Velocity Dependence Of Cross Sections Research Articles

Threshold laws for collisional reorientation of electronic angular momentum

It is shown that the velocity dependence of cross sections for projection-changing transitions in collisions of paramagnetic atoms or molecules with structureless targets near threshold has the form ${v}^{2\ensuremath{\Delta}m}$ when $\ensuremath{\Delta}m$ is even and ${v}^{2(\ensuremath{\Delta}m+1)}$ when $\ensuremath{\Delta}m$ is odd, where $\ensuremath{\Delta}m$ is the change in the projection quantum number and $v$ is the relative velocity.

Observational Constraints on the Self‐interacting Dark Matter Scenario and the Growth of Supermassive Black Holes

We consider the consequences of SIDM for a velocity dependent cross section per unit mass. Accretion of SIDM onto seed black holes can produce supermassive black holes that are too large for certain combinations of parameters,which is used to obtain a new constraint on the dark matter interaction. Constraints due to other considerations are presented and previous ones are generalized. The black hole constraint is extremely sensitive to the slope \alpha, of the inner density profile of dark halos. For the most probable value of \alpha=1.3, there exists a narrow range in parameter space, such that all constraints are satisfied. However, the adiabatic compression of the dark halo by baryons as they cool and contract in normal galaxies yields a steeper cusp, \alpha=1.7. This gives a tighter constraint, which would exclude SIDM as a possible solution to the purported problems with CDM in the absence of other dynamical processes. Nevertheless, SIDM with parameters consistent with this stronger constraint, can explain the ubiquity of supermassive black holes in the centers of galaxies. A ``best fit'' model is presented which reproduces the supermassive black hole masses and their observed correlations with the velocity dispersion of the host bulges. Specifically, the fourth power dependence of black hole mass on velocity dispersion is a direct consequence of the power spectrum having an index of n=-2. Although the dark matter collision rates for this model are too small to directly remedy problems with CDM, mergers between dark halos harboring supermassive black holes at high redshift could ameliorate the cuspy halo problem. This scenario also explains the lack of comparable supermassive black holes in bulgeless galaxies like M33.

Regularization for the non-cutoff 2D radially symmetric boltzmann equation with a velocity dependent cross section

Abstract We extend in this work previous results of regularization for the spatially homogeneous non cutoff 2D radially symmetric Boltzmann equation which held only in the case of Maxwellian molecules. Velocity dependent cross sections can now be taken in account.

Velocity Dependence of Quasi-Resonant Vibrotational Transfer in Li2*−Rare Gas Collisions

We report measurements of velocity-dependent cross sections for vibrotationally inelastic scattering in the system Li2 + X → Li2 + X, with vi = 9, ji = 42, and X = Xe, Ar, and Ne. The measurements range over a factor of 30 in energy. Quantum levels were chosen to elucidate the quasi-resonant vibrotational transfer process studied previously. A reduction in collision velocity results in both an increase in total vibrationally inelastic cross section and an enhancement of the quasi-resonant effect, with final rotational state distributions as narrow as 2.5ℏ (fwhm) observed. The largest cross section for Δv < 0 is given by the formula Δjpeak = −4Δv and possesses a roughly 1/vrel velocity dependence. For Δv = +1, energy thresholds shift the peak cross section at low velocity to the nearly energy resonant value of Δjpeak = −6. The similarity of the final state distributions for different target gases observed in previously measured rate constants does not hold in the velocity-dependent data; this results in part from the appearance of low-velocity dynamical thresholds for exoergic cross sections in the Ar and Ne systems. We compare the experimental results for X = Ne with cross sections calculated from quasi-classical trajectories on an ab initio potential energy surface; for jf ≥ 46, agreement is quantitative, while for jf < 46, the calculation overestimates the cross sections.

Classical dynamics of vibrational transfer in [formula omitted] collisions

Classical trajectory calculations on an ab initio potential surface for the Li 2 A 1 Σ u +-Ne system show that vibrationally inelastic collisions at low reagent excitation are dominated by impacts of the atom with the side of the molecule. As molecular excitation increases, impacts nearer the end of the molecule increase in importance. The two classes of collisions are clearly distinguishable in computed velocity-dependent cross sections, and should be observable in some cases as a bimodal angular momentum distribution in velocity-averaged rate constants. We discuss experimental data in light of these observations and suggest measurements that should clearly display evidence of the two mechanisms.

Cross Section Dependent Transport Properties of Thermal Gases

The velocity distribution and transport properties of model gases in thermal equilibrium at 300 K with mass of He having three cross sections proportional to the power of relative speed as v r 0 , v r -1/2 and v r -1 are calculated by using the flight time integral (FTI) method. Gas particles of all the cross sections are settled in a Maxwell distribution with a mean energy of 3 k T g /2 e eV, but some of transport properties, mean colliding energies, reaction rates take different values due to relative velocity dependent cross sections even reduced to a common mean collision frequency. The fact that the gas can have different transport properties and reaction rates in the same temperature and collision frequency is noticeable.

Velocity dependent O atom IR excitation cross sections: Connections with flight data

A fast oxygen atom source has been used to study the velocity dependence of O atom infrared excitation reactions with various molecular species in a crossed beam experiment. These short wave infrared (SWIR) measurements are performed under single collision conditions, simulating the low Earth orbit environment. Such data are fundamental to the analysis and interpretation of atmospheric oxygen atom interaction with plume exhaust species and with the local environment about structures in low Earth orbit. Measurements have been performed over the oxygen atom velocity range of 6 to 12 km/s. These are the first such experimental measurements, and they may be used to validate theoretical estimates presently used in predictive models. We specifically discuss the velocity dependent cross sections for the reaction O + N2 → NO(v) + N. This reaction is endothermic for O atom velocities ≤ 8 km/s. Preliminary data are also shown for the reaction O + CO2 → CO2(ν3) + O → CO(v) + O2. Both band integral and spectrally resolved results will be presented. The spectrally resolved data provide information on the rotation/vibrational distribution of the excited states. Limited observations of infrared emissions resulting from atmospheric interactions have become available in recent years from both shuttle‐ and rocket‐borne experiments. Comparisons between our experimental database and selected data from several different flight experiments are provided. These comparisons clearly identify the kinetic mechanisms responsible for the flight observations.

Computer simulations of encounters between massive black holes and binaries

Over 800,000 encounters of binaries with black holes having masses that range from 10 to 10,000 times that of the binary components were simulated. The calculations at many collision velocities and impact parameters were made, which made it possible to find the velocity-dependent cross sections for exchange collisions, for binary dissociation, and for changing the orbital energy and eccentricity. The distribution of closest approaches of the stars to the black hole was also found. The probability of the black hole tidally disrupting a star in the close encounters that produce exchange collisions was determined. Exchange collisions dominate over tidal dissociation if the sum of the radii of the stars is less than the binary semimajor axis. Even encounters of black holes with soft binaries can lead to exchange collisions in which the black hole captures one binary component and ejects the other at high speed. 12 refs.

The influence of realistic velocity-dependent cross sections on the correlation between Doppler and collisional broadening of the Na D1 spectral line

The theoretical shape of a hyperfine component of the Na D1 line, perturbed by collisions with Ne and Xe atoms, is used for analysing the influence of the velocity dependence of optical cross sections on the correlated Doppler and collisional broadening. For the first time, line profiles have been calculated using optical cross sections that were derived from experimentally established interaction potentials for the collision partners instead of a power law assumption. The latter assumption is shown to give lineshapes that may differ from the realistic results. However, these errors in lineshape are generally smaller than deviations due to the complete neglect of correlation in the Na-Ne(Xe) interaction.

Intramultiplet mixing collisions of chromium 3d54p 7P J with gases. Absolute cross sections and velocity dependence

An atomic Cr beam has been excited with a cw dye laser to the 7P°4 and 7P°3 states in a beam-gas study of intramultiplet mixing transitions between these states and to the 7P°2 state. Absolute cross sections for these transitions have been found for the collision partners He, Ar, H2, D2, N2, CO, O2, N2O, NH3, and C2H4 by comparison of fluorescence intensity of laser excited and collisionally excited states. Cross sections are large in all cases, being larger than gas kinetic for NH3, and comparable to gas kinetic for N2, CO, and C2H4. Smaller cross sections for the others may be due to competing reactions. Time-of-flight measurements using a mechanically chopped Cr beam have yielded the velocity dependence of cross sections. Very little variation with relative velocity is found. Comparisons have been made for Cr scattering with He and Ar of experimental relative cross sections and velocity dependence with predictions of radial and Coriolis coupling models for nonadiabatic processes. Neither model alone can explain the observations. An application of the principle of microscopic reversibility to the N2 and CO time-of-flight results indicates that product energy partitioning in translation and rotation in a thermal experiment is quite similar to that of the reactants.

Excitation in gas-phase collisions at intermediate and high velocities

A summary of experimental and theoretical total excitation cross sections of light ion atom systems for intermediate and high velocities is given. The velocity dependence of cross sections is compared and similarities for different collision systems are pointed out. The experimental data are compared with theoretical calculations.

Velocity dependence of absolute total cross sections for LiF scattered by nonpolar targets

Total cross sections accurate to 1–2 percent were measured in the thermal energy range for LiF scattered by rare gas atoms (He, Ne, Xe) and nonpolar molecules (D2, CH4). In all cases, the cross sections were pressure independent, indicating that (1) the scattering was not a discernable function of the internal state of the primary beam molecule, and (2) the degree of inelasticity occuring at the outermost impact parameter regions probed was small. This allowed the observed velocity dependence of the cross sections to be interpreted in terms of spherically averaged monotonic potentials except in the cases of LiF–He, LiF–Ne, and LiF–D2 where the repulsive and well regions are probed. For every system, the slope d lnQ/d ln v of the cross section deviated from the theoretical slope of −0.4 predicted for a pure van der Waals 1/r6 interaction, suggesting the presence of higher order forces. As the size of the impact parameters explored increased, as increasingly large scattering targets were used, the slopes approached −0.4. For systems which sampled attractive regions of the intermolecular potential, cross sections which were calculated from the Schiff-Landau-Lifschitz (SLL) relation using the induction energy and the Slater-Kirkwood dispersion energy were 6–8 percent smaller than the corresponding experimental cross sections. For LiF–Xe, the system which most closely approached pure van der Waals behavior (with a slope of −0.389), the calculated cross section was 8 percent smaller than experiment. The absence of glory oscillations in the cross sections, attributed to rotational transitions at small impact parameters, provided an estimate of the lower limit for opacity at the glory impact parameter.

Velocity dependence of the cross section for the quenching of Ar(3P0,2) and Kr(3P0,2) by O2

Measurements of the velocity dependence of the absolute cross sections for the quenching of metastable Ar(3P0,2) and Kr(3P0,2) by molecular oxygen were performed using a velocity selected metastable beam and a collision chamber. The Ar(3P0,2)−O2 cross section was equal to 35 Å and was independent of velocity for average relative velocities ḡ = 500–1700 m/sec. The Kr(3P0,2)−O2 cross section decreased as ḡ−1/5 from 500–1200 m/sec with a value of 39.5 Å2 at 600 m/sec. Application of an inhomogeneous magnetic field to the metastable beam showed that the 3P0 cross sections were larger than the 3P2 cross sections by 30 ± 20% and 60 ± 30% for Ar* and Kr*, respectively.

Low-Energy Repulsive Interaction Potential for Helium

New measurements of the integral elastic cross section for a 4He velocity selected supersonic molecular beam scattered by a 4He gas target at 2°K are reported. The structure in the velocity dependent cross section arising from the quantum statistics is well resolved and gives precise information about the weakly repulsive potential at values corresponding to the collision energies (5–30 meV). It is shown that the measured property is insensitive to both the attractive and strongly repulsive parts of the potential. The error in the determination of the potential due to the uncertainty of the velocity selector calibration is discussed. A comparison of the présent data with predictions from recently proposed helium potentials is made, and information on the weakly repulsive interaction obtained from this and other experimental data is summarized.

Neutron flux perturbations due to absorbing foils

An assessment is made of the accuracy of the variational method for calculating neutron reaction rates in plane foils in problems involving velocity-dependent cross sections. This is achieved by using a separable scattering kernel and cross sections which are inversely proportional to velocity, thereby allowing the problem to be solved by analytic methods. We find that the error in the reaction rate, as calculated by the variational method, is at most 7%. This error is an order of magnitude larger than that incurred in one-speed calculations.

Transport of drifting electrons in a gas

An expression given by Hertz for the density of electron flow in a gas under the influence of an electric field is expanded to the case of a velocity-dependent cross section and preferential scattering for elastic collisions by electrons.

Cross Section for Ionization of Alkali Atoms by Collision with Excited Noble Gas Atoms

MHD power generator in which ionization of alkali atoms occurs by collision with excited noble gas atoms, calculating velocity-dependent cross section

Microwave Diagnostics of Plasmas

The theory of wave propagation in plasma media where temperature and collision effects are important is formulated by combining the wave equation and Boltzmann's equation for average electron velocity. Usually it is assumed that the electron collision frequency is independent of velocity, but most gases are characterized by a velocity-dependent collision cross section and the electron collision frequency is velocity dependent. It has been shown that when the velocity dependence of the collision frequency is neglected, electron density predictions are in considerable error. A wave theory which accounts for the velocity-dependent electron collision frequency has been worked out and applied to the measurement of electron density, temperature, and collision frequency in a rocket exhaust plasma.