Optical Potential Method Research Articles

Study of electron impact inelastic scattering of chlorine molecule (Cl2)

A theoretical study is carried out for electron interactions with the chlorine molecule (Cl2) for incident energies ranging from 0.01 to 5000 eV. This wide range of energy has allowed us to investigate a variety of processes and report data on symmetric excitation energies, dissociative electron attachment (DEA), total excitation cross sections, and ionization cross section (Qion) along with total inelastic cross sections (Qinel). The present study is important since Cl2 is a prominent gas for plasma etching and its anionic atoms are important in the etching of semiconductor wafers. In order to compute the total inelastic cross sections, we have employed the ab initio R-matrix method (0.01 to 15 eV) together with the spherical complex optical potential method (∼15 to 5000 eV). The R-matrix calculations are performed using a close coupling method, and we have used DEA estimator via Quantemol-N to calculate the DEA fragmentation and cross sections. The present study finds overall good agreement with the available experimental data. Total excitation and inelastic cross sections of scattering for a wide energy range (0.01 to 5 keV) are reported for the first time, to the best of our knowledge.

Positron scattering studies of different inelastic channels for group IIA elements

This article reports the study of various inelastic channels such as positronium formation and ionization for positron scattering from group IIA elements. Modified spherical complex optical potential method developed by our group is employed for the present calculations for an extensive energy range from positronium formation threshold to 5 keV. Furthermore, a modified absorption threshold is introduced, which is utilized for targets having ionization threshold <6.8 eV. Comparison with existing data shows overall good agreement. Due to limited cross section studies on present targets, most of the results presented in this article have been reported for the first time.

Absolute cross section measurements for the scattering of low- and intermediate-energy electrons from PF3. I. Elastic scattering.

We report absolute elastic differential cross sections (DCSs) for electron collisions with phosphorus trifluoride, PF3, molecules (e- + PF3) in the impact energy range of 2.0-200 eV and over a scattering angle range of 10°-150°. Measured angular distributions of scattered electron intensities were normalized by reference to the elastic DCSs of He. Corresponding integral and momentum-transfer cross sections were derived by extrapolating the angular range from 0° to 180° with the help of a modified phase-shift analysis. In addition, due to the large dipole moment of the considered molecule, the dipole-Born correction for the forward scattering angles has also been applied. As a part of this study, independent atom model calculations in combination with screening corrected additivity rule were also performed for elastic and inelastic (electronic excitation plus ionization) scattering using a complex optical potential method. Rotational excitation cross sections have been estimated with a dipole-Born approximation procedure. Vibrational excitations are not considered in this calculation. Theoretical data, at the differential and integral levels, were found to reasonably agree with the present experimental results. Furthermore, we explore the systematics of the elastic DCSs for the four-atomic trifluoride molecules of XF3 (X = B, N, and P) and central P-atom in PF3, showing that, owing to the comparatively small effect of the F-atoms, the present angular distributions of elastic DCSs are essentially dominated by the characteristic of the central P-atom at lower impact energies. Finally, these quantitative results for e- - PF3 collisions were compiled together with the previous data available in the literature in order to obtain a cross section dataset for modeling purposes. To comprehensively describe such a considerable amount of data, we proceed by first discussing, in this paper, the vibrationally elastic scattering processes whereas vibrational and electronic excitation shall be the subject of our following paper devoted to inelastic collisions.

Elastic electron scattering by the CF3 radical in the 1–1000 eV energy range

Elastic scattering of electrons by a CF3 radical has been studied theoretically in a wide energy range of 1–1000 eV in the framework of an independent-atom model (IAM). The optical potential method is used for calculating the electron scattering amplitudes of the different atoms of the target molecule. The differential and integral cross sections are calculated for equilibrium internuclear distances of the ground state of the CF3 radical in two approaches—IAM and additivity rule (IAM-AR) approximations. The calculated cross sections are compared with the experimental data for e + CF3 and e + CF3H scattering and with other theoretical results. It is justified that the IAM performs slightly better for the differential cross sections, while the simpler IAM-AR approximation describes the integral cross sections better.

Cross sections for electron collision with difluoroacetylene

We report a detailed calculation of total elastic, differential elastic, momentum transfer and electronic excitation for electron impact on difluoroacetylene (C2F2) molecules using the R-matrix method at low energies. After testing many target models, the final results are reported for the target model that gave the best target properties and predicted the lowest value of the shape resonance. The shape resonance is detected at 5.86 eV and 6.49 eV with the close-coupling and static exchange models due to 2Πg (2B2g, 2B3g) states. We observed that the effect of polarization becomes prominent at low energies below 4 eV, decreasing the magnitude of the elastic cross section systematically as it increases for C2F2. We have also computed elastic cross sections for C2H2, C2F4 and C2H4 with a similar model and compared with the experimental data for these molecules along with C2F2. General agreement is found in terms of the shape and nature of the cross section. Such a comparison shows the reliability of the present method for obtaining the cross section for C2F2. The calculation of elastic scattering cross section is extended to higher energies up to 5 keV using the spherical complex optical potential method. The two methods are found to be consistent, merging at around 12 eV for the elastic scattering cross section. Finally we report the total ionization cross section using the binary encounter Bethe method for C2F2. The perfluorination effect in the shape and magnitude of the elastic, momentum transfer and ionization cross sections when compared with C2H2 showed a similar trend to that in the C2H4–C2F4 and C6H6–C6F6 systems. The cross-section data reported in this article could be an important input for the development of a C2F2 plasma model for selective etching of Si/SiO2 in the semiconductor industry.

Scattering of electrons with formyl radical

ABSTRACTA detailed theoretical study is carried out for electron interactions with formyl radical (HCO) with incident energies ranging from 0.01 to 5000 eV. This wide range of energy has allowed us to investigate a variety of processes and report data on vertical electronic excitation energies, dissociative electron attachment (DEA) and total cross-section along with scattering rate coefficients. We observed Ramsaur–Townsend minimum at 0.59 and 0.74 eV using DZP and cc-pDVZ basis sets, respectively. HCO has large number of low-lying excited states and the present study finds an overall good agreement with earlier reported data. In order to compute total cross-section, we have employed ab initio R-matrix method (0.01 to ∼ 20 eV) and the spherical complex optical potential method (∼ 10 to 5000 eV) employing static-exchange plus polarisation potential. The R-matrix calculations are performed using a close coupling method with the aid of 21 target states, 1191 configuration state functions and 195 channels. The DEA cross-sections of fragmentation of H−, excitation cross- sections and scattering rate coefficients are reported for the first time. Total cross section presented here will provide a reference data set over an extensive impact energy range.

Calculation of total and ionization cross sections for electron scattering by primary benzene compounds.

The total and ionization cross sections for electron scattering by benzene, halobenzenes, toluene, aniline, and phenol are reported over a wide energy domain. The multi-scattering centre spherical complex optical potential method has been employed to find the total elastic and inelastic cross sections. The total ionization cross section is estimated from total inelastic cross section using the complex scattering potential-ionization contribution method. In the present article, the first theoretical calculations for electron impact total and ionization cross section have been performed for most of the targets having numerous practical applications. A reasonable agreement is obtained compared to existing experimental observations for all the targets reported here, especially for the total cross section.

Induced chemistry by scattering of electrons from magnesium oxide

A detailed theoretical study is carried out for electron interactions with magnesium oxide (MgO) with incident energies ranging from 0.01 to 5000 eV. This wide range of energy has allowed us to investigate a variety of processes and report data on resonances through eigenphase study, vertical electronic excitation energies, differential, momentum transfer, and total cross sections (TCS), as well as scattering rate coefficients. MgO has a large number of low-lying π excited states and the present study finds overall a good agreement with earlier reported data. In order to compute total cross sections, we have employed the ab initio R-matrix method (0.01 to ∼20 eV) and the spherical complex optical potential method (∼20 to 5000 eV). The R-matrix calculations are performed using a close-coupling method with the aid of 34 target states, 1436 configuration state functions, and 213 channels employing a static exchange plus polarization model. The present study reports evidence for electron scattering resonances through analysis of eigenphase diagrams at low energies below the ionization threshold. In the absence of any theoretical or experimental data for resonances, we have done double differentiation of TCS to confirm the resonances reported here. The present study is a maiden effort to report excitation cross sections, differential cross sections, momentum transfer cross sections, and scattering rate coefficients at low energies below the ionization threshold of the target. Additionally, in the absence of any experimental data and sparse theoretical data for a total elastic cross section, the present comprehensive study will provide a reference data set over such an extensive impact energy range.

Positronium formation for positron scattering from helium ion

Positronium (Ps) formation processes from helium ions by positron impact are studied using the two-channel two-center eikonal final state–continuum initial distorted wave method. The Ps(n = 1 and 2) and total Ps formation cross sections are calculated from the threshold to the high energy region, and the results are compared with other theoretical calculations available in the literature. It is found that the present results agree reasonably well with the close-coupling calculations, while other predictions, such as the Coulomb–Born approximation, the optical potential method, and the recent classical trajectory Monte Carlo method (Naginey 2014 Phys. Rev. A 89, 062704), are all much higher in the entire energy region. The maximum positions of the Ps(n) formation cross sections in our present work are in good agreement with the wave vector matching model of (Charlton 2014 J. Phys. B: At. Mol. Opt. Phys. 39, 4575). Finally, we discuss the scaling law of the Ps(n) formation cross sections with respect to the principal quantum number n of the Ps atom.

Optical potentialmethod for electron scattering by molecule

Метод релятивістського оптичного потенціалу запропоновано для вивчення потенціального розсіювання електрона молекулою у рамках моделі незалежних атомів. Для узгодженого опису процесу розсіювання електрона на атомах молекули, потенціали взаємодії і характеристики атомів визначено в локальному наближенні стаціонарної, з виключенням енергії самодії електронів, та нестаціонарної теорії функціоналу густини з урахуванням релятивістських ефектів.

Electron impact ionization cross sections of atoms

In this article, we report the electron impact ionization cross sections for atoms Si, P, S, Sc, Cr, Mn, Co, Zn, Ga, Ge, Nb, Rh, and Cd, having applications in different areas of applied science and technology. The energy regime for the calculation is from the ionization threshold of the target to 2000 eV. We have employed the spherical complex optical potential method to calculate inelastic cross sections. A semiempirical complex scattering potential ionization contribution method is then used to estimate the ionization cross section from the inelastic cross section. In general, good agreement between the present results with available theoretical datasets and measurements are observed. The prime focus of this study was to investigate electron impact ionization phenomena in less studied targets. The results obtained are found to be quite encouraging. The values presented here are reasonable estimates of cross section for all the atoms studied.

Radiative charge transfer in cold and ultracold sulphur atoms colliding with protons

Radiative decay processes at cold and ultra cold temperatures for sulfur atoms colliding with protons are investigated. The MOLPRO quantum chemistry suite of codes was used to obtain accurate potential energies and transition dipole moments, as a function of internuclear distance, between low-lying states of the SH+ molecular cation. A multi-reference configuration-interaction approximation together with the Davidson correction is used to determine the potential energy curves and transition dipole moments, between the states of interest, where the molecular orbitals are obtained from state-averaged multi-configuration-self-consistent field calculations. The collision problem is solved approximately using an optical potential method to obtain radiative loss, and a fully two-channel quantum approach for radiative charge transfer. Cross sections and rate coefficients are determined for the first time for temperatures ranging from 10 μK up to 10 000 K. Results are obtained for all isotopes of sulfur, colliding with H+ and D+ ions and comparison is made to a number of other collision systems.

Elastic differential cross sections for C₄F₆ isomers in the 1.5-200 eV energy electron impact: similarities with six fluorine containing molecules and evidence of F-atom like scattering.

We report absolute elastic differential cross sections for electron interactions with the C4F6 isomers, hexafluoro-1,3-butadiene (1,3-C4F6), hexafluoro-2-butyne (2-C4F6), and hexafluorocyclobutene (c-C4F6). The incident electron energy range is 1.5-200 eV, and the scattered electron angular range for the differential measurements varies from 15° to 150°. In all cases the absolute scale of the differential cross section was set using the relative flow technique, with helium as the reference species. Atomic-like behaviour in these scattering systems is shown here for the first time, and is further investigated by comparing the elastic cross sections for the C4F6 isomers with other fluorinated molecules, such as SF6 and CnF6 (n = 2, 3, and 6). We note that for all the six-F containing molecules, the scattering process for electron energies above 30 eV is indistinguishable. Finally, we report results for calculations of elastic differential cross sections for electron scattering from each of these isomers, within an optical potential method and assuming a screened corrected independent atom representation. The level of agreement between these calculations and our measurements is found to be quite remarkable in all cases.

Electron-impact scattering by arsine

We present elastic cross sections for electron interactions with arsine (${\mathrm{AsH}}_{3}$) in gas phase over an extensive energy range from 0.5 to 5000 eV by combining two computational methods. The ab initio R-matrix method is employed for low-energy computations up to 15 eV and the intermediate to high-energy calculations were performed using the spherical complex optical potential (SCOP) method. The elastic cross section computed through the $R$ matrix and SCOP formalism shows consistency at crossover energy (11--12 eV) and gives reasonable accord with the available data. Besides elastic cross sections, the differential cross section at low and intermediate incident electron energies is reported. The electronic excitation cross section is also reported at low energies. Shape resonance is observed at around 2.4 eV due to the formation of a transient negative ion state.

Cold ion-atom chemistry driven by spontaneous radiative relaxation: a case study for the formation of the YbCa+ molecular ion

Using both quantum and semi-classical methods, we calculate the rates for radiative association and charge transfer in cold collisions of Yb+ with Ca. We demonstrate the fidelity of the local optical potential method in predictions for the total radiative relaxation rates. We find a large variation in the isotope dependence of the cross sections at ultra-cold gas temperatures. However, at cold temperatures, 1 mK < T < 1 K, the effective spontaneous radiative rates for the different isotopes share a common value of about 1.5 × 10−15 cm3 s−1. It is about five orders of magnitude smaller than the chemical reaction rate measured in Rellergert et al (2011 Phys. Rev. Lett. 107 243201).

Positronium formation in the noble gases

We present results based upon our ab initio relativistic optical potential method for the simulation of positronium formation in the noble gases neon, argon, krypton and xenon. The method used in this simulation is based upon an approach, first suggested by Reid and Wadehra, whereby the ionization threshold of the atom is effectively reduced by 6.8 eV, the binding energy of positronium in its ground state. This procedure is then modified in order to account for the fact that positronium formation cross sections tend to zero much more rapidly than the corresponding direct ionization cross sections as the energy of the incident positron increases. The agreement of our positronium formation cross sections with experiment is quite good for argon, krypton and xenon over most of the energy region while for neon our cross sections are generally too small at all energies. Nonetheless, our method predicts positronium formation cross sections in better agreement with experiment than the much more sophisticated theoretical approaches used in the past. We also show that adding positronium formation in this way improves agreement with the measured elastic differential cross section at small scattering angles.

Computation of electron-impact rotationally elastic total cross sections for methanol over an extensive range of impact energy (0.1 – 2000 eV)

Theoretical rotationally elastic total cross sections for electron scattering from methanol over the incident energy range 0.1--2000 eV are presented. The computation of such cross sections for methanol is reported over such an extended energy range. We have employed two distinct formalisms to compute the cross sections across this energy range; between 0.1 eV and the ionization threshold of the target we have used the ab initio R-matrix method, while at higher energies the spherical complex optical potential method is invoked. The results from both formalisms match quite well at energies where they overlap and hence imply that they are consistent with each other. These total cross-section results are also in very good agreement with available experimental data and earlier theoretical data. The composite methodology employed here is well established and can be used to predict cross sections for other targets where data is scarce or not available.

Unnatural parity resonances in the positron-excited hydrogen system

We present an investigation of resonances with unnatural parities in positron scattering by excited hydrogen. The momentum space coupled channels optical potential method has been used. Positronium formation channels have been included via a complex equivalent local potential. States with angular momenta L = 1 to L = 2 and parity (−1)L+1 are calculated.

Electron scattering cross sections from HCN over a broad energy range (0.1–10 000 eV): Influence of the permanent dipole moment on the scattering process

We report theoretical integral and differential cross sections for electron scattering from hydrogen cyanide derived from two ab initio scattering potential methods. For low energies (0.1-100 eV), we have used the symmetry adapted-single centre expansion method using a multichannel scattering formulation of the problem. For intermediate and high energies (10-10,000 eV), we have applied an optical potential method based on a screening corrected independent atom representation. Since HCN is a strong polar molecule, further dipole-induced excitations have been calculated in the framework of the first Born approximation and employing a transformation to a space-fixed reference frame of the calculated K-matrix elements. Results are compared with experimental data available in the literature and a complete set of recommended integral elastic, inelastic, and total scattering cross sections is provided from 0.1 to 10,000 eV.

Refined theoretical study of radiative association: Cross sections and rate constants for the formation of SiN

Radiative association of silicon mononitride (SiN) in its two lowest molecular electronic states is studied through quantum and classical dynamics. Special attention is paid to the behavior of the cross section at high collision energies. A modified expression for the semiclassical cross section is presented which excludes transitions to continuum states. This gives improved agreement with quantum mechanical perturbation theory at high energies. The high energy cross section is overestimated if conventional semiclassical theory is used. The modified semiclassical theory should be valid in general for radiative association transitions from an upper to a lower electronic state. We also implement a quantum dynamical optical potential method with the same type of modification. The rate coefficient is calculated using Breit-Wigner theory and the modified semiclassical formula for the resonance and direct contributions, respectively, for temperatures from 10 K to 20,000 K. A rapid decrease in the rate constant for formation of ground state SiN is observed above 2000 K which was not seen previously.