Correlation-polarization Potential Research Articles

Study of electron and positron elastic scattering cross-sections of astro molecule H2S

Abstract The elastic, integrated, momentum transfer, viscosity, energy-dependent, and differential cross-sections and the Sherman function for electron and positron H2S scattering are reported at impact energies ranging from 1 eV to 1 MeV. The average orientations of the polar molecule H2S are considered, and the electron and positron elastic scattering cross-sections of H2S are typically calculated using single scattering-independent atom approximation. The relativistic Dirac equation is solved using the free atom optical potential, which includes the electrostatic interaction potential, exchange potential, correlation polarization potential, and imaginary absorption potential. The present computed cross-section results are compared with the available experimental and theoretical results, and a reasonable agreement is observed.

Cross Sections of Scattering Processes in Electron-Beam Lithography

Modern models that are used to describe the processes of elastic, quasi-elastic, and inelastic scat-tering are considered. For elastic scattering, various forms of the electrostatic interaction potential, the exchange interaction potential, and the correlation-polarization potential are presented. For quasi-elastic processes, including electron-phonon and electron-polaron scattering, a model based on the theory of dielectrics and an empirical model are presented. Inelastic scattering is described based on the energy loss function, which is constructed using three different approaches.

Study of Positron Impact Scattering from Methane and Silane Using an Analytically Obtained Static Potential with Correlation Polarization

A detailed study of positron impact elastic scattering from methane and silane is carried out using a model potential consisting of static and polarization potentials. The static potential for the molecular target is obtained analytically by using accurate Gaussian molecular wavefunctions. The molecular orbitals are expressed as a linear combination of Gaussian atomic orbitals. Along with the analytically obtained static potential, a correlation polarization potential is also added to construct the model potential. Utilizing the model potential, the Schrödinger equation is solved using the partial wave phase shift analysis method, and the scattering amplitude is obtained in terms of the phase shifts. Thereafter, the differential, integrated and total cross sections are calculated. These cross-section results are compared with the previously reported measurements and theoretical calculations.

Vibrational Excitation Cross-Section by Positron Impact: A Wave-Packet Dynamics Study

The vibrational excitation cross-section of a diatomic molecule by positron impact is obtained using wave-packet propagation techniques. The dynamics study was carried on a two-dimensional potential energy surface, which couples a hydrogenlike harmonic oscillator to a positron via a spherically symmetric correlation polarization potential. The cross-section for the excitation of the first vibrational mode is in good agreement with previous reports. Our model suggests that a positron couples to the target vibration by responding instantly to an interaction potential, which depends on the target vibrational coordinate.

Electron backscattering coefficients of molybdenum and tungsten based on the Monte Carlo simulations

Monte Carlo simulation is employed for the calculation of electron backscattering coefficients of molybdenum (Mo) and tungsten (W) at normal incidence angle and at energies between 100 eV to 100 keV. For the modelling of the electron elastic scattering we have applied the partial-wave expansion method using the Mott's cross-section, where the scattering potential includes the electron electrostatic potential, exchange potential and correlation-polarization potential. A relativistic dielectric functional approach with full Penn's algorithm is adopted for the calculation of the electron inelastic cross-section. The effect of phonon excitation, the interband transition of the loosely bound valance electrons, and the inner-shells electrons excitations are considered in the energy loss functions of the materials via the optical constants. We found that our present simulated data agree well with the experimental data at energies above 20 keV for both elements while they are well above the experimental data at lower incident energies. The disagreement can be explained by the possible surface contamination of carbonaceous atomic layers exist in the measurements by additional simulation for the contaminated surfaces. Moreover, for the better and detailed understanding of the energy dependence of the backscattering coefficients, we also present the backscattered electron energy spectra, angular distributions, and depth distributions for both samples.

Positron-electron correlation-polarization potential model for positron binding in polyatomic molecules.

Positron binding energies (PBEs) of 41 polyatomic molecules were calculated using the positron-electron correlation-polarization potential (CPP) approach and compared with experimentally measured values. In this approach, the short-range positron-electron potential is modeled using the density-functional expression, whereas the long-range potential is approximated by the attractive polarization potential. The positron-electron CPP model based on local-density approximation yields larger PBEs than experimental values; however, the calculated values can be substantially improved by introducing generalized gradient approximation. We also investigated the conformational dependence of PBEs for representative molecules.

Electron-impact cross sections of X2CO (X = H, F, Cl, Br) from ionization threshold to 5 keV

Various electron-impact cross sections are obtained for halogenated derivatives of formaldehyde like H2CO, F2CO, Cl2CO, Br2CO using the Single Centre Expansion method. The molecular wavefunction of the targets are obtained from the multi-centre expansion of the Gaussian-type orbitals within the single determinant Hartree Fock self consistent field scheme. The effects due to static, correlation-polarization and exchange included to model the electron-molecule interactions are approximated by their local nature. The correlation-polarization potential includes short and long range polarization electron dynamical effects. The dipole and higher order multipole terms are considered in the multipole expansion of the target at centre of mass. The coupled scattering equations are solved using Volterra integral form to obtain the elastic cross sections. The inelastic contributions to collision process are approximated by ionization cross sections. The two cross sections are added to obtain the total cross sections from ionization threshold to 5 keV. The collision data generated from this approach are consistent with the available results. The study of scattering from homologous series has helped in proposing a simple empirical formula to estimate the total cross sections for any member of the homologous family.

A comparative study of electron-impact cross sections of C4F6 isomers from 15 to 5000 eV

Electron-impact differential, integral, and momentum transfer cross sections (CS) are computed for C4F6 isomers from 15 to 5000 eV by employing the Single Center Expansion formalism. The molecular wavefunctions of isomers are obtained using the multicenter expansion of Gaussian-type orbitals within the single determinant Hartree-Fock self-consistent field scheme. The electron-molecule interaction is modeled by summing the static, exchange, and correlation-polarization types of potentials. The exchange and correlation-polarization potentials account for the indistinguishability of incident electron and target electrons and the distortion of charge density of target by the impinging electron, respectively. The multipole expansion of the target at center of mass includes the dipole and higher order terms. The local description of potential permits us to rewrite the scattering radial equations in a simplified form. The electron impact ionization CS are obtained using the Binary-Encounter-Bethe model. The elastic and inelastic CS are summed incoherently to obtain total CS over a wide energy range. A good agreement is observed with the available data for different types of CS obtained.

Elastic scattering of electrons from the ions of argon isonuclear series

Absolute angular differential, integrated elastic and momentum transfer cross-sections for elastically scattered electrons from the ions () of argon isonuclear series, over the energy range 3.3–100 eV, are calculated employing a complex electron-ion optical potential within the framework of Dirac relativistic partial wave analysis. The cross sections are analyzed in terms of the contributions from pure Coulomb filed and the short range electron-ion complex optical potential comprising static, exchange, correlation-polarization and absorption potentials. Comparison of our calculations with the available experimental data and other theoretical calculations shows a satisfactory agreement.

Differential and Integral Cross Sections of Electron Elastic Scattering by PH3 Molecule in the Energy Ranging from 10 eV up to 20 keV

Differential and integral cross sections for electron elastic scattering by phosphine molecule at the incident energies ranging from 10 eV up to 20 keV are calculated using the well known partial wave expansion formalism. The considered interaction potential is essentially an optical spherical one including a static contribution, exchange and correlation-polarization ones. The first one is numerically calculated considering a single-center Hartree-Fock model, while two expressions of the well-known exchange potential and two others for the correlation-polarization potential are rigorously selected from the literature. The differential and integral cross sections obtained for the four potential combinations investigated in the present work, exhibit a general agreement and show clearly the role played by the exchange and correlation-polarization effects, particularly at lower scattering angles and lower impact energies. In addition, the differential and integral cross sections are compared to the experimental and theoretical results available in the literature and a good agreement is found.

Doubly differential and integral cross sections for electron elastic scattering by hydrogen chloride and hydrogen fluoride

We report theoretical doubly differential and integrated cross sections for electron elastic scattering by hydrogen chloride as well as by hydrogen fluoride over wide impact energies ranging from 10 eV up to 20 keV, where the non-relativistic theory is available. The calculations are performed by considering a target molecular state described by means of single-center molecular wave functions within the partial-wave formalism by means of a spherical optical potential model taking into account a static contribution deduced from a single-center Hartree-Fock target description as well as fine effects, like correlation-polarization and exchange contributions. The theoretical results obtained in this model pointed out clearly the role played by the exchange and correlation-polarization potentials, particularly at lower incident energies. The numerical results, obtained in this parameter free model for both doubly differential and integral cross sections for electron scattering by HCl and HF molecular targets, are compared with the available experimental data and satisfactory agreements are observed in the whole energy range.

Calculated cross sections for elastic scattering of slow positrons by silane

In this work we investigate elastic collisions of low-energy positrons with silane (${\mathrm{SiH}}_{4}$). We employed the Schwinger multichannel method to calculate integral and differential cross sections for impact energies up to 10 eV. The calculations were performed within the static plus polarization approximation. We carried out a systematic study employing different schemes to account for the polarization effects of the target due the presence of the incoming positron. We investigate how the inclusion of extra functions in different extra (chargeless) centers affects the calculated cross sections and the physical phenomena such as the Ramsauer--Townsend minimum and the virtual state formation. Our results are compared with available experimental total cross sections and with integral and differential cross sections computed with a model correlation-polarization potential. In particular, our integral cross section agrees well with the experiment at low energies and our differential cross sections agree well with the results from previous calculations.

Nuclear dynamics in a positron-CO collision using close-coupling methods

Apart from the electronic motion of the target in the molecular collision process, collision probabilities strongly depend on the dynamics of nuclear motions (rotation and vibration). Here we have studied this nuclear dynamical dependency of collision cross sections for a positron--carbon monoxide collision using rovibrational close-coupling, rotational laboratory frame close-coupling (rotational LFCC), and LFCC adiabatic nuclear vibration (LFCC-ANV) methods. Here we have computed the angle-integrated elastic and state-to-state rotational excitation, the elastic and state-to-state vibrational (summed over rotational) excitation, and the total (summed over rotational and vibrational) cross sections for the incident positron energy between 0.0 and 7.0 eV using the rovibrational close-coupling method. The rotational LFCC method is also employed to calculate elastic, (state-to-state) rotational excitation, and total cross sections. To estimate the effects of the nuclear dynamics we have calculated vibrational elastic and state-to-state vibrational excitation cross sections using the LFCC-ANV method. In these calculations the model correlation-polarization potential is used to include the correlation-polarization potential. The effect of nuclear dynamics on the collision probabilities is discussed comparing calculated total cross sections using the rovibrational close-coupling and the rotational LFCC method with other theoretical calculations and experimental results. The discussion includes comparison of the present vibrational $0\ensuremath{\rightarrow}1$ excitation process with the theoretical and measured values. The other vibrational and rotational elastic and excitation cross sections are also compared with the existing theoretical results and we have discussed the relevance of the effect of nuclear rotational and vibrational dynamics. We have also presented a comparison among the energy transfer parameters using different coupling schemes and have discussed the implications of the results.

Cross sections for electrons scattering from silver at low energies

SynopsisDifferential cross sections for scattering of electrons from silver atoms are calculated in the low energy region using the relativistic Dirac equation. The projectile target interaction is represented as sum of three local and real terms i.e. the static, a parameter free correlation polarization potential and the modified semi classical exchange potentials. We compare our results for differential cross sections with the available calculations and experimental measurements.

Positron-electron correlation-polarization potentials for the calculation of positron collisions with atoms and molecules*

We present correlation-polarization potentials for the calculation of scattering cross sections of positrons with atoms and molecules. The potentials are constructed from a short-range correlation term and a long-range polarization term. For the short-range correlation term we present four different potentials that are derived from multi-component density functionals. For the long-range polarization term we employ a multi-term expansion. Quantum scattering calculations are presented for low energy collisions of positrons with two atomic targets (argon and krypton) and two molecular targets (nitrogen and methane). For collision energies below the threshold for Positronium formation our calculations of scattering cross sections are in good agreement with recent data sets from experiments and theory.Graphical abstract

Low-energy positron scattering by pyrimidine.

This work reports elastic integral and differential cross sections for positron collisions with pyrimidine, for energies up to 20 eV. The cross sections were computed with the Schwinger multichannel method in the static plus polarization approximation. We also employed the Born closure procedure to account for the long range potential due to the permanent dipole moment of the molecule. Our results are compared with the experimental total cross section of Zecca et al. [J. Phys. B 43, 215204 (2010)], the experimental grand-total, quasi-elastic integral and differential cross section of Palihawadana et al. [Phys. Rev. A 88, 12717 (2013)]. We also compare our results with theoretical integral and differential cross sections obtained by Sanz et al. [Phys. Rev. A 88, 62704 (2013)] with the R-matrix and the independent atom model with screening-corrected additivity rule methods, and with the results computed by Franz and Gianturco [Phys. Rev. A 88, 042711 (2013)] using model correlation-polarization potentials. The agreement between the theory and the experiment is encouraging.

Low-energy positron–nitrogen-molecule scattering: A rovibrational close-coupling study

We study the positron--nitrogen-molecule scattering process under the rovibrational coupling method to include the effect of rotational and vibrational motion of the nuclei dynamically during the scattering process. Here we compute the angle integrated elastic and (state-to-state) rotational excitation, elastic and (state-to-state) vibrational (summed over rotational) excitation, and total (summed over rotational and vibrational) cross sections for the incident positron energy between 0.0 and 10 eV. However, in present paper we concentrate our discussion on the results in the lower-energy region, especially below 3.0 eV. To calculate the cross sections we use the model correlation polarization potential to include the distortion effect of the target electronic state in the presence of the positron. The calculated total cross sections are compared with the theoretical calculations and experimental results. The present theoretical results agree quite well with the recent theoretical and measured values. The vibrational and rotational elastic and excitation cross sections are also compared with the existing theoretical results. The state-to-state potential coupling and dynamical coupling effects on different cross sections are studied.

Потенціальне розсіювання електрона на атомі фосфору

Elastic scattering of electrons by phosphorus atoms within the collision energy range of 0.01– 200 eV has been studied theoretically for the first time. The integral and differential cross sections are calculated in the spin-polarized approximation for a parameter-free real optical potential. The total and spin electron densities, the electrostatic potential, and the spin exchange and correlation-polarization potentials are found for the phosphorus atom in the local spin density approximation of the density functional theory. The features of the integral cross section at energies lower than 10 eV are studied in detail in various approximations and compared with the data for neighbor sulfur, chlorine, and argon atoms. The spin exchange asymmetry in the electron scattering by the phosphorus atom with a half-filled valence 3p3 -subshell was studied with regard for the spin dependence of the exchange and polarization interactions.

Studies on the vibrational excitation differential cross sections of non-resonant e-N2 scattering using augmented polarization potentials

Distributed spherical Gaussian (DSG) correlation-polarization model potentials with higher-order terms and exact exchange effects in single-configuration Slater determinant are taken into account for low-energy vibrational excitation e-N2 scattering system. The integrodifferential coupled channel equations are solved using a combination of linear-algebraic and R-matrix-propagator algorithms. Analytic Born completion is used to calculate high-order scattering matrix elements in order to obtain convergent differential cross sections. The energy range is set to 4–15 eV which is not tested by the present theoretical method before. The overall agreement of theoretical results with the latest experiments emphasizes the importance of higher-order correlation-polarization potentials and rigorous exchange effects in vibrational excitation scattering.

Calculation of (e, 2e) triple differential cross sections of Mg in coplanar geometry

We report the results of triple differential cross section of coplanar (e, 2e) processes on Mg (3s) atom in modified distorted wave Born approximation (DWBA). The standard DWBA formalism has been modified by including the correlation-polarization potential (which is function of electron density) and post collision interaction. We compare our computed results with the available experimental data and observe that the inclusion of polarization potential in the standard DWBA is able to improve the agreement with experimental results.