which are expandable in ascending even powers of r and are nonsingular in coordinate space, is calculated. The Gaussian potential, which serves as a prototype of these potentials, is dealt with extensively. The first Born approximation is completely inadequate to estimate the amplitude off the forward direction. We show that the amplitude decreases faster than any power law as function of the momentum transfer q, and thus in that respect is similar in behavior to that of elastic scattering of elementary particles. Essentially, the whole range of the scattering angle is covered. Some speculations concerning shrinkage and antishrinkage effects are briefly mentioned.     

Theory of inelastic atom-surface scattering: A three-dimensional treatment

Inelastic scattering of atoms by solid surfaces is treated within the first order distorted wave Born approximation. The solid is treated as a semi-infinite elastic continuum and the phonon excitations of this system are properly taken into account, including the Rayleigh waves. No restriction concerning the scattering angles (in and out) are made. In particular momentum transfers parallel to the surface are taken into account. The contribution of all these effects to the sticking coefficient are considered in detail. It turns out, that the Rayleigh phonons contribute about 25% to the local density of phonon states at the surface and roughly 50% to the sticking coefficient. The three dimensional motion of the scattered particle (in particular the transfer of parallel momentum) increases the sticking coefficient by a factor of about three as compared to one dimensional treatments.     

The microstructure of amorphous Co−P and Ni−P investigated with TEM and SAXS

The lowest order quantum corrections to the energy of a static soliton, of an easy plane spin chain, are calculated. The discreteness of the lattice of spins is shown to significantly effect the quantum corrections. However, if one uses a similar approximation to treat the spin wave dispersion relation, then the parameters which one extracts from the experimentally determined dispersion are such that the magnitude of the quantum corrections calculated in the continuum approximation are essentially exact.     

Computer simulation of proton channelling in beryllium

The channelling of protons through a thin beryllium crystal is simulated in a computer. The angular dependence of the momentum density is computed using particle trajectory approximation and is reported as the transmission spectra. In obtaining the spectra, the energy loss suffered by protons due to electron multiple scattering is considered and the effect of thermal vibrations treated separately. The spectra obtained are characteristic of the hcp structure of Be. Positions of the major dips in the transmission spectra are found to correlate well with the directions of neighbouring strings. Variations in the angle of incidence of the beam and in its initial azimuthal angle bring about modifications in the spectra depending on the transverse kinetic energy of the incident particles and the crystalline structure of Be. Thermal vibration of the lattice does not modify the spectra appreciably.     

Coulomb effects on single-particle exchange singularities

We consider the singularity in the scattering amplitude arising from the exchange of a massive neutral particle. It is shown that the presence of Coulomb distortion in the entrance or exit channel modifies the exchange pole residue. Within the framework of the Coulomb wave Born approximation the exchange pole residue is modified by an energy-dependent factor that is independent of the orbital angular momentum of the bound states involved in the exchange process. The implications of this result on the polarization observables and on recent determinations of the deuteron asymptotic D- to S-state ratio, by analytic continuation in cos θ to the neutron exchange pole, are discussed.     

Intra and inter-ionic multiphonon transitions in rare earth doped crystals

A theory has been developed for non-radiative multiphonon transitions in ionic crystals doped by RE-impurities. The degeneration of final electronic states has been taken into account in the framework of the first cumulant approximation. An analytical expression has been obtained for the rate of non-resonant energy transfer caused by electrostatic inter-ionic interaction and numerical estimations for Yb → Tm and Yb → Ho transitions in YAlO₃ and YLiF₄ crystals are listed. The intra-center multiphonon non-radiative relaxation has been considered in the case where acoustical modes of lattice vibrations are the promoting ones.     

Diffusion and the BFKL pomeron

We study the high energy behaviour of elastic scattering amplitudes within the leading logarithm approximation. In particular, we cast the amplitude in a form which allows us to study the internal dynamics of the BFKL Pomeron for general momentum transfer. We demonstrate that the momentum transfer acts as an effective infrared cut-off which ensures that the dominant contribution arises from short distance physics.     

An extraction algorithm for core‐level excitations in non‐resonant inelastic X‐ray scattering spectra

Non‐resonant inelastic X‐ray scattering of core electrons is a prominent tool for studying site‐selective, i.e. momentum‐transfer‐dependent, shallow absorption edges of liquids and samples under extreme conditions. A bottleneck of the analysis of such spectra is the appropriate subtraction of the underlying background owing to valence and core electron excitations. This background exhibits a strong momentum‐transfer dependence ranging from plasmon and particle–hole pair excitations to Compton scattering of core and valence electrons. In this work an algorithm to extract the absorption edges of interest from the superimposed background for a wide range of momentum transfers is presented and discussed for two examples, silicon and the compound silicondioxide.     

Gravitational evolution of a perturbed lattice and its fluid limit

We apply a simple linearization, well known in solid state physics, to approximate the evolution at early times of cosmological N-body simulations of gravity. In the limit that the initial perturbations, applied to an infinite perfect lattice, are at wavelengths much greater than the lattice spacing l, the evolution is exactly that of a pressureless self-gravitating fluid treated in the analogous (Lagrangian) linearization, with the Zeldovich approximation as a subclass of asymptotic solutions. Our less restricted approximation allows one to trace the evolution of the discrete distribution until the time when particles approach one another (i.e., "shell crossing"). We calculate modifications of the fluid evolution, explicitly dependent on l, i.e., discreteness effects in the N-body simulations. We note that these effects become increasingly important as the initial redshift is increased at fixed l.     

Energy exchange in atom-surface collisions

Abstract

A theoretical treatment of inelastic scattering of low energy particles from surfaces is developed which treats the regime of multiple quantum phonon exchange. Good agreement is obtained with recently measured multiphonon backgrounds in the scattering of He by alkali halide and metal surfaces over a large range of surface temperatures and incident conditions. The results show that the multiphonon scattered intensity can give important information on the particle-surface interaction potential.