Motion Of Heavy Particles Research Articles

Semiclassical three-charged-particle system in the framework of the Pechukas self-consistent method.

To describe the rearrangment channels for three-particle atomic reactions and for three-particle muonic processes a semiclassical formalism of the Faddeev-Hahn equations is applied. The relative motion of heavy particles is treated from the classical point of view while the motion of the lighter particle is described from the quantum-mechanical point of view. To find correct trajectories of heavy particles the self-consistent Pechukas method, based on the Feynman path-integral theory, is employed.

Nonadiabatic formulation of the slow-atomic-collision problem in the finite electronic basis.

The resonating-group method developed for nuclear collisions is used to obtain equations describing the collisions of slow atoms. On one hand, these equations correctly take into account the indistinguish- ability of electrons and scattering boundary conditions and therefore are free from the drawbacks of conventional equations in the adiabatic electronic basis. On the other hand, they retain the form of the latter equations and therefore are in agreement with the generally accepted picture of heavy-particle motion in the fields of adiabatic electronic potentials accompanied by nonadiabatic transitions. The general theory is illustrated by considering the interaction of two ground-state hydrogen atoms in the Heitler-London electronic basis.

Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence

The average settling velocity in homogeneous turbulence of a small rigid spherical particle, subject to a Stokes drag force, has been shown to differ from that in still fluid owing to a bias from the particle inertia (Maxey 1987). Previous numerical results for particles in a random flow field, where the flow dynamics were not considered, showed an increase in the average settling velocity. Direct numerical simulations of the motion of heavy particles in isotropic homogeneous turbulence have been performed where the flow dynamics are included. These show that a significant increase in the average settling velocity can occur for particles with inertial response time and still-fluid terminal velocity comparable to the Kolmogorov scales of the turbulence. This increase may be as much as 50% of the terminal velocity, which is much larger than was previously found. The concentration field of the heavy particles, obtained from direct numerical simulations, shows the importance of the inertial bias with particles tending to collect in elongated sheets on the peripheries of local vortical structures. This is coupled then to a preferential sweeping of the particles in downward moving fluid. Again the importance of Kolmogorov scaling to these processes is demonstrated. Finally, some consideration is given to larger particles that are subject to a nonlinear drag force where it is found that the nonlinearity reduces the net increase in settling velocity.

Phase-integral halfway-house variational continuum distorted waves

Symmetric resonant charge transfer in proton-hydrogen collisions is examined theoretically using phase-integral halfway-house variational continuum distorted wave theory. The formulation involves the factorization of the scattering matrix into two Moller matrices, one describing the motion for - infinity <or=t<or=O- and the other the motion for + infinity >or=t>or=O+. The authors use outgoing continuum distorted waves for t(O and incoming continuum distorted waves for t)O with a matching at t=O, the associated heavy particle motion remaining incoming for t(O and outgoing for t)O. Results for total cross sections are presented and compared to previous theoretical models and experimental results. Differential cross sections in the centre-of-mass range 0-3.2 mrad are presented at 25, 60 and 125 keV and are compared with the same theoretical models and previous experimental results.

Lagrangian statistical simulation of the turbulent motion of heavy particles

A Lagrangian stochastic model for the motion of heavy particles has been developed by coupling a stochastic model for the motion of fluid elements to the Stokes equations of motion of a particle in a turbulent flow. The effects of crossing trajectories and continuity are incorporated by generalising Csanady's (1963) ideas developed for stationary homogeneous turbulence; effects of turbulence inhomogeneity and nonstationarity are embodied in the stochastic model for the fluid motion.

Angular distributions for electron capture from He by multiply charged C, N, O, F, and Ne ions.

Angular distributions of the projectile products have been measured for electron capture from He by C, N, O, F, and Ne ions in charge states between 5+ and 8+ at energies ranging from 7.4 to 16 keV. The angular distributions depend in character more on the incident charge state than on ionic species. A strong forward peaking is found for the 5+ and 7+ incident ions, whereas the 6+ ions show a maximum at an angle outside the half-Coulomb scattering angle. Oscillatory structure is seen for ${\mathrm{O}}^{6+}$ on He. The general features of the distributions can be understood on the basis of classical deflection functions for the heavy-particle motion.

Angular distributions of reaction products from low energy capture by multicharged ions

The angular deflection of the projectile which occurs when a slow multiply charged ion captures electrons from a neutral target depends sensitively on the potential curve history of the interaction throughout the encounter. We have measured angular distributions for a variety of projectiles capturing from targets of He, Ar and d 2. Some of the major features may be understood in terms of classical deflection functions for the heavy particle motion. Where quantal treatments of the scattering is available, the calculations are in good agreement with the data.

New oscillatory structure in electron energy spectra from autoionizing quasi-molecules: Subthermal collisions of He(2(3)S) atoms with He(2(1)S,2(3)S) atoms.

We report the first study of the energy spectra of electrons from autoionizing quasimolecules formed at very low collision energies (E${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathrm{rel}=1.6}$ meV). The electron spectra due to ionizing He(${2}^{3}$S)-He(${2}^{3}$S) and He(${2}^{1}$S)-He(${2}^{3}$S) collisions in a single atomic beam show significant structure, which is explained on the basis of accurate new ab initio potentials for the relevant excited states. Fast oscillations due to the interference of incoming and outgoing waves of the heavy-particle motion are observed in both the experimental He(${2}^{3}$S)-He(${2}^{3}$S) spectrum and the corresponding quantum mechanical calculations.

Orientation-dependent scattering of alkali (2P3/2) atoms with mj = +3/2 and mj = -3/2 from rare gas atoms

The scattering of alkali (/sup 2/P/sub 3/2/) atoms with m/sub j/ = +3/2 or -3/2 from atomic rare gas targets shows a left/right asymmetry. The origin of this asymmetry is shown to be due only to different couplings of the orbital angular momenta of the heavy-particle motion. The quantitative variations in the series of measurements with Kr, Ar, and Ne are found to depend on the different ratios of spin-orbit to orbit-axis interactions. Stereospecificity is clearly seen in the particular case of relatively strong spin-orbit interaction only.

Critical test of first-order theories for electron transfer in collisions between multicharged ions and atomic hydrogen: The boundary condition problem.

We have thoroughly investigated electron capture from a hydrogen atom by bare nuclei at intermediate and high energies. The first Born approximation with and without correct boundary conditions is used to compute total cross sections. Both methods possess the same perturbation potential for the reaction under study. The only difference is in the logarithmic phase distortion of the exit channel state due to the long-range Coulomb interaction between the two aggregates. Evidence is presented which substantiates that these Coulomb phases for the relative motion of heavy particles are of paramount importance for an adequate description of charge exchange. The standard Jackson-Schiff approximation which does not consider the boundary condition problem fails completely in comparison with the measurement. In contrast, the first Born approximation with the correct boundary conditions, which takes the asymptotic Coulomb effect into full account, is found to be systematically in excellent agreement with the experimental data for values of the projectile charge ranging from 1 to 6.

Quantal treatment of three-particle break-up: collisional detachment

A full quantum mechanical treatment of three-particle break-up in the negative-ion-atom collision A-+B to A+B+e- is presented. The continuum states of the heavy-particle motion are described as a superposition of the AB relative motion in an arbitrary large box. The double continuum problem is then reduced to a pseudo-associative detachment problem: A-+B to AB( nu )+e-. Results for the detachment probability, as well as a histogram representation of the spectrum of ejected electrons, are presented for a model problem in which the ejected electron has p-wave character. This allows for a discussion of the method as well as of some of the characteristics of this detachment process.

The effect of the electron spin on angular momentum transfer in Na*(32 P 3/2)+Na+ collisions ? crossed beam experiment and semiclassical calculation

The angular momentum transfer between electronic and heavy particle motion has been studied for inelastic collisions of laser state-prepared Na*(32P3/2,MJ) with Na+ leading to Na*(32D) or Na(32S) in the energy rangeEcm=5−47.5 eV. The measurements are compared to semiclassical calculations employing the coupled channel method in the impact parameter approximation but including dynamics of the electron spin coupling to the heavy particle motion.

Excitation process in alkali-atom-He collisions in the keV energy range

The excitation of the ground state to the first excited state of an alkali atom (Li, Na, K, Rb, Cs) by collision with a He atom has been studied theoretically in the low keV collision energy regime. The electron translation factor corrected multichannel perturbed-stationary-state method was used assuming a straight-line trajectory for the heavy-particle motion. The molecular eigenstates and eigenvalues used in these calculations were generated from the l-dependent pseudo-potential method. Eight molecular states for the alkali-atom-He system (five Sigma states plus three Pi states) have been employed in the close-coupling calculations. The results for excitation into the first excited level of the alkali atom, in the LiHe and NaHe systems, show an improved agreement with experimental results, both qualitatively and quantitatively, over all the other available theoretical results. For the KHe system, the result shows a good accord with a peak observed at E approximately=25 keV, while the agreement in the peak at E approximately 3.5 keV is only qualitative.

Σ-Π coherences for resonant charge exchange in Na *(3p) + Na + collisions

The angular momentum transfer between electronic and heavy particle motion has been studied for resonant electron capture at an energy E c.m. = 100 eV in collisions of laser excited Na *(3 2P 3 2 , F = 3, M F = ±3) with Na +. The experimental results are compared to calculations employing a quasiclassical treatment with correct asymptotic conditions assured by a common translation factor and including eight molecular states.

Theory of excitation transfer between Rydberg atoms

A quantal theory of laser-induced Penning and associative ionization is extended to field-free excitation transfer processes between Rydberg atoms, where an appropriate local potential approximation is applied. Formulae for total and differential cross sections are presented. Cross section formulae which are specific to a semiclassical description of the heavy-particle motion are also constructed.

Vertical dispersion of spherical, heavy particles in turbulent open channel flow

The results of an experimental study on the motion of heavy particles (heavierthan water) in an open channel flow over a smooth bed are presented in the paper. Some aspects of the diffusion and dispersion of the particles are analysed and especially the effects of lift force and the quadratic nature of drag forces when present. The results show that for a given fall velocity in still water, the vertical dispersion increases with increase in particle diameter. Measured mean particle downward velocities are lower than the settling velocities in still water.

Modified method of perturbed stationary states. IV. Electron-capture cross sections for the reactionC6++H(1s)→C5+(n,l)+H+

Previously reported ten-state perturbed stationary-state calculations for ${\mathrm{C}}^{6+}\ensuremath{-}\mathrm{H}(1s)$ collisions are extended by increasing the basis to include all molecular states correlating to the principal levels $n=3,4, \mathrm{and} 5$ of the final ${\mathrm{C}}^{5+}(\mathrm{nlm})$ atomic ion. This allows cross sections to be computed for the angular momentum sublevels, $l$, of each of the above $n$. The H-atom energy range extends from 13 eV to 27 keV. Adiabatic calculations are done for energies below 1.3 keV, and partially diabatic calculations are done at higher energies. The inclusion of states with magnetic quantum number $m\ensuremath{\ge}2$ in the new basis leads to significant increases in the $n=5$ capture cross section even at rather low energies. Two translational factors, which depend on the internuclear separation, are employed in the construction of the scattering basis. One is used for the state which correlates to $\mathrm{H}(1s)$; the other is used for all states correlating to states of ${\mathrm{C}}^{5+}$. For purposes of comparison, cross sections are also computed for the same scattering basis, with the use of the method of Bates and McCarroll and the method of Piacentini and Salin. The heavy-particle motion is treated semiclassically, with the use of Riley's average approximation at energies below 1.3 keV and the straight-line impact-parameter method at higher energies. As in the ten-state calculations, it is shown that adiabatic and diabatic formulations lead to rather different values for the cross sections at the higher energies. The results are compared with the experimental and theoretical cross sections obtained by other researchers.

Multichannel Siegert quantization with complex rotated coordinates: Application to molecular resonances

A coupled-channel approach with complex rotated coordinates and boundary conditions identical to those used for bound states is shown to lead to an accurate determination of the widths of resonances in the heavy particle motion of molecular systems.

Theory of near-adiabatic collisions. II. Scattering coordinate method

A rigorously correct and fully quantum-mechanical theory of slow atomic collisions is presented, which removes the formal defects and spurious nonadiabatic couplings of perturbed-stationary-states theory, and arrives at coupled equations for the heavy-particle motion which are the same as those obtained in the preceding paper by the electron translation factor formulation. Here, however, the theory is formulated in terms of suitably defined scattering coordinates, and electron translation factors do not appear. A unified physical interpretation of both approaches can thereby be made, and smaller terms in the coupled equations, describing corrections of order $\frac{m}{\ensuremath{\mu}}$ to electronic binding energies and to the collision kinetic energy, are placed on a firmer footing. Particular attention is paid to the critical test case of isotopic systems such as H${\mathrm{D}}^{+}$ and it is shown how a correct theory of isotopic charge exchange can be formulated.

Oscillations in the cross sections for electronic excitation in heavy particle collisions

The electronic excitation in atom-atom collisions is treated by describing the heavy particle motion in the Born approximation. To deal with the electronic wavefunction it will be in many cases a reasonable first approximation to assume a one-electron model for one atom and keep the other atom in the initial state. In this model the scattering amplitude is shown to depend only on the interaction of this one electron with the target and the form-factor of the respective states. Calculations for this one-electron model are presented, showing an oscillatory behaviour in the integral cross section. These oscillations are due to the electron-target interaction. The results are in good agreement with experimental data.