Non-physical consequences of the Muffin-tin-type intra-molecular potential

We demonstrate using a simple model that in the frame of muffin-tin - like potential non-physical peculiarities appear in molecular photoionization cross-sections that are a consequence of jumps in the potential and its first derivative at some radius. The magnitude of non-physical effects is of the same order as the physical oscillations in the cross-section of a two-atomic molecule. The role of the size of these jumps is illustrated by choosing three values of it. The results obtained are connected to the studied previously effect of non-analytical behavior as a function of r the potential V(r)acting upon a particle on its photoionization cross-section. In reality, such potential has to be analytic in magnitude and first derivative function in distance. Introduction of non-analytic features in model potential leads to non-physical features in the corresponding cross-section - oscillations, additional maxima etc.Comment: 11 pages, 5 figure

Interference Phenomenon in Electron-Molecule Collisions

This article discusses how the pattern of elastic scattering of an electron on a pair of identical atomic centers is modified if we abandon the assumption, standard in molecular physics, that outside of some molecular sphere surrounding the centers, the wave function of the molecular continuum is atomic-like, being a linear combination of the regular and irregular solutions of the wave equation. For this purpose, the elastic scattering of slow particles by a pair of non- overlapping short-range potentials has been studied. The continuum wave function of the particle is represented as a combination of a plane wave and two spherical s-waves propagating freely throughout space. The asymptotic behavior of this function determines the amplitude of elastic particle scattering in closed form. It is demonstrated that this amplitude can be represented as a partial expansion in a set of the orthonormal functions Zλ(r) other than spherical harmonics Ylm(r). General formulas for these functions are obtained. The coefficients of the scattering amplitude expansion into a series of functions Zλ(r) and determine the scattering phases ηλ(k) for the considered two- atomic target. The special features of the S-matrix method for the case of arbitrary non-spherical potentials are discussed

Huygens–Fresnel picture for electron-molecule elastic scattering

The elastic scattering cross sections for a slow electron by C2 and H2 molecules have been calculated within the framework of the non-overlapping atomic potential model. For the amplitudes of the multiple electron scattering by a target the wave function of the molecular continuum is represented as a combination of a plane wave and two spherical waves generated by the centers of atomic spheres. This wave function obeys the Huygens–Fresnel principle according to which the electron wave scattering by a system of two centers is accompanied by generation of two spherical waves; their interaction creates a diffraction pattern far from the target. Each of the Huygens waves, in turn, is a superposition of the partial spherical waves with different orbital angular momenta l and their projections m. The amplitudes of these partial waves are defined by the corresponding phases of electron elastic scattering by an isolated atomic potential. In numerical calculations the s- and p-phase shifts are taken into account. So the number of interfering electron waves is equal to eight: two of which are the s-type waves and the remaining six waves are of the p-type with different m values. The calculation of the scattering amplitudes in closed form (rather than in the form of S-matrix expansion) is reduced to solving a system of eight inhomogeneous algebraic equations. The differential and total cross sections of electron scattering by fixed-in-space molecules and randomly oriented ones have been calculated as well. We conclude by discussing the special features of the S-matrix method for the case of arbitrary non-spherical potentials

Electronic quantum confinement in cylindrical potential well

The effects of quantum confinement on the momentum distribution of electrons confined within a cylindrical potential well have been analyzed. The motivation is to understand specific features of the momentum distribution of electrons when the electron behavior is completely controlled by the parameters of a non-isotropic potential cavity. It is shown that studying the solutions of the wave equation for an electron confined in a cylindrical potential well offers the possibility to analyze the confinement behavior of an electron executing one- or two-dimensional motion in the three-dimensional space within the framework of the same mathematical model. Some low-lying electronic states with different symmetries have been considered and the corresponding wave functions have been calculated; the behavior of their nodes and their peak positions with respect to the parameters of the cylindrical well has been analyzed. Additionally, the momentum distributions of electrons in these states have been calculated. The limiting cases of the ratio of the cylinder length H and its radius R0 have been considered; when the cylinder length H significantly exceeds its radius R0 and when the cylinder radius is much greater than its length. The cylindrical quantum confinement effects on the momentum distribution of electrons in these potential wells have been analyzed. The possible application of the results obtained here for the description of the general features in the behavior of electrons in nanowires with metallic type of conductivity (or nanotubes) and ultrathin epitaxial films (or graphene sheets) are discussed. Possible experiments are suggested where the quantum confinement can be manifested

Partial time delays in elastic electron scattering by rectangular potential well with arising discrete levels

We have studied the time delays of slow electrons scattered by a rectangular in spherical coordinates potential well as function of the well parameters. We have shown that electron interaction with the scattering center qualitatively depends on the presence of discrete levels in the well. While electron retention by the scattering center dominates for the potential well with no discrete levels, the appearance of a level leads to an opposite situation where the incident electron hardly enters the scatterer. Such a behavior of the time delay is universal since it is found not only for the first s-level but also for the subsequent arising s-, p-, and d-levels

Strong correlation effects in atomic photoelectron angular distributions far above thresholds

We scrutinize individual interchannel coupling effects on atomic dipole and nondipole [Formula Presented] photoelectron angular distribution parameters of valence electrons far above thresholds, choosing [Formula Presented] photoionization of N and Ne in the photon energy range from 1 to 10 keV as case studies. It is found that individual correlation effects are strong far above thresholds. However, a cancellation effect is also discovered that largely obviates the net correlation effect on photoelectron angular distributions. It is shown that the cancellation can be removed, i.e., strong correlation effects can be observed, by considering core-ionized (core-excited) initial states; this is expected to be quite general. The importance of this work is that it shows that the tacit belief in the insignificance of correlation in nondipole parameters far above thresholds is quite misleading. In addition, it suggests studies of core-ionized or core-excited atoms as a means of exploring these large correlation effects in nondipole photoelectron angular distributions far above thresholds. © 2001 The American Physical Society

Theory of inner-shell photoionization of fixed-in-space molecules

A theory of deep-subshell photoionization of atoms confined in fixed-in-space molecules is presented. The theory is a good approximation near the photoionization thresholds where the formulas derived are exact expressions within the framework of a non-overlapping central atomic-potential model

Inner-shell near-threshold photoionization of A @ C60 endohedral atoms

Calculations were performed to provide insight into both differential and total photoionization cross sections of endohedral atoms with particular emphasis on confinement and molecular resonances in these cross-sections. Low-energy inner-shell photoelectron angular distribution spectra for at-the-center endohedral atoms were found to be identical in shape to those for free atoms, but as the photoelectron energy increases, the similarity disappears. In addition, for low-energy spectra, this similarity was explained physically and, thus, a justification for the use of empirically adjusted spherical model potentials to represent the role of the confinement in photoionization of endohedral atoms was presented

Huygens–Fresnel picture for electron-molecule elastic scattering

The elastic scattering cross sections for a slow electron by C2 and H2 molecules have been calculated within the framework of the non-overlapping atomic potential model. For the amplitudes of the multiple electron scattering by a target the wave function of the molecular continuum is represented as a combination of a plane wave and two spherical waves generated by the centers of atomic spheres. This wave function obeys the Huygens–Fresnel principle according to which the electron wave scattering by a system of two centers is accompanied by generation of two spherical waves; their interaction creates a diffraction pattern far from the target. Each of the Huygens waves, in turn, is a superposition of the partial spherical waves with different orbital angular momenta l and their projections m. The amplitudes of these partial waves are defined by the corresponding phases of electron elastic scattering by an isolated atomic potential. In numerical calculations the s- and p-phase shifts are taken into account. So the number of interfering electron waves is equal to eight: two of which are the s-type waves and the remaining six waves are of the p-type with different m values. The calculation of the scattering amplitudes in closed form (rather than in the form of S-matrix expansion) is reduced to solving a system of eight inhomogeneous algebraic equations. The differential and total cross sections of electron scattering by fixed-in-space molecules and randomly oriented ones have been calculated as well. We conclude by discussing the special features of the S-matrix method for the case of arbitrary non-spherical potentials