Elastic Integral Cross Sections Research Articles

Integral Electron Scattering Cross Sections from N2O for Impact Energies Ranging from 1 to 1000 eV.

Accurate total cross sections (TCS), within 5%, for electron scattering by N2O molecules have been measured with a magnetically confined electron transmission apparatus for impact energies ranging from 1 to 200 eV. For higher energies, these measurements have been complemented with our independent atom-based screening corrected additivity rule, including interference (IAM-SCAR + I) method to determine a complete reference TCS data set in the energy range (1-1000 eV). After a critical discussion that includes our calculated integral elastic and ionization cross sections and the theoretical and experimental data available in the literature, a complete set of integral elastic and inelastic (rotational, vibrational, and electronic excitation, ionization and electron attachment) cross sections, consistent with the reference TCS data, have been derived. This update on the N2O collisional database may help to improve the accuracy of radiation-induced transport models.

Positron scattering from structurally related biomolecules.

We report the integral elastic, momentum transfer, and inelastic (positronium formation and ionisation) cross sections for positron scattering from structurally related molecules. The molecules chosen for the current investigation are formamide, formylphosphine, formic acid, N-methylformamide, acetone, acetic acid, and formaldehyde. The cross sections were calculated using the optical potential approach and the complex scattering potential-ionisation contribution method for impact energies between 1 and 5 keV. A sizable repository of data is now available for positron scattering from various atoms and molecules; however, data on the impact of positrons on current targets is still scarce and fragmented. While most cross sections are the first of their kind, we analyze our total cross sections (TCSs) with the previous literature available, which has become attractive to researchers trying to model the tracks of charged particles in matter. TCSs have recently seen a resurgence in popularity thanks to their utility in specifying the mean-free path between the collisions of such simulations. We find good qualitative convergence between experimental and theoretical results below and above the positronium formation threshold. However, around the threshold region, a significant discrepancy is encountered, which can be accounted for due to the experiment's lack of forward angle scattering effect discrimination. This level of agreement evolves to become quantitative at intermediate and higher energies.

Theoretical investigations of positron collisions with phosphorus-containing compounds

A theoretical investigation of positron scattering from phosphorus-containing compounds (viz., PH3, P2H4, PCl3, PF3, PBr3, POF3, POCl3, and H2PO4) is reported in this article. The quantum mechanical potential scattering approach is utilized to calculate integral elastic, excitation, momentum transfer, direct ionization, positronium formation, total ionization, inelastic, differential, and total cross sections on a fine energy grid from 1 to 5000 eV. The ionization contribution in the inelastic scattering is estimated using the complex scattering potential-ionization contribution technique. Prior research on positron collisions with these targets is scarce; as a result, the purpose of this study is to make up, at least in part, for this deficiency in cross-section data. In addition to being pertinent to positron transport analyses, such as Monte Carlo methods, the current results should be useful to benchmark the accuracy and validity of positron molecule collision computations and, more significantly, to compare these calculations with related electron scattering outcomes. Furthermore, the calculated cross sections of PH3 are compared with NH3 and other phosphorus-containing compounds. The analysis makes it abundantly evident that the atoms on the periphery of a molecule have a substantially larger impact on the scattering process than the central atom. To analyze the scattering dynamics of positrons and their anti-particle electrons, a comparative study of cross sections of H2PO4 and H2SO4 is also presented. For most of these targets, positron calculations are carried out for the first time.

Electron Scattering from Methyl Formate (HCOOCH3): A Joint Theoretical and Experimental Study.

Elastic low-energy electron collisions with methyl formate have been studied theoretically at the level of various theories. The elastic integral cross section was calculated using Schwinger multichannel and R-matrix methods, in the static-exchange and static-exchange plus polarization levels of approximations for energies up to 15 eV. The absolute total cross section for electron scattering from methyl formate has been measured in a wide energy range (0.2-300 eV) using a 127° electron spectrometer working in the linear transmission configuration. The integral elastic and the absolute total cross sections display a π* shape resonance at around 1.70-1.84 eV, which can be related to the resonance visible for formic acid, and a broad structure located at 7-8 eV, which can be associated to a superposition of σ* shape resonances. Our results were compared with theoretical and experimental results available in the literature and with the results of electron collisions with formic acid. The additivity rule was used to estimate the total cross section of methyl formate and the results agree well with the experimental data.

Low-Energy Electron and Positron Scattering by para-Difluorobenzene.

The Schwinger multichannel method is employed in calculations of the elastic integral and differential cross sections for collisions of low-energy electrons and positrons with para-difluorobenzene (1,4-C6H4F2). The present calculations involving electron scattering have been performed using both static-exchange and static-exchange plus polarization levels of approximation. Our results indicate the presence of three resonances of π*-character in the low-energy region and a fourth resonance, of σ*-character, at higher energy levels. With respect to the positron scattering, the calculations were conducted using the static plus polarization approximation at three different polarization levels. The present calculated electron and positron cross sections show a reasonable agreement with the total cross sections measured by Makochekanwa et al. (J. Phys. B, 2004, 37, 1841). It is also important to highlight that our computed integral cross section for electron scattering indicates the presence of a Ramsauer-Townsend minimum, while the integral cross section for positron scattering indicates the presence of a virtual state.

Combined experimental and theoretical study on the elastic electron scattering cross sections of ethanol

Combined theoretical and experimental studies on the elastic scattering of electrons on ethanol were performed in the energy range of 30–800 eV. The differential elastic electron scattering cross sections (DCS) of ethanol were measured for scattering angles of 30° to 150° using the relative flow technique and nitrogen (N2) as the reference gas. From these experimental DCS, integral elastic and momentum transfer cross sections were estimated. The comparison of the experimental results from the present work to those of other groups showed good agreement within the experimental uncertainty. In addition to the experimental determination, the DCS of ethanol were calculated by applying the independent atomic model with screening-corrected additivity rule and the modified independent atomic model. These theoretical calculations reproduced the experimental data well within the experimental uncertainty, with agreement better at high electron energies as was expected.Graphical abstract

Theoretical study of low-energy electron collision with normal-pentane using R-matrix method

Low-energy electron collisions with normal-pentane (n-C5H12) that initiate the plasma to assist combustion are critical in understanding the underlying physics and chemistries. In the present work, we studied this collisional process using the R-matrix method at the static-exchange plus polarization and close-coupling model levels. The scattering calculation was performed by running the UKRmol+ code using the Quantemol Electron Collision interface to obtain elastic differential, momentum transfer, integral, and electronic excitation cross sections up to 20 eV and ionization cross sections up to 1000 eV. Our computed cross-section data are in better agreement with the available experimental results both regarding the magnitude and shape. We also demonstrated the importance of using a diffuse basis set in describing the scattering due to the Rydberg nature of the lowest unoccupied molecular orbitals of n-C5H12.

Low-Energy Positron Scattering by Pyridine and Aniline.

Calculated differential and integral cross sections for elastic scattering of low-energy positrons by pyridine and aniline are presented here. The cross sections were obtained using the Schwinger multichannel method in the static-plus polarization approximation, and the Born closure procedure was employed to account for the long-range potential due to the permanent dipole moment of the molecule. The elastic integral cross sections are compared with available theoretical and experimental data for the same molecules finding an overall good agreement. The present results are also compared with available calculated cross sections for the close-related molecules benzene and pyrimidine, where an overall similar angular behavior of the differential cross sections is found.

Low Energy Positron Scattering by F and F2.

We have determined integral and differential elastic cross sections for positron scattering with atomic F and F2 molecules from 0.01 to 1000 eV with different theoretical approaches. Higher order polarizabilities were successively considered in the scattering potential, and we observed that the differential and integral cross sections converge only when the pure dipole second hyperpolarization level is taken into account, demonstrating the importance of the hyperpolarization effects on the low energy positron scattering dynamics. Ramsauer structures were found for both targets, and in the particular case of the F atom, the effect of its quadrupole moment proved to be relevant around the position of the Ramsauer minimum, which was determined together with the scattering length for each of the adopted polarization schemes. A relation of these quantities with the matching radius between the correlation and polarization interactions is also discussed. Agreement between the model potential and ab initio cross sections for the lowest level of target polarization is found for F2. Since there is no previous theoretical or experimental determination of cross sections for these targets, we compared the differential cross sections of F2 with experimental data available for N2 and O2 and found reasonable agreement.

Joint experimental and theoretical study on electron scattering from titanium tetrachloride (TiCl4) molecule.

Absolute grand-total cross section for electron scattering from titanium tetrachloride, TiCl4, molecule was measured at electron-impact energies ranging from 0.3 to 300eV, in the linear electron-transmission experiment. The elastic integral, differential, momentum transfer, and total ionization cross sections for TiCl4 molecule were also calculated for low and intermediate collisional energies at the level of various theories. The low-energy elastic integral, differential, and momentum transfer cross sections were calculated with the Schwinger multichannel method implemented with pseudopotentials, in the static-exchange and static-exchange plus polarization levels of approximation, for energies up to 30eV. The integral cross section calculated for low-energy electron scattering with the R-matrix method within the static-exchange and static-exchange plus polarization approximations for energies up to 15eV are also reported. By the inspection of the cross sections, the presence of resonances is discussed. In particular, the calculated integral cross sections and the measured total cross section display a minimum at around 1eV, which is consistent with the presence of a Ramsauer-Townsend minimum and a sharp increase at low energies, which is consistent with the presence of a virtual state. Additionally, interactions in elastic and ionization channels for intermediate collision energies were investigated with the additivity rule and the binary-encounter-Bethe methods.

Electron impact cross-sections of tetraethyl silicate

Understanding the interactions of electrons with molecules in plasma is of vital importance from both academic and technological points of view. Reliable electron collision data is required to model the electron and ion components of low-temperature and nonequilibrium plasmas. Various electron impact cross sections such as the differential, integral, momentum transfer, partial and total ionizations are reported for tetraethyl silicate (TEOS), a plasma-relevant molecule in the energy range between the ionization threshold and 5 keV. The elastic (differential, integral and momentum transfer) cross sections are obtained by invoking the molecular approach and local potential approximation within the single center expansion formalism. The dissociative ionization cross sections are reported within the binary encounter Bethe (BEB) model formalism. The elastic and ionization cross sections are summed incoherently to estimate total cross sections. A good agreement is observed between the present results and others that are available. This work validates the efficacy of the modified BEB model in computing the partial ionization cross sections.

Study of electron impact elastic scattering from Kr@C60 and Xe@C60 using a fully relativistic approach

In the present work, a detailed study has been reported on electron impact elastic scattering from krypton (Kr) and xenon (Xe) atoms when confined in two different types of C60 potentials viz (a) hard annular square well (ASW) and (b) diffused Gaussian annular square well (GASW). The Dirac equations are solved using these potentials for encaged Kr and Xe in C60. First, bound state Dirac–Fock wave functions of these encaged Kr and Xe atoms are found by utilizing modified general relativistic atomic structure package and thereafter, the charge densities and static potentials of the endohedral Kr@C60 and Xe@C60 are obtained. Further, using these, the Dirac equations are solved by the relativistic partial wave phase shift analysis method and the scattering amplitudes in terms of phase shifts are obtained. Thereafter, the electron elastic differential and integrated cross sections of Kr@C60 and Xe@C60 along with the C60 are calculated in the range of 0.1–15 eV incident electron energies. Presently, no experimental and theoretical results are available to compare our electron scattering cross section results from Kr@C60 and Xe@C60; thus, we have shown the cross section results obtained from ASW and GASW potential and compared them.

R-matrix calculations for elastic electron and positron scattering from pyrazine: effect of the polarization description

We present R-matrix calculations of electron and positron low energy scattering from the highly polarizable pyrazine molecule. We compare integral and differential elastic cross sections with experimental results and assess the quality of the models used for describing collisions of either projectile. Static-exchange-plus-polarization models give a good description of electron scattering (including that of shape resonances), whereas both the integral and small-angle differential cross sections are underestimated for positron collisions for the same models. We discuss whether the absence of a permanent dipole moment improves the comparison with experiment for this molecule, as well as future calculations that may improve the description of polarization effects and thus positron scattering.Graphical abstract

Elastic positron-uracil scattering cross sections

We report elastic integral and differential cross sections for positron collisions with uracil (${\mathrm{C}}_{4}{\mathrm{H}}_{4}{\mathrm{N}}_{2}{\mathrm{O}}_{2}$) for impact energies up to 10 eV. The cross sections were calculated employing the Schwinger multichannel (SMC) method in the static plus polarization approximation. The Born-closure procedure was applied to account for the long-range potential due to the permanent dipole moment of uracil. The present results are compared with experimental and theoretical data available in the literature, showing an overall good agreement with previously reported results. We also applied our differential cross sections to provide a correction to the total cross-section measurements by Anderson et al. [J. Chem. Phys. 141, 034306 (2014)] in order to account for the lack of angular resolution in the apparatus used by these authors. Besides, we applied a simple model employed by Franz and Gianturco [Phys. Rev. A 88, 042711 (2013)] to estimate the temperature effects on the uracil cross section. In particular, the level of agreement of the SMC differential cross sections as compared with the experimental findings is encouraging.

A study of critical minima and spin polarization in the e±–Ba elastic scattering

A complex optical potential (OP) is employed to study the critical minima (CM) and spin polarization in the elastic e−–Ba and e+–Ba scattering for collision energies in the range Ei = 1–1500 eV and Ei = 1–100 eV respectively in terms of the Dirac partial wave method (OPMD) and the Schrodinger partial wave method (OPMS). The energy dependence of the integral elastic cross sections (IECSs), momentum transfer cross sections (MTCSs), viscosity cross sections (VCSs), inelastic cross sections (INCSs) and total cross sections (TCSs) is also calculated and discussed for both the projectiles in the same energy range. The OPMD optical potential is composed of the static, exchange, polarization and absorption components. On the other hand, the OPMS comprises the static, local exchange, polarization, spin–orbit, and absorption potentials. The number of CM in the DCS distribution of e−–Ba scattering has been found to be 11 using the OPMD method, while the OPMS calculation produces 12 CM points. However, the OPMS calculation with the static and spin–orbit potentials only produces 9 CM. The critical energies and the angular positions of these CM are revealed and discussed. There are 22 and 24 maximum spin polarization points found in the e−–Ba scattering using OPMD and OPMS respectively. For the case of e+–Ba scattering, we have found 2 CM with OPMD calculations of which the angular positions along with the critical energies are discussed. There are 4 maximum polarization points noted with OPMD calculations which fail to attain the condition for sharpness of S(θ) distribution. To the best of our knowledge, the present is the first work to determine the CM in the DCS distribution of e±–Ba scattering. The Sherman function and the DCSs for some energy points are also calculated for the first time.

Theoretical and experimental study on scattering of low-energy electrons by dimethyl and diethyl ethers

We report a joint theoretical and experimental investigation on low-energy electron scattering by dimethyl and diethyl ethers. The experimental elastic differential cross sections were measured at impact energies from 1 eV up to 30 eV and scattering angle range of 10° to 130°. Theoretical elastic differential, integral and momentum-transfer cross sections are calculated at impact energies up to 30 eV, employing the Schwinger multichannel method implemented with norm-conserving pseudopotentials, in the static-exchange and static-exchange plus polarization approximations. Our experimental and theoretical results for dimethyl and diethyl ether are compared with previous data for their isomers, ethanol and butanol, respectively. These comparisons reveal that although the cross sections for the ether and its respective alcohol present similar magnitudes, the angular behavior of their differential cross sections shows some significant differences. From the analysis of the integral cross sections for electron scattering by dimethyl and diethyl ether, we observe a broad structure, at around 9.5 eV, which we assign as the overlap of several resonant structures.

Elastic electron scattering by tetramethylmethane, tetramethylsilane, and tetramethylgermane

We report integral, differential, and momentum transfer cross sections for elastic scattering of electrons by tetramethylmethane [$\mathrm{C}{({\mathrm{CH}}_{3})}_{4}$], tetramethylsilane [$\mathrm{Si}{({\mathrm{CH}}_{3})}_{4}$], and tetramethylgermane [$\mathrm{Ge}{({\mathrm{CH}}_{3})}_{4}$]. The scattering cross sections were calculated with the Schwinger multichannel method implemented with pseudopotentials, in the static-exchange and static-exchange plus polarization levels of approximation, for impact energies up to 30 eV. All three molecules present in their integral elastic cross section a broad structure between 5 and 15 eV, which is a superposition of two shape resonances assigned to the $E$ and ${T}_{2}$ symmetries of ${T}_{d}$. The low-energy behavior of the $s$-wave integral cross section and the $s$-wave eigenphase support the presence of a Ramsauer-Townsend minimum for $\mathrm{C}{({\mathrm{CH}}_{3})}_{4}$ at 0.16 eV, for $\mathrm{Si}{({\mathrm{CH}}_{3})}_{4}$ at 0.32 eV, and for $\mathrm{Ge}{({\mathrm{CH}}_{3})}_{4}$ at 0.40 eV. In general, the present elastic integral cross sections show a good qualitative agreement with the experimental total cross sections of Stefanowska-Tur et al. [J. Chem. Phys. 150, 094303 (2019)].

Elastic-electron-scattering from 1,2-ethylenediamine and dimethyldiazene

We present elastic integral, differential and momentum transfer cross sections for scattering of electrons by 1,2-ethylenediamine (NH2C2H4NH2) and by dimethyldiazene (CH3N2CH3). The cross sections were computed with the Schwinger multichannel method implemented with norm-conserving pseudopotentials. The calculations were carried out in the static-exchange and static-exchange plus polarization approximations for energies up to 20 eV. We found the presence of a Ramsauer–Townsend minimum at around 0.38 eV in the integral cross section of 1,2-ethylenediamide and a π* shape resonance at around 1.0 eV in the integral cross section of dimethyldiazene, both cross sections computed in the static-exchange plus polarization approximation. In the static-exchange approximation the resonance is located at 3.5 eV. For dimethyldiazene we also employed an empirical scaling relation to estimate the vertical attachment energy and the value of 1.1 eV agree well with the position of the resonance of 1.0 eV obtained through the scattering calculation. We compare our results with recent calculations [G. L. C. de Souza, J. Electron Spectrosc. Relat. Phenom. 234, 64 (2019)] and found in general a very good agreement in the shape of the cross sections, but there are some discrepancies regarding their magnitude.

Electron and Positron Scattering by the Formamide Molecule.

We report calculated elastic integral, differential, and momentum transfer cross sections for electron and positron collisions with the formamide (HCONH2) molecule, for impact energies up to 10 eV. We have used the Schwinger multichannel method in the static-exchange and static-exchange plus polarization approximation for collisions of electrons and the static plus polarization approximation for collisions of positrons. The Born-closure procedure was applied to account for the long-range potential due to the permanent dipole moment of formamide. We obtained the well-characterized π* shape resonance located at around 2.38 eV, which belongs to the A″ symmetry of the Cs point group. Our integral and differential cross sections for collisions of electrons were compared with the data available in the literature and showed a good qualitative agreement. To the best of our knowledge, no experimental and theoretical data are currently available for positron-formamide collision, so our present cross sections were compared with the cross sections of formic acid, which is also polar and is isoeletronic to formamide.

The Rb + –Rb collision rate in the energy range of 103–104 K

We study both theoretically and experimentally the energy dependence of the low-energy Rb+–Rb total collision rate k ia in the energy range from 103 to 104 K. We calculate the integral elastic cross-section and the resonant charge-transfer cross-section by the quantum mechanical molecular orbital close-coupling method, and then obtain k ia for temperatures by averaging the cross-sections over a Maxwell–Boltzmann velocity distribution. The experiments are conducted in an ion–neutral hybrid trap, where the Rb+ ions are created by photo-ionization of the cold atoms in a magneto-optic trap (MOT) and accumulated in the linear Paul ion trap. The total ion–atom collision rate k ia is measured by monitoring the fluorescence reduction of the steady-state MOT atoms by sequentially introducing photo-ionization and ion–atom collisions. The ion–atom collision energy E col ≈ T i is modified by changing T i due to T i being more than six orders of magnitude larger than the T a of cold atoms. The temperature of ions T i is obtained by comparing the time-of-flight mass spectrometry of Rb+ from experimental results to that obtained by SIMION simulation. The equilibrium steady T i is modified by changing the initial root-mean-squared position of the ion cloud, and the k ia are measured with E col from 8000 to 16 000 K. Both the theoretical and experimental results show that k ia increases with E col. More specifically, the measured k ia increases rapidly with the enlargement of E col near 10 000 K. The theoretical calculation results show that k ia increases slowly with E col. The specific difference may be due to the influence of the ratio of excited states f e on the trend of k ia at different E col.