Positron and electron scattering on atoms and molecules–modified effective range theory revisited

New experiments on the very low-energy electron and positron scattering allow to verify the old question on applicability of modified effective range theory (MERT). We perform it using an analytical solution of the Schrödinger equation with the long-range polarization potential. In this work two atomic (He, Ar) and molecular (H₂, CH₄) target are studied using this approach. Total cross sections were used for obtaining parameters characterizing the scattering phase shifts related to the short-range interaction potential; differential cross sections were used for comparison. Differently from previous works, we conclude that MERT with few (2-3) partial waves applies very well up to energies of few eV in all four targets studied. For positrons, reliable experimental data indicate occurrence of zeros in the s-wave phase shifts for all four targets. This should be recognized as Ramsauer-Townsend minima.     

Modified effective-range theory for low energy ${\sf e}$-N2 scattering

We analyze the low-energy e-N₂ collisions within the framework of the modified-effective range theory (MERT) for the long-range potentials, developed by O’Malley et al. [J. Math. Phys. 2, 491 (1961)]. In comparison to the traditional MERT we do not expand the total cross-section in the series of the incident momentum ?k, but instead we apply the exact analytical solutions of the Schrödinger equation for the long-range polarization potential, as proposed in the original formulation of O’Malley et al. This extends the applicability of MERT up to few eV regime, as we confirm using some simplified model potential of the electron-molecule interaction. The parameters of the effective-range expansion (i.e. the scattering length and the effective range) are determined from experimental, integral elastic cross-sections in the 0.1–1.0 eV energy range by fitting procedure. Surprisingly, our treatment predicts a shape resonance that appears slightly higher than experimentally well known resonance in the total cross-section. Agreement with the experimentally observed shape-resonance can be improved by assuming the position of the resonance in a given partial wave. Influence of the quadrupole potential on resonances is also discussed: we show that it can be disregarded for N₂. In conclusion, the modified-effective range formalism treating the long-range part of the potential in an exact way, reproduces well both the very low-energy behavior of the integral cross-section as well as the presence of resonances in the few eV range.     

Elastic and total cross-sections for electron scattering by acetylene in the intermediate energy range

We present a joint theoretical-experimental study on electron scattering by C₂H₂ in the intermediate energy range. We report calculated elastic differential, integral, and momentum-transfer as well as total (elastic + inelastic) and absorption cross-sections at impact energies ranging from 10 to 500 eV. Also, experimental absolute elastic cross-sections are reported in the (50-500)-eV energy range. A complex optical potential is used to represent the electron-molecule interaction dynamics. The iterative Schwinger variational method, combined with the distorted-wave approximation, is used to solve the scattering equations. Experimentally, the angular distributions of the scattered electrons are converted to absolute cross-sections using the relative flow technique. The comparison of our calculated with our measured results, as well as with other experimental and theoretical data available in the literature, is encouraging.Received: 26 August 2004, Published online: 5 October 2004PACS: 34.80.Bm Elastic scattering of electrons by atoms and molecules     

Elastic scattering of electrons by europium and ytterbium atoms

The method of relativistic optical potential is applied to studying elastic scattering of electrons by europium and ytterbium atoms in a wide range of collision energies up to 2 keV. The angular dependences of the scattering differential cross sections and the energy dependences of the scattering integral (total, elastic, momentum transfer, and viscosity) cross sections are calculated in both spin-polarized and spin-unpolarized approximations. It is shown that the spin-polarized approximation should be used to calculate the scattering cross sections at energies below 10 eV for a europium atom. The low-energy scattering of an electron by a europium atom is characterized by P-, D-, and F-wave shape resonances. For an ytterbium atom, the calculated cross sections are in good agreement with available experimental data and with those obtained by calculation in terms of the relativistic convergent close-coupling method.     

Streuung von 25 keV-Elektronen an Gasen

The differential cross section of neon, argon, krypton, and xenon for the elastic scattering and for the excitation of optical transitions has been measured. For neon and argon the elastic angular distribution can be described by the cross section calculated according toWentzel andLenz. For krypton and xenon there are considerable deviations from the Wentzel-Lenz cross section. In these cases it is better to calculate the elastic differential cross section from Slater eigenfunctions, from Thomas-Fermi-Dirac or from Hartree-Fock electron density distribution. The differential cross sections for the excitation of optical transitions, so far as measured here, obey for?<? _c the dipol approximation, i.e. for angles not to small the inverse square angular dependence is valid.? _c is higher for the heavier rare gases. The oscillator strengths for some transitions have been determined from the scattering measurements in satisfactory agreement with theoretical values.     

Collision between two ortho-positronium (Ps) atoms: A four-body Coulomb problem

The elastic collision between two ortho-positronium (e.g. S = 1) atoms is studied using an ab-initio static exchange model (SEM) in the centre of mass (CM) frame by considering the system as a four-body Coulomb problem where all the Coulomb interaction terms in the direct and exchange channels are treated exactly. A coupled channel methodology in momentum space is used to solve Lippman–Schwinger equation following the integral approach. A new SEM code is developed in which the Born–Oppenheimer (BO) scattering amplitude acts as input to derive the SEM amplitude adapting the partial wave analysis. The s-, p- and d-wave elastic phase shifts and the corresponding partial cross-sections for the spin alignment S = 0, i.e., singlet (+) and S = 2, i.e., triplet (?) states are studied. An augmented Born approximation is used to include the contribution of higher partial waves more accurately to determine the total/integrated elastic cross-section (σ), the quenching cross-section (σ_q) and ortho-to-para conversion ratio (σ/σ_q). The effective range theory is used to determine the scattering lengths and effective ranges in the s-wave elastic scattering. The theory includes the non-adiabatic short-range effects due to exchange.     

Elastic scattering and fusion cross-sections in 7Li + 27Al reaction

With an aim to understand the effects of breakup and transfer channels on elastic scattering and fusion cross-sections in the ⁷Li + ²⁷Al reaction, simultaneous measurement of elastic scattering angular distributions and fusion cross-sections have been carried out at various energies (E _lab?=?8.0–16.0 MeV) around the Coulomb barrier. Optical model (OM) analysis of the elastic scattering data does not show any threshold anomaly or breakup threshold anomaly behaviour in the energy dependence of the real and imaginary parts of the OM potential. Fusion cross-section at each bombarding energy is extracted from the measured α-particle evaporation energy spectra at backward angles by comparing with the statistical model prediction. Results on fusion cross-sections from the present measurements along with data from the literature have been compared with the coupled-channels predictions. Detailed coupled-channels calculations have been carried out to study the effect of coupling of breakup, inelastic and transfer, channels on elastic scattering and fusion. The effect of 1n-stripping transfer coupling was found to be significant compared to that of the projectile breakup couplings in the present system.     

Vibrational inelastic electron-H<Subscript>2</Subscript> scattering revisited: numerically converged coupled channels space frame calculations with model interactions

The collisional excitation of the lower vibrational levels of H₂(¹Σ_g⁺) molecules by low-energy electron impact is computed using an empirical model potential and by solving the coupled-channels scattering equations within a space-fixed (SF) frame of reference formulation. Numerically converged partial, integral inelastic and elastic cross-sections are obtained from what is an essentially exact treatment of the dynamics and the results are compared with measurements and with earlier calculations on the same system. The usefulness of the SF method for handling excitation processes at near-threshold collision energies is discussed and analyzed through the calculations of collisional superelastic partial cross-sections down to 10^-2 meV of collision energy.     

Analysis of intermediate energy nucleon-deuteron elastic scattering

We present a theoretical analysis of a broad range of aspects of intermediate energy nucleon-deuteron scattering. This analysis is based on a multiple scattering approach using knowledge of the deuteron's structure and nucleon-nucleon interactions. Conversely, comparison of this theory with experiment can yield information about low and intermediate energy strong interactions. The relationship of this multiple scattering type of approach to the complementary Faddeev equation approach is discussed. Our program consists of calculating the single scattering and one nucleon exchange contributions in a realistic way then parametrizing the remaining contributions as an S-wave. We argue that the largest error in this analysis is the P-wave part of the double scattering and we give estimates of its size. The single scattering integral is evaluated numerically. Coulomb effects are neglected. We derive the relativistic expressions for single scattering and nucleon exchange and discuss the approximations made, including the off-mass-shell extrapolation of the nucleon-nucleon scattering amplitude. Fits are made to experimental measurements of differential cross sections, nucleon polarizations, and total elastic cross sections. Unitarity is maintained. We tabulate the partial waves for $\text{J ?}\text{5}\text{2}$, L ? 2. They are consistent with recent Faddeev calculations. We argue that with the additional calculation of double scattering the deuteron D-state percentage can be determined to the same relative uncertainty as the differential cross section. Even without the calculation of double scattering, our results indicate a D-state percentage around 8%. In an effort to provide benchmarks for future work, we have tried to be conscientious in describing our techniques and in tabulating numerical results. Comparisons are also made with earlier analyses.     

Interaction potentials and rotational scattering for H2 and MuH with He

Elastic and inelastic differential cross-sections for the rotational scattering of p-H₂ and MuH by He at a single collision energy are calculated with potential surfaces obtained by varying the parameters in a model potential. The importance of the attractive and repulsive terms in the potential, and of the available kinetic energy in the different channels is demonstrated, and it is shown that the whole potential surface determines the scattering cross-sections. Inelastic and elastic scattering are compared, and the differences between the rotational scattering of homonuclear and heteronuclear homopolar molecules are ascribed to the molecular constants rather than to the numbers of open channels.     

Experimental study on influence of cooling on glow discharge parameters

The influence of cooling of the discharge tube walls by the liquid nitrogen on some basic parameters of the neon glow discharge positive column is studied. By probe measurements, the longitudinal electrical fieldE _z, the electron concentrationn _e and the electron temperatureT _e are determined. The equation for determination of the radial profile of the relative electron concentration is derived and, on base of experimentally obtained quantities of the radial potentialV(r), this radial profile is computed.     

The scattering of the Manning-Rosen potential with centrifugal term

In this Letter the approximately analytical scattering state solutions of the l-wave Schrödinger equation for the Manning-Rosen potential are carried out by a proper approximation to the centrifugal term. The normalized radial wave functions of l-wave scattering states are presented and the calculation formula of phase shifts is derived. It is well shown that the poles of the S-matrix in the complex energy plane correspond to bound states for real poles and scattering states for complex poles in the lower half of the energy plane. We consider and verify two special cases: the l=0 and the s-wave Hulthén potential.     

Excitation of optically forbidden transitions in argon and neon by electron impact

A radial electron monochromator and analyser system employing several new features has been used to study low energy differential inelastic electron scattering by ground state argon and neon atoms. Angular distributions for a number of optically inaccessible states are reported at energies between 30 and 100 eV and over a range of scattering angles from 0–90°. In particular, results are shown for the metastable states (³P₂, ³P₀) of argon as well as for various J levels in the parity forbidden bands (ns²np⁶ → ns²np⁵(n + 1)p) for argon and neon.     

Evaluation of the inelastic mean free path (IMFP) of electrons in polyaniline and polyacetylene samples obtained from elastic peak electron spectroscopy (EPES)

The inelastic mean free path (IMFP) of electrons was determined experimentally for selected polyaniline and polyacetylene samples with Ag and Ni references using elastic peak electron spectroscopy (EPES). The surface composition was determined by XPS and density by helium pycnometry. The high resolution hemispherical ESA-31 and ADES-400 spectrometers were used for measurements in the energy range E = 0.5–3.0 keV and E =0.4 − 1.6 keV, respectively. The integrated elastic peak intensity ratios for sample and reference were calculated using the Monte Carlo (MC) algorithm based on the electron elastic scattering cross-sections database NIST SRD64 version 3.1 and applying TPP-2M IMFPs for polymers. Surface excitation parameters (SEP) and material parameters ( _ach ) for polymers were determined, using the model of Chen, from comparison of measured and MC calculated elastic peak intensity ratios. These corrections proved to be efficient in decreasing the percentage deviations between the obtained IMFPs and the TPP-2M formula IMFPs. The elastic peak of hydrogen was observed in the EPES spectra of polymers. The experimental contribution of the hydrogen to the total elastic peak was 0.58%, while this value obtained from the MC simulations was 1.98%.      

The critical position for elastic electron scattering in neon

A measurement of the electron energy and scattering angle where the differential cross section for elastic electron scattering by neon atoms reaches its smallest value is reported. This is compared with our derivations of the critical position from seven theoretical models and from two sets of phase shifts obtained by analysis of experimental data. The latter show poor agreement with our value. The theoretical critical positions tend to lie at a lower energy and angle than our measurement, but theR-matrix calculations of Blum and Burke yield a critical position closest to it.     

Systematic trends in the transport mean free path with electron energy and atomic number

The inelastic mean free path, λ_i, and the transport mean free path, λ_tr, hold the key to understanding the effects of elastic scattering of electrons in electron spectroscopy techniques such as Auger electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS). Systematic trends in the variation of λ_tr and χ=λ_i/λ_tr with atomic number, Z, and electron energy, E, are explored using the differential elastic scattering cross-section data of Czyzewski et al. (J. Appl. Phys., 68 (1990) 3066). At low Z, λ_tr increases with energy in accord with the predictions of the Born approximation, but at higher Z, a more complex behaviour is revealed. In the first and second transition metal series, χ varies little with energy over much of the kinetic energy range probed in XPS in accord with the energy scaling ideas from the semi-classical scattering theory of Tilinin (Soviet Physics JETP, 67 (1992) 1570). In the third transition series, a pronounced minimum is found at around 200 eV, with χ for Au lower than for the corresponding transition metals. The results identify regions of the periodic table where elastic scattering effects are particularly pronounced.     

Intensities and satellites of 4ƒ-photoelectrons in thorium and uranium dioxides

In a comparison between photoelectron-spectroscopic intensities and theoretical orbital ionization cross-sections, it is found that whereas the intensities and cross-sections agree for the ratio of Th(4?) to O(1s) in ThO₂, the ratio for U(4?) to O(1s) in UO₂ differs from the theoretical ratio by 36%. It is shown that the deviation is attributable to the loss of U(4?) photoelectrons through the degradation of their kinetic energies into the tail on the high binding energy side of the spectrum. The results for ThO₂ imply a linear dependence of the inelastic scattering mean free path on kinetic energy; the results for UO₂ imply extensive configuration interaction between the 4? core-hole and unoccupied states of the cation, and they demonstrate the use of theoretical cross-sections to determine the extent.     

Elastic scattering of electrons from tetrahydrofurfuryl alcohol

Differential cross-sections (DCSs) for elastic scattering of electrons from tetrahydrofurfuryl alcohol (THFA), which can be considered as an analogue molecule to DNA sugar deoxyribose, were determined using crossed beam measurements for incident energies from 40 eV to 300 eV and scattering angles from 30° to 110°. The relative DCSs were measured both as a function of incident electron energy and scattering angle, allowing absolute calibration of the whole data set via normalization to a single point. The absolute calibration has been performed according to calculated absolute DCSs obtained by the corrected independent atom method using an improved quasifree absorption model. The calculated data-set includes DCSs and integral elastic and inelastic cross-sections in the incident energy range from 5 eV to 5000 eV. The theoretical results agree very well with the experimental ones, regarding the shape of DCSs. Moreover, the same theoretical procedure has been used to obtain DCSs for elastic electron scattering from a simpler deoxyribose analogue tetrahydrofuran (THF), which agree very well, both in shape and on the absolute scale, with the recent experimentally obtained absolute DCSs [A.R. Milosavljević et al., Eur. Phys. J. D 35, 411 (2005)]. The present results are also compared with the recent theoretical data for THF and THFA. Finally, according to both experimental and theoretical data, the DCSs for elastic electron scattering from THFA and THF molecules appear to be very similar both in shape and absolute scale.     

Calculations of inelastic cross sections for rotational excitation

Cross sections for scattering of N₂ (j=0) molecules on He atoms have been calculated for relative energies below 5 · 10^?3 eV (58 °K). The time independent scattering formalism ofArthurs andDalgarno was used together with an assumed Lennard-Jones type potential with anisotropicP ₂(cos?) terms in the attractive and repulsive parts. The resulting system of coupled differential equations was solved in the distorted wave and close coupling approximations for the differential and integral cross sections for elastic and inelastic (j=0→j=2) scattering. In the integral inelastic cross section several sharp resonances were found to contribute 40% to the cross section at energies below 40 °K. The resonance peaks are attributed to orbiting or short-lived compound states since they are also observed in the elastic cross section at energies which are lower by the excitation energy of 1.5 · 10^?3 eV. Finally, the effect of varying the potential parameters on the integral inelastic cross section was studied at 50 °K and a rough formula for the cross section as a function of the parameters is obtained. The formula shows that a certain ratio of repulsive and attractive anisotropies leads to a small inelastic cross section indicating a mutual cancellation.