Inelastic Collision Cross Sections Research Articles

Atomic data necessary for the non-LTE analysis of stellar spectra

The determination of physical parameters and chemical abundances of stars based on non-local thermodynamic equilibrium (non-LTE) line formation requires a large amount of accurate atomic data on energy levels, photoionization cross-sections, oscillator strengths, inelastic collision cross-sections, and related data. In this paper, we briefly review astrophysical problems where non-LTE modelling leads to a better interpretation of observed data due to the use of advanced atomic data and where atomic data are still missing or uncertain. For the statistical equilibrium of atoms in cool stars, a top priority problem is the efficiency of inelastic collisions with hydrogen atoms.

Inelastic semiclassical collisions in cold dipolar gases

Two elementary models of molecular structure are used to investigate inelastic collisions in cold trapped dipolar gases. A two-state model of a polar molecule (such as one with a Λ-doublet) permits analytic description of the inelastic collision process at energies considerably higher than the gap energy, predicting rate constants and cross sections given by elementary formulae. Alternatively, a three-state model of a rotor molecule in an electric field is investigated, with resultant rate constants and cross sections scaling simply with molecular mass, rotational constant, dipole moment and polarizing field strength. Semiclassical inelastic collision cross sections and rate constants are demonstrated to depend strongly on the model used, especially as regards their dependence on the polarizing field. Inelastic cross sections among doublet dipoles decrease with increasing field strength, while they increase in proportion to the square of the field strength for collisions between rotor dipoles.

Detection of TeV to PeV Neutrinos and Gamma-Rays with the High Mountain SHALON Mirror Cherenkov Telescope

Problems in observation of extensive air showers generated by neutrinos are connected with an extremely small cross section of inelastic collisions of neutrinos with nuclei. However, two facts allow to search for showers generated by neutrinos: (1) a hadron cascade with the primary energy of more than 10 13 eV leaves a mountain ridge to the atmosphere from the depth 300 g/cm 2 without an essential loss of the total energy in the hadron cascade, and (2) air Cherenkov radiation from such hadron cascades will be observed with a 7.5 km distant telescope over an area of more than 7 ×10 5 m 2 . This partially compensates the small cross section of inelastic neutrino collisions. The observation has been carried out since 1992 at high mountainous Tien-Shan station with SHALON Cherenkov mirror telescope with ∼11.2 m 2 mirror area and image matrix of 144 PMT with full angle >8°. The telescope characteristics permitted to start the search of local neutrino sources with energy 10 13 –10 16 eV on EAS generating in mou...

Differential scattering of cold molecules in superimposed electric and magnetic fields

We present a detailed theoretical study of differential cross sections for inelastic collisions of (2)Sigma molecules in the presence of superimposed electric and magnetic fields. Using rigorous quantum dynamical calculations, we show that the angular dependence of cross sections for Zeeman relaxation in collisions of CaD molecules with He atoms at low temperatures can be significantly modified by electric fields of less than 100 kVcm. Our results suggest that the differential scattering cross sections are more sensitive to the electric field than the averaged integral cross sections. We show that the integral cross sections corresponding to a fixed orientation of the incoming collision flux may exhibit interference effects induced by electric fields.

Fine-structure-changing collisions in atomic titanium

We have measured cold titanium-helium collisions that cause transitions between the fine-structure levels of the $[3{d}^{2}4{s}^{2}]\phantom{\rule{0.3em}{0ex}}^{3}F_{J}$ electronic ground state of atomic titanium, over a temperature range from 5 to $20\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The $\mathrm{Ti}\text{\ensuremath{-}}\mathrm{He}$ inelastic collision cross section is significantly smaller than cross sections measured for collisions of non-transition-metal atoms with noble gas atoms. Our theoretical calculations of the inelastic cross sections reproduce the magnitude and temperature dependence of the measurements, and attribute the suppression of inelastic collisions to titanium's ``submerged'' $d$-shell valence electrons.

Rotational Transitions of CO+Induced by Atomic Hydrogen

The CO+ molecular ion has been observed in photon-dominated regions. Recent modeling has not been able to explain the abundances of CO+ in these regions. The most abundant collision partners are believed to be hydrogen atoms, hydrogen molecules, and electrons. The reactions of these species with CO+ have been studied previously and found to be fast. The only inelastic processes studied before were collisions of CO+ with electrons. Here we investigate the inelastic collisions of CO+ with hydrogen atoms. We argue that this can be done on the lowest triplet electronic state. This implies that CO+ ions, in a hydrogen atom dominated surrounding, experiences a few inelastic collisions before reacting. Rotationally inelastic state-to-state cross sections (j ≤ 8) are presented together with state-resolved thermal rate coefficients. The results suggest that the rotationally inelastic collision cross sections can be of comparable magnitude to the reactive ones. Implications for the rotational temperature of CO+ in PDRs are discussed. To perform the calculations, a potential energy surface is fitted using the reproducing-kernel Hilbert space method based on multireference configuration-interaction calculations employing the aug-cc-pVQZ basis set.

Electron-impact study of NeF using theR-matrix method

a configuration-interaction expansion which is shown to yield accurate potential energy curves and target properties. Elastic and inelastic collision cross sections for the four states are calculated ab initio using the R-matrix method. Special care is needed to treat the large dipole moments found for the charge-transfer states which are predicted to have electron collision cross sections almost two orders of magnitude bigger than the lower states. Differential and momentum transfer cross sections are also considered for the electron impact on the repulsive ground state. Rate constants for electron deexcitation of the excimer states of NeF have been calculated for electron temperature corresponding up to 10 eV. The superelastic processes are dominated by the 1 2+ →X 2+ transition with thermal rate constant of 2–5 10 �9 cm 3 s �1 in the entire range of electron temperature considered.

Ultracold Inelastic Collisions in Two Dimensions

We show that cross sections for inelastic collisions of ultracold atoms or molecules confined by a harmonic potential have the same energy dependence as in pure 2D geometry. This indicates that chemical reactions and inelastic collisions may be suppressed in an ultracold gas under strong confinement in one dimension. We present a numerical proof of the threshold collision laws in 2D. Our results indicate that inelastic collisions in weak electromagnetic fields may be controlled by varying the orientation of the external field axis with respect to the plane of confinement.

Quantum scattering of NO(X 2Π) with He( 1S): Temperature dependence of rotational (de)-excitation rate coefficients

We report fully-quantum, coupled-state (CS) calculations of inelastic integral cross sections for collisions of NO( 2Π) with He. The scattering calculations, which take into account the fine structure of the NO radical, were done on a grid of collision energies large enough to ensure converged state-to-state rate coefficients for temperatures ranging from 1 K up to 350 K.

Monte Carlo model of electron transport for the calculation of Mars dayglow emissions

A model of the photoelectron collision‐induced component of the Mars dayglow using recent cross sections and solar flux is described. The calculation of the photoelectron source of excitation is based on a stochastic solution of the Boltzmann equation using the direct simulation Monte Carlo method. The neutral atmosphere is taken from outputs of a global circulation model, and recent inelastic collision cross sections are adopted. The calculated vertical profiles of the CO Cameron bands and CO2+ doublet emissions integrated along the line of sight compare well with the Spectroscopy for the Investigation of the Characteristics of the Atmosphere of Mars (SPICAM) limb profiles observed with the SPICAM spectrograph on board Mars Express made at Ls = 166° during the summer season at northern midlatitudes. The comparison shows agreement to within the uncertainties of the excitation cross sections. Seasonal changes in the brightness and the altitude of the emission peaks are predicted with intensity variations in the range 15–20%.

TeV to PeV neutrinos and gamma-rays with Mountain SHALON Mirror Cherenkov Telescope

Problems in observation of extensive air showers generated by neutrinos are connected with an extremely small cross-section of inelastic collisions of neutrinos with nuclei. However, two facts allow to search for showers generated by neutrinos: (1) a hadron cascade with a primary energy of more than 10 13 eV leaves a mountain ridge to the atmosphere from a depth ∼ 300 g / cm 2 without any essential loss of the total energy in the hadron cascade, and (2) air Cherenkov radiation from such hadron cascades will be observed with a 7.5 km distant telescope over an area of more than 7 × 10 5 m 2 . This partially compensates for the small cross-section of inelastic neutrino collisions. Observations have been carried out since 1992 at the high mountain Tien-Shan station using the SHALON Cherenkov mirror telescope with ∼11.2 m 2 mirror area and image matrix of 144 PMT with full angle >8°. The telescope characteristics allowed to start searching for local neutrino sources with energy 10 13 –10 16 eV on EAS generated in the mountain-range located at some 7.5 and more kilometers from the gamma-telescope (in Russian the abbreviation SHALON means - the Extensive Air Showers from Neutrino).

The rotational excitation partial cross sections for the He-HI collisions

The close coupling approach is used to calculate the elastic and inelastic partial cross sections for collisions of helium atoms with hydrogen iodide molecules based on the intermolecular potential introduced in our previous research. The calculations are performed separately at the incident energies of 40, 75 and 100 meV. This study indicates that the excitation partial cross sections converge faster than the elastic partial cross section for each of the incident energies considered here. The excitation partial cross sections converge more rapidly for the higher excited states, and more slowly for the higher incident energies.

Meson cascade in the atmosphere, uncertainties in calculating the fluxes of high-energy muons, and data of direct measurements

A new calculation of the atmospheric fluxes of cosmic-ray hadrons and muons in the energy range 10–104 GeV is performed on the basis of the method for solving nuclear-cascade equations with allowance for a nonscaling behavior of inclusive hadron-production cross sections, the growth of cross sections for inelastic hadron-nucleus collisions with increasing energy, and a non-power-law character of the primary spectrum. The fluxes of secondary cosmic rays at various levels in the atmosphere are calculated for three models of the spectrum and composition of primary cosmic rays. The effect of uncertainties in the spectrumand composition of primary cosmic rays on the flux of atmosphericmuons and their charge ratio at sea level is investigated. The calculated energy spectra of muons at sea level are compared with the results of previous experiments and the results of recent measurements performed by means of the L3 + Cosmic and CosmoALEPH spectrometers, as well as with the results of other calculations.

Uncertanties of atmospheric high-energy muon fluxes and spectrum of primary cosmic rays

New results of calculations of nucleon, π-and K-meson, and muon fluxes generated during high energy cosmic ray interactions with the Earth’s atmosphere are presented. The calculations are based on the method of solving the nuclear cascade equations with allowance for non-scaling behavior of inclusive hadron production cross sections, increase of cross sections of inelastic hadron-nucleus collisions with energy, and non-power-law character of primary spectrum. The hadron and muon fluxes are calculated at different atmospheric altitude levels for several spectral models and compositions of primary cosmic rays. Results of calculations are compared with recent measurements using the L3+Cosmic and CosmoALEPH facilities.

Inelastic-collision cross sections for the interactions of totally stripped H, He and C ions with liquid water

The HKS and CDW-EIS models are implemented to determine single ionization cross sections (SICS) corresponding to the impact of H +, He 2+ and C 6+ ions on liquid water, for incident energies from 0.3 to 10 MeV/u. Corrected expressions for the HKS method have been used. The same kind of initial electron wave functions and binding energies have been used with both methods, in order to compare the formalisms themselves. Double and single differential as well as total SICS of liquid water have been calculated by use of both formalisms and comparisons have been made between their theoretical predictions. Also, these results have been compared with experimental values reported previously for ionization of water vapor due to protons and alpha particles. Despite its sophistication, the CDW-EIS method does not show better results than the more simple HKS model when comparing liquid water single and double differential cross sections with experimental water vapor values. However, once the excitation cross sections are included to determine electronic stopping cross sections in liquid water, the results based on the CDW-EIS method provide the best agreement when compared with corresponding data published in ICRU reports, obtaining discrepancies of about 9%, 16% and 19% for incident protons, alpha particles and carbon ions respectively.

Resonances and threshold effects in low-energy electron collisions with methyl halides

Cross sections for elastic and inelastic electron collisions with $\mathrm{C}{\mathrm{H}}_{3}X$ $(X=\mathrm{Cl},\mathrm{Br},\mathrm{I})$ molecules are calculated. For the lowest partial wave, the resonance $R$-matrix theory, and for the higher partial waves, the theory of scattering by dipolar plus polarization potential, are used. It is shown that the rotationally elastic scattering amplitude for a polar molecule in the fixed-nuclei approximation is logarithmically divergent for the forward direction, and a closure formula is derived to speed up the convergence at small angles. In treating the nuclear motion, only $\mathrm{C}\text{\ensuremath{-}}X$ stretch vibrations are taken into account. The dipole moment as a function of the $\mathrm{C}\text{\ensuremath{-}}X$ distance is modeled by a function incorporating the experimental value of the molecular dipole moments at the equilibrium distance and the derivatives of the dipole moments extracted from the experimental data on infrared intensities. This is supplemented by ab initio calculations of the dipole moment function for $\mathrm{C}{\mathrm{H}}_{3}\mathrm{Br}$ using the multiconfigurational valence bond method. The results for scattering cross sections show pronounced features caused by vibrational Feshbach resonances and threshold cusps. The features are most noticeable at the $v=6$, 7, and 8 thresholds in $\mathrm{C}{\mathrm{H}}_{3}\mathrm{Cl}$, at the $v=3$ and 4 thresholds in $\mathrm{C}{\mathrm{H}}_{3}\mathrm{Br}$, and at the $v=1$ threshold in $\mathrm{C}{\mathrm{H}}_{3}\mathrm{I}$.

Ultracold atom-molecule collisions and bound states in magnetic fields: Tuning zero-energy Feshbach resonances inHe−NH(Σ−3)

We have generalized the BOUND and MOLSCAT packages to allow calculations in basis sets where the monomer Hamiltonians are off diagonal and used this capability to carry out bound-state and scattering calculations on $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$ and $^{4}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$ as a function of magnetic field. Following the bound-state energies to the point where they cross thresholds gives very precise predictions of the magnetic fields at which zero-energy Feshbach resonances occur. We have used this to locate and characterize two very narrow Feshbach resonances in $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$. Such resonances can be used to tune elastic and inelastic collision cross sections, and sweeping the magnetic field across them will allow a form of quantum control in which separated atoms and molecules are associated to form complexes. For the first resonance, where only elastic scattering is possible, the scattering length shows a pole as a function of magnetic field and there is a very large peak in the elastic cross section. For the second resonance, however, inelastic scattering is also possible. In this case the pole in the scattering length is dramatically suppressed and the cross sections show relatively small peaks. The peak suppression is expected to be even larger in systems with stronger inelasticity. The results suggest that calculations on ultracold molecular inelastic collisions may be much less sensitive to details of the potential energy surface than has been believed.

Cold collisions between OH and Rb: The field-free case

We have calculated elastic and state-resolved inelastic cross sections for cold and ultracold collisions in the $\mathrm{Rb}(^{1}S)+\mathrm{O}\mathrm{H}(^{2}\ensuremath{\Pi}_{3∕2})$ system, including fine-structure and hyperfine effects. We have developed a set of five potential energy surfaces for $\mathrm{Rb}\text{\ensuremath{-}}\mathrm{O}\mathrm{H}(^{2}\ensuremath{\Pi})$ from high-level ab initio electronic structure calculations, which exhibit conical intersections between covalent and ion-pair states. The surfaces are transformed to a quasidiabatic representation. The collision problem is expanded in a set of channels suitable for handling the system in the presence of electric and/or magnetic fields, although we consider the zero-field limit in this work. Because of the large number of scattering channels involved, we propose and make use of suitable approximations. To account for the hyperfine structure of both collision partners in the short-range region we develop a frame-transformation procedure which includes most of the hyperfine Hamiltonian. Scattering cross sections on the order of ${10}^{\ensuremath{-}13}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}$ are predicted for temperatures typical of Stark decelerators. We conclude that spin orientation of the partners is completely disrupted during the collision. Implications for both sympathetic cooling of OH molecules in an environment of ultracold Rb atoms and experimental observability of the collisions are discussed.

Rotational Collision Number and Rotationally Collision Cross Section of Inelastic Collision Model for Nitrogen Molecule in the Direct Simulation Monte Carlo Method

Transport coefficients and rotational collision number of nitrogen molecule were evaluated using the Monte Carlo integration with the classical trajectory calculation (CTC) for a set of equations in the Wang-Chang-Uhlenbeck (WCU) theory, and then the rotationally inelastic collision cross section for the statistical inelastic cross section (SICS) model was made so as to reproduce the rotational collision number of CTC. Transport coefficients and rotational collision number of SICS model with the rotationally inelastic cross section presented in this study were in reasonable agreement with those of CTC. SICS model was applied to the simulation of nitrogen normal shock wave structure and compared with CTC and experimental results. The density and translational structure in the shock wave were in reasonable agreement with those of CTC results. However, the structures of rotational temperature in the highly non-equilibrium state were in poor agreement with those of CTC.

Electron scattering and ionization of NO, N2O, NO2, NO3 and N2O5 molecules: theoretical cross sections

We have investigated the scattering of electrons from atmospheric molecules NO, N2O, NO2, NO3 and N2O5 at incident electron energy Ei from the ionization threshold (∼10 eV) to 2000 eV. Basically total cross sections for elastic and inelastic collisions are calculated and hence total ionization cross sections are deduced in the ‘complex scattering potential-ionization contribution’ method, developed earlier. Various calculated cross sections are compared extensively with experimental and theoretical data wherever possible. Recommended data can now be prepared for the well-known NO target. New results are presented for lesser known targets.