Inelastic Collision Cross Sections Research Articles

Elastic and electronically inelastic scattering of electrons by 2H-pyran and 4H-pyran molecules

We report on elastic and electronically inelastic integral and differential cross sections for electron collisions with the 2H-pyran and 4H-pyran molecules. The scattering calculations were performed with the Schwinger multichannel method and aimed to (i) investigate the formation of resonant states, (ii) assign and compare the resonance spectrum of these isomers, and (iii) evaluate the influence of multichannel coupling effects upon elastic and electronically inelastic scattering processes. In the elastic channel, calculations carried out at the static-exchange and static-exchange plus polarization levels of approximation revealed the presence of three shape resonances for each one of the pyran isomers. For the 2H-pyran molecule, we found two resonances related to the formation of long-lived π∗ anion states that are centered at 1.38 or 1.32 eV (π1∗) and 4.54 or 4.46 eV (π2∗), depending on the polarization model used in the calculations, and a broad resonance of σ∗ character located around 9.50–10.00 eV. The resonances observed in the case of the 4H-pyran molecule have the same character with centers located at 2.08 or 2.20 eV (π1∗), 3.92 or 3.94 eV (π2∗), and 9.24–10.00 or 9.50–10.00 eV (σ∗), depending on the polarization model used in the calculations. The difference in the position of the resonances when comparing the results for the 2HPY and 4HPY molecules is explained in terms of the inductive effect. The electronically inelastic calculations employed the minimal orbital basis for single configuration interactions strategy and considered up to 129 open channels for 2H-pyran and up to 249 open channels for 4H-pyran. According to these levels of channel coupling, we computed integral and differential cross sections for the excitation from the ground state to the 13A′, 23A′, 11A′′, and 21A′ electronic excited states of 2H-pyran and to the 13B2, 13A1, 11B1, and 11B2 electronic excited states of 4H-pyran. As a general trend, for both isomers, we observed that the magnitude of the cross sections is reduced as more channels are considered open in the scattering calculations. We also obtained the total ionization cross sections for 2H- and 4H-pyran using the binary-encounter-Bethe model, which next was summed to the elastic and electronically inelastic cross sections to estimate the total cross sections. As a whole, these results correspond to the first set of cross sections for these targets published to date. Such an effort is aimed at addressing the demand of different communities regarding the expansion of the cross section data set for electron collisions with molecules of technological, environmental, and biological relevance, a need that has been raised by several reviews on the subject.

Electron transport characteristics in water under electrostrictive effect

The transport characteristics of electrons are crucial for the initiation and development of pulse discharge in water. In this work, we develop a physical model of electron transport that consides elastic and inelastic collision cross sections. The purpose of this study is to investigate frequency variations of elastic collisions, ionization and excitation collisions with different initial electron energy values, and to explore the characteristic of electron energy loss in water. The Monte Carlo method is employed to track structure characteristics of electron transmission and scattering under varying energy values. The results show that the electrons of lower energy (~20 eV) are significantly impacted by the water molecule scattering, hence their transmission capacities are weakened. When the incident energy of electron reaches 100 eV, the scattering deviation distance is roughly equivalent to the transmission depth, about 6–8 nm, and the maximum deviation angle <i>θ</i><sub>shift</sub> ~ 60°. When the electron incident energy is in a range of 10–1000 eV, the number of elastic collisions is much greater than the number of excitation and ionization collisions, and the number of ionization collisions and excitation collisions increases significantly with the increase of electron energy. The higher the electron incident energy, the greater the energy loss is. However, the energy loss decreases sharply with the extension of penetration distance. For the ionization collision, the average ionization energy loss, <i>W</i>, decreases rapidly with the increase of electron energy, and ultimately maintains at a level of 20–30 eV, which is consistent with the experimental results reported.

State-to-state rovibrational transition rates for CO2 in the bend mode in collisions with He atoms.

Modeling environments that are not in local thermal equilibrium, such as protoplanetary disks or planetary atmospheres, with molecular spectroscopic data from space telescopes requires knowledge of the rate coefficients of rovibrationally inelastic molecular collisions. Here, we present such rate coefficients in a temperature range from 10 to 500K for collisions of CO2 with He atoms in which CO2 is (de)excited in the bend mode. They are obtained from numerically exact coupled-channel (CC) calculations as well as from calculations with the less demanding coupled-states approximation (CSA) and the vibrational close-coupling rotational infinite-order sudden (VCC-IOS) method. All of the calculations are based on a newly calculated accurate abinitio four-dimensional CO2-He potential surface including the CO2 bend (ν2) mode. We find that the rovibrationally inelastic collision cross sections and rate coefficients from the CSA and VCC-IOS calculations agree to within 50% with the CC results at the rotational state-to-state level, except for the smaller ones and in the low energy resonance region, and to within 20% for the overall vibrational quenching rates except for temperatures below 50K where resonances provide a substantial contribution. Our CC quenching rates agree with the most recent experimental data within the error bars. We also compared our results with data from Clary et al. calculated in the 1980s with the CSA [A. J. Banks and D. C. Clary, J. Chem. Phys. 86, 802 (1987)] and VCC-IOS [D. C. Clary, J. Chem. Phys. 78, 4915 (1983)] methods and a simple atom-atom model potential based on abinitio Hartree-Fock calculations and found that their cross sections agree fairly well with ours for collision energies above 500 cm-1, but that the inclusion of long range attractive dispersion interactions is crucial to obtain reliable cross sections at lower energies and rate coefficients at lower temperatures.

Rotational state-changes in C5N− by collisions with He and H2

ABSTRACT The anion C5N− is one of the largest linear (C,N)-bearing chains detected in the interstellar medium. Here we present and discuss the general features of new ab initio potential energy surfaces describing the interaction of this linear anion with He and H2. We employ a Legendre Polynomials expansion representation for the former and an artificial neural network fit for the latter. We then carry out quantum scattering calculations to yield rotationally inelastic cross-sections for collisions with He and H2, using relative translational energy values in the range of 0.1–300 cm−1. We then obtained the corresponding inelastic rate coefficients as a function of temperature covering the range from 1 to 100 K. The results for these two systems are compared with each other, as well as with the earlier results on the C3N− colliding with the same partners. We found that the final inelastic rate coefficients for this anion are all fairly large, those from collisions with H2 being the largest. The consequences of such findings on their non-equilibrium rotational populations in interstellar environments are discussed in our conclusions.

Quantum state-resolved molecular dipolar collisions over four decades of energy.

Collisions between cold polar molecules represent a fascinating research frontier but have proven hard to probe experimentally. We report measurements of inelastic cross sections for collisions between nitric oxide (NO) and deuterated ammonia (ND3) molecules at energies between 0.1 and 580 centimeter-1, with full quantum state resolution. At energies below the ~100-centimeter-1 well depth of the interaction potential, we observed backward glories originating from peculiar U-turn trajectories. At energies below 0.2 centimeter-1, we observed a breakdown of the Langevin capture model, which we interpreted in terms of a suppressed mutual polarization during the collision, effectively switching off the molecular dipole moments. Scattering calculations based on an ab initio NO-ND3 potential energy surface revealed the crucial role of near-degenerate rotational levels with opposite parity in low-energy dipolar collisions.

Implementation of the ELECTR module in NJOY

The ELECTR module of NJOY is designed to produce complete and accurate multigroup electroatomic cross sections from ENDF/B-VII data[1, 2]. electr produces restricted cross sections consistent with a solution of the multigroup Boltzmann-Fokker-Planck (BFP) equation. Total, elastic, inelastic (collision and bremsstrahlung) cross sections can be averaged using a variety of group structures and weighting functions. The Legendre components of the within-group elastic and group-to-group inelastic collision cross sections are calculated using tabulated data in energy and analytic expressions of the angular deviation recovered from the CEPXS code[3]. Here, we propose an Open-Source implementation of this module, named electr in NJOY2012 and NJOY-2016.[4] electr also computes partial energy deposition and charge deposition cross sections for each reaction and sum these partial contributions. The resulting multigroup constants are written on an intermediate gendf file for later conversion to any desired format.

Electron impact elastic scattering by a calcium atom using the first order distorted wave method with a complex potential

Electron-atom scattering data is required in diverse fields of physics. In particular, inelastic collision cross sections data are needed in photonics and radiation physics. Elastic collision data, on the other hand, are useful in material science for surface analysis. There is a lack of accuracy and completeness of atomic data obtained using theoretical methods relative to experimental techniques. Furthermore, the distorted wave Born approximation method with a complex potential is yet to be applied in calculating cross sections. Differential and total cross sections have been calculated for electron-calcium scattering in the impact energy range 10 – 100 eV. There is good shape resonance between the present results with a complex potential and experimental values as well as other theoretical results

Analytical Formulas for Approximating Cross Sections of Electron Collisions with Hydrogen, Noble Gases, Alkali and Other Atoms

This paper presents an analysis of data on the cross sections of elastic and inelastic collisions of electrons with noble gases, alkali and other atoms. For the selected sets of experimental and theoretical data, optimal analytical formulas are found, and approximation coefficients are calculated. The obtained semi-empirical formulas reproduce the values of the transport (diffusion), excitation and ionization cross sections for noble gases. Much attention is paid to the ionization cross sections of metal atoms, which are often present as an impurity in gas-discharge plasma. The approximation formulas reproduce the values of the ionization cross sections for hydrogen, metal and other elements in a wide range of energies with accurate orders of errors of the available theoretical and experimental data. For some elements with a two-hump plot of the dependence of the ionization cross section on the collision energy, it is proposed to use a two-term formula that takes into account ionization from both external and internal shells.

Collision-Induced C60 Rovibrational Relaxation Probed by State-Resolved Nonlinear Spectroscopy

Quantum state-resolved spectroscopy was recently achieved for C60 molecules when cooled by buffer gas collisions and probed with a midinfrared frequency comb. This rovibrational quantum state resolution for the largest molecule on record is facilitated by the remarkable symmetry and rigidity of C60, which also present new opportunities and challenges to explore energy transfer between quantum states in this many-atom system. Here we combine state-specific optical pumping, buffer gas collisions, and ultrasensitive intracavity nonlinear spectroscopy to initiate and probe the rotation-vibration energy transfer and relaxation. This approach provides the first detailed characterization of C60 collisional energy transfer for a variety of collision partners, and determines the rotational and vibrational inelastic collision cross sections. These results compare well with our theoretical modeling of the collisions, and establish a route towards quantum state control of a new class of unprecedentedly large molecules.

Elastic and Inelastic Cross Sections for Low-Energy Electron Collisions with ClF Molecule Using the R-Matrix Method

The ClF molecule belongs to an interhalogen family and is important in laser physics and condensed phase molecular dynamics. The elastic and excitation scattering cross sections are obtained in a fixed nuclei approximation using the UKRmol+ codes based on R-matrix formalism. The scattering calculations were performed in the static-exchange (SE), static-exchange-plus-polarisation (SEP), and close-coupling (CC) models. Three CC models with different target states were employed, namely, the 1-state, 5-states, and 12-states. In the CC model, the target states were represented by configuration interaction (CI) wavefunctions. A good agreement of dipole and quadrupole moments of the ground state was obtained with the experimental values, which indicates a good representation of the target modelling. The study predicted the existence of a shape resonance in the SE, SEP, and 5-states CC models. This resonance vanished in the 12-states CC model. The excitation cross sections from ground to the lowest two excited states were also reported. The elastic differential and momentum transfer cross sections were obtained in the 12-states CC models. The contribution of long-range interactions to elastic scattering was included via Born closure approach. The quantities like collision frequencies and rate coefficients were also presented over a wide range of electron temperatures. The ionization cross sections were computed using the binary-encounter-Bethe (BEB) model. The results were reported in C2v point group representation.

Analytical approximation of cross sections of collisions of electrons with atoms of inert gases

The paper presents an analysis of data on the cross sections of elastic and inelastic collisions of electrons with noble gas atoms. The transport (diffusion) cross sec-tion, the excitation and ionization cross sections are considered. For the selected sets of experimental and theoretical data, optimal analytical formulas are found and approximation coefficients are selected for them. The obtained semi-empirical formulas allow us to reproduce the cross section values in a wide range of colli-sion energies from 0.001 to 10000 eV with an accuracy of several percent.

Cross sections of electron collisions with noble gases atoms

Consideration is given to the analysis of data on the cross sections of elastic and inelastic col-lisions of electrons with noble gas atoms. The transport (diffusion) cross section, the excita-tion and ionization cross sections are studied. For the selected sets of experimental and theo-retical data, optimal analytical formulas are found and approximation coefficients are select-ed for them. The obtained semi-empirical formulas allow us to reproduce the cross section values in a wide range of collision energies from 0.001 to 10000 eV with an accuracy of sev-eral percent.

Multi-channel distorted-wave Born approximation for rovibrational transition rates in molecular collisions.

Modeling protoplanetary disks and other interstellar media that are not in local thermal equilibrium require the knowledge of rovibrational transition rate coefficients of molecules in collision with helium and hydrogen. We present a computational method based on the numerically exact coupled-channel (CC) method for rotational transitions and a multi-channel distorted-wave Born approximation (MC-DWBA) for vibrational transitions to calculate state-to-state rate coefficients. We apply this method to the astrophysically important case of CO2-He collisions, using newly computed ab initio three-dimensional potential energy surfaces for CO2-He with CO2 distorted along the symmetric and asymmetric stretch (ν1 and ν3) coordinates. It is shown that the MC-DWBA method is almost as accurate as full CC calculations, but more efficient. We also made computations with the more approximate vibrational coupled-channel rotational infinite-order sudden method but found that this method strongly underestimates the vibrationally inelastic collision cross sections and rate coefficients for both CO2 modes considered.

Universal stereodynamics of cold atom-molecule collisions in electric fields

We use numerically exact quantum dynamics calculations to demonstrate universal stereoselectivity of cold collisions of $^2\Pi$ molecules with $^1$S-state atoms in an external electric field. We show that cold collisions of OH molecules in their low-field-seeking $f$ states, whose dipole moments are oriented against the field direction, are much more likely to lead to inelastic scattering than those of molecules oriented along the field direction, causing nearly perfect steric asymmetry in the inelastic collision cross sections. The universal nature of this effect is due to the threshold suppression of inelastic scattering between the degenerate $\pm M$ Stark sublevels of the high-field-seeking $e$-state, where $M$ is the projection of the total angular momentum of the molecule on the field axis. Above the $\Lambda$-doublet threshold, the stereodynamics of inelastic atom-molecule collisions can be tuned via electric-field-induced resonances, which enable effective control of Ne + OH scattering over the range of collision energies achievable in current merged beam experiments.

Analytical approximation of cross sections of collisions of electrons with atoms of inert gases

The paper presents an analysis of data on the cross sections of elastic and inelastic collisions of electronswith noble gas atoms. The transport (diffusion) cross section, the excitation and ionization cross sectionsare considered. The bibliography on the cross sections of electron-atomic collisions includes manythousands of works. But the critical analysis of the results of experimental data in the review work is verydifficult due to the fact that the necessary initial data can only be available to the authors of the work. Theerrors of the order of 1-3% given in the original works are contrasted with each other, sometimesdiffering by 50%. Comparisons of the electron cross sections sets in noble gases was made. For theselected sets of experimental and theoretical data, optimal analytical formulas are found andapproximation coefficients are selected for them. The obtained semi-empirical formulas allow us toreproduce the cross-section values for them in a wide range of collision energies from 0.001 to 10000 eVwith an accuracy of several percent. Key words: electron atomic collisions, transport cross section, excitation cross section, ionization crosssection, approximation of cross sections, noble gases.

High-energy-resolution measurements of an ultracold-atom–ion collisional cross section

The cross section of a given process fundamentally quantifies the probability for that given process to occur. In the quantum regime of low energies, the cross section can vary strongly with collision energy due to quantum effects. Here, we report on a method to directly measure the atom-ion collisional cross section in the energy range of 0.2-12 mK$\cdot$ k$_B$, by shuttling ultracold atoms trapped in an optical-lattice across a radio-frequency trapped ion. In this method, the average number of atom-ion collisions per experiment is below one such that the energy resolution is not limited by the broad (power-law) steady-state atom-ion energy distribution. Here, we estimate that the energy resolution is below 200 $\mu$K$\cdot$k$_B$, limited by drifts in the ion's excess micromotion compensation and can be reduced to the 10's $\mu$K$\cdot$k$_B$ regime. This resolution is one order-of-magnitude better than previous experiments measuring cold atom-ion collisional cross section energy dependence. We used our method to measure the energy dependence of the inelastic collision cross sections of a non-adiabatic Electronic-Excitation-Exchange (EEE) and Spin-Orbit Change (SOC) processes. We found that in the measured energy range, the EEE and SOC cross sections statistically agree with the classical Langevin cross section. This method allows for measuring the cross sections of various inelastic processes and opens up possibilities to search for atom-ion quantum signatures such as shape-resonances.

Collisions between cold molecules in a superconducting magnetic trap

SynopsisWe decelerate and trap molecular oxygen using time-dependent magnetic fields and superconducting magnets. The density-dependent, non-exponential decay in particle number provides a clear proof of molecule-molecule collisions within the trapped ensemble. The spatial distribution of molecules in the trap is found to change over time, allowing to set limits on the ratio between the elastic and inelastic collision cross sections. Our experimental scheme opens up new possibilities for studying quantum effects in chemistry as well as for evaporative cooling of molecules.

Investigation of rotational state-changing collisions of C2N− ions with helium

AbstractThe cross sections for rotational inelastic collisions between atoms and a molecular anion can be very large, if the anion has a dipole moment. This makes molecular anions very efficient in cooling atomic gases. We address rotational inelastic collisions of Helium atoms with the molecular anion C2N–. Here we present preliminary calculations of the potential energy surface.

Description of the Charge–Energy Distribution of Fast Ions

A theoretical model is proposed; it describes the evolution of the charge and energy distributions of ions passing through a target as a Markov process, in which the probability of transitions between elements of phase space is proportional to the cross sections of inelastic collisions and to the corresponding ion energy losses. The inclusion of correlations between charge-exchange processes and the target-atom ionization makes it possible to describe the influence of the energy distribution of ions not only on the process of formation of the equilibrium charge distribution, but also on the change in the ion energy mean in the case where the charge distribution is nonequilibrium.

Collisional cooling of internal rotation inMgH+ions trapped with He atoms: Quantum modeling meets experiments in Coulomb crystals

Using the ab initio computed Potential Energy Surface (PES) for the electronic interaction of the MgH$^+$ ($^1\Sigma$) ion with the He($^1$S) atom, we calculate the relevant state-changing rotationally inelastic collision cross sections from a quantum treatment of the multichannel scattering problem. We focus on the quantum dynamics at the translationally low energies for the present partners discussed in the earlier, cold ion trap experiments (see below) which we wish to model in detail. The corresponding state-changing rates computed between the lower rotational states of the molecular ion are employed to describe the time-evolution kinetics followed by recent experiments on Coulomb-crystalized MgH$^+$ ($^1\Sigma$), where the ions are rotationally cooled by micromotion tuning after the uploading into the trap of He as a buffer gas. The present computational modeling of the final ions' rotational temperatures in the experiments turns out to agree very well with their observations and points at a fast equilibration between rotational and thermal temperatures of the ions.