Quantal description of inelastic heavy-ion scattering

A model Schrödinger equation for scattering with energy loss is discussed. The equation is linear and is closely related to the coupled-channels approach to elastic and inelastic scattering. A possible parametrization of the model for applications to heavy-ion scattering is considered.     

Isobar-hole description of pion-nucleus inelastic scattering

The Δ−h formalism is applied to a systematic study of π-nucleus inelastic scattering. In the formal part of this work, the following basic excitation mechanisms are identified in π-nucleus inelastic scattering: coupling to the transition density, coupling to convection and magnetization currents and coupling to the spin-flux tensor. The properties of these modes of coupling are discussed, in particular implications of certain symmetries of the corresponding transition amplitudes. As an application, calculations are presented for various excitations in π−¹²C scattering in the resonance region. In the comparison with the data the interplay is emphasized between the nuclear structure aspects, on the one hand, and the reaction mechanisms contained in the Δ−h formalism, on the other hand.     

Semiclassical description of scattering with internal degrees of freedom

The scattering of systems with internal degrees of freedom is studied in the semi-classical approximation. It is found that a special set of states, named coherent internal states, are specially relevant for the semi-classical treatment. A classical trajectory is defined for each coherent internal state. The semi-classical expressions obtained satisfy the superposition principle and are valid for arbitrary coupling strength.     

Resonance inelastic scattering of an x-ray photon by the xenon atom

The effect of many-particle and relativistic effects on the absolute values and the shape of the doubly differential cross section of resonance inelastic scattering of a linearly polarized x-ray photon by the free xenon atom in the energy region of the K ionization threshold is studied theoretically. The evolution of the spatially extended structure of the scattering cross section in the Kα,β structure of the x-ray emission spectrum of the xenon atom is demonstrated. The calculations were performed in the dipole approximation for the anomalous dispersion part of the total amplitude of probability of inelastic scattering and in the impulse approximation for the contact part of this amplitude. The radial relaxation of electronic shells, the spin-orbit splitting, the double excitation/ionization of the ground atomic state, as well as the Auger and radiative decays of the atomic core vacancies being formed were taken into account. In constructing the probability amplitude of the process, the relativistic effects were taken into account as a passage from the nonrelativistic Hartree-Fock wave functions to the relativistic Dirac-Hartree-Fock wave functions of the one-particle scattering states and as the passage (for the radiative transition amplitudes) to the relativistic form of the operator of the photon-atom interaction. The calculation results are predictive in character and, at the incident photon energy 34.42 keV, agree well with the results of the synchrotron experiment.     

Closed-form quantal description of inelastic heavy ion scattering

The amplitude for inelastic heavy ion scattering, given by the distorted-wave theory for excitation of low-lying collective states, is evaluated in closed form. Use is made of the Austern-Blair relation and of other approximations appropriate for strongly absorptive interaction to express the inelastic partial-wave amplitude entirely in terms of the elastic S-matrix elements in the initial and final channels. The resulting formulae display explicitly the various contributions to the transition amplitude, whose superposition gives rise to the variety of interference patterns observable in the angular distributions and excitation functions of inelastic heavy ion scattering. It is shown that, as for elastic scattering, the dominant mechanism in inelastic heavy ion collisions near and above the Coulomb barrier is diffractive scattering of Fresnel type.     

Focussed inelastic resonances in particle scattering from surfaces

Particles, such as atoms or electrons, inelastically scattered from a crystal surface in resonance with a bound state are predicted to focus around a discrete set of final angles with a defined energy for each angle. The final angle and energy of such focussed inelastic resonances (FIR) are shown to be independent of the initial state. A calculation of the FIR amplitude indicates favorable conditions for the observation of the so far elusive bound states of He on low-index metal surfaces and of image states on stepped metal surfaces.     

Many-particle effects in resonant inelastic scattering of an X-ray photon by an atom

The influence of many-particle effects on the shape and values of the double differential cross section for the resonant inelastic scattering of a linearly polarized X-ray photon by a free atom near the K and KL₂₃ ionization thresholds has been theoretically analyzed for the neon atom. The calculations have been performed using the nonrelativistic Hartree-Fock approximation for single-electron wavefunctions and the dipole approximation for the anomalous dispersion component of the cross section. The analytical structure of the contact part of the scattering cross section has been obtained beyond the dipole approximation. The effects of the radial relaxation of electron shells, spin-orbit and multiplet splitting, and configuration interaction in the doubly excited atomic states, as well as the Auger and radiative decays of the produced vacancies, are taken into account. The nature and role of the effect of correlation amplitudes, which is responsible for the appearance of the nonzero amplitudes of nonradiative transitions between intermediate and final single-electron states of the same symmetry that are obtained in different Hartree-Fock fields, have been analyzed also. The calculations are predictive and, for an incident-photon energy of 5.41 keV, agree well with experimental results for the Kα X-ray emission spectrum of the neon atom.     

Theory of inelastic scattering of slow electrons by molecules absorbed on metal surfaces

This paper presents a quantum-mechanical theory of the inelastic scattering of slow electrons by molecules adsorbed on metal surfaces. The differential cross section for vibrational excitation of one single molecule is computed.     

Equations for the description of wave scattering by multi-valued random surfaces

We consider a scattering theory for multi-valued rough surfaces which cannot be described by the conventional equation of the type z = ζ(x,y). Both Dirichlet and Neumann problems are analyzed. Starting with Green's theorem we obtain a representation of the scattered field, the surface integral equation, and the extinction theorem for such surfaces. In contrast to conventional theory, these equations contain three random functions x = x(u ₁,u ₂), y = y(u ₁,u ₂), and z = z(u ₁,u ₂), where u ₁ and u ₂ are the parameters describing the surface. We introduce two scattering amplitudes S _± for describing the scattered wave above and below the surface. The extinction theorem, if formulated in terms of S _?, allows us to determine S _? for an arbitrary multi-valued surface and after this it becomes possible to derive a simple integral equation for surface sources. Knowledge of the surface sources allows us to find S ₊ by integration.     

Effects of radial relaxation and intershell correlations during resonance inelastic photon scattering by an atom

The absolute value and shape of the double differential cross section of the resonance inelastic scattering of a linearly polarized photon in the ionization threshold energy range of the subvalence s shell of the free neon or argon atom are calculated in the nonrelativistic approximation for one-electron wavefunctions and in the dipole approximation for the anomalously dispersive scattering probability amplitude. The effects of radial relaxation, intershell correlations, bremsstrahlung, spin-orbit splitting, and a finite decay width of s vacancies are taken into account. The effects of radial relaxation and intershell correlations substantially affect the near-threshold scattering intensity: they decrease the contribution of the leading Compton anomalously dispersive component of the total cross section calculated in the one-electron approximation by several times. The calculation results have a predictive character.     

A puzzle in the inelastic scattering of atoms from surfaces

The insensitivity of helium atoms to possible inelastic scattering involving bulk phonons that terminate at the surface is explained in terms of the experimental parameters that need to be incorporated into the scattering theory.     

Elastic diffuse and inelastic electron scattering from surfaces with disordered overlayers

The elastic diffuse scattering of electrons can be used for structure analysis of disordered species on surfaces. Effective data acquisition is achieved with instruments which do not resolve between elastic diffuse scattering and inelastic scattering due to phonons. With a newly designed high resolution spectrometer it is shown that the inelastic intensity is of the same magnitude or larger than the elastic diffuse scattering. It is also shown however, that the total inelastic intensity changes little when a lattice gas of adsorbates is present on the surface, whereas the elastic diffuse intensity increases linearly with coverage. Thus instruments with low energy resolution may be used for the analysis of local structure of disordered adsorbates provided one measures the difference between the total diffuse scattering of the adsorbate covered and the clean surface.     

Fine structure of the cross section of contact inelastic scattering of an X-ray photon by an atom

The analytical structure of the double differential cross section of contact inelastic scattering of an X-ray photon by a free atom is established by the methods of the theory of irreducible tensor operators beyond impulse approximation. For the example of an Ne atom in the energy region of the ionization threshold of the 1 s shell, the existence of a fine structure of the cross section caused by transitions of electrons of the atomic core to excited states of the discrete spectrum is predicted theoretically. The results of the calculation with the effects of radial relaxation, inelastic scattering via the formation of intermediate states, and elastic Rayleigh scattering taken into account are predictive in character and, at the incident photon energy of 22 keV, are in good agreement with the results of the synchrotron experiment. Original Russian Text ? A.N. Khoperskiĭ, A.M. Nadolinskiĭ, A.S. Kasprzhitskiĭ, 2008, published in Optika i Spektroskopiya, 2008, Vol. 105, No. 1, pp. 5–10.