Diffusion Cross Sections Research Articles

Ion Mobilities with Charge Exchange

Quantum-mechanical calculations are presented for various elastic cross sections that describe the motion of atomic ions through their parent gases; the effects of nuclear spin are included. The cross sections are linear in the gerade–ungerade pairs of molecular states. An exact relation between the diffusion and charge-exchange cross sections is derived. Detailed calculations are given for the total, charge-exchange, and first three transport cross sections over the energy range of about 10—6–10 eV, for potentials and masses corresponding to He+ in He, and Cs+ in Cs. The cross sections exhibit structure due to orbiting resonances and glory interferences, but the ion mobility depends smoothly on temperature. The semiclassical, impact-parameter, random-phase, and polarization approximations are tested and found to be surprisingly accurate, apart from the quantum-mechanical structure.

Stossfrequenzen der neutralteilchen in wasserstoffund argonplasmen

Abstract The collision frequencies electron-atom, ion-atom and atom-atom are calculated in the temperature range 0.1 eV to 10 eV. The used diffusion cross sections are taken from both experimental and theoretical sources.

Elastic scattering of Li+by He

A linear combination of atomic orbitals-self-consistent field- molecular orbital (LCAO-SCF-MO) calculation of the interaction potential of the ground state of LiHe+ is reported, and the results compared with other quantal calculations and with semi-empirical potentials. The potential is used to investigate the elastic scattering of Li+ by He. Values of the differential cross section I( theta ), the cross section for scattering through an angle theta > theta 0, S( theta 0), total elastic cross section Qel(k2), diffusion cross section QD(k2) and mobility K(T) are obtained and compared with experiment. Excellent agreement is obtained except for I( theta ), theta cm >70 degrees . Orbiting occurs at k=0.03 (l=2) and k=0.34 (l=7). Seven non-orbiting oscillations are found in Qel(k2), and seven bound vibrational states are predicted.

A phase-shift analysis of electron-helium scattering: I - Elastic scattering below the 2S resonance

A phase-shift analysis of electron-helium elastic scattering in the energy range 31 to 191 ev has been made. s- and p-wave phase shifts consistent with the dispersion relation and with experimental information on the total elastic scattering cross section, the diffusion cross section and recent measurements of the differential cross section, to within 5% are obtained. The Gibson-Dolder measurements of the differential scattering cross section are shown to be theoretically preferable to the earlier measurements of Ramsauer and Kollath. The d-wave phase shift cannot be determined to better than 25% by available experimental information. The phase shifts obtained are consistent with, but do not distinguish between, recent non-adiabatic theoretical calculations, but exclude the simple polarized orbital model. They satisfy Spruch bounds based on the experimental polarizability and yield a scattering length of 11a0 in agreement with other determinations.

Charge-transfer cross sections and mobilities for Hg+ ions in atomic mercury

By treating the mercury atomic ion and the mercury atom as one-electron and two-electron systems respectively, and employing the Coulomb approximation to derive the atomic orbitals, the interaction energies between a Hg+ ion and a Hg atom at large nuclear separations have been calculated for the 2Σu ground state and the 2Σg repulsive state of the Hg2+ molecular ion. These interaction energies have then been used to calculate semi-classical approximation phase shifts for the elastic scattering of Hg+ ions by Hg atoms, from which resonance charge-transfer and diffusion cross sections have been derived. Comparison is made with the results of calculations employing cruder approximations and with the rather meagre experimental data on charge transfer. Finally, the diffusion cross sections have been used to calculate the mobility of Hg+ ions in atomic mercury as a function of temperature. The theoretical mobility curve corresponding to the Coulomb approximation atomic orbitals lies somewhat above the rather uncertain experimental data.

Mobility and diffusion cross section of atomic xenon ion in xenon

An x-band microwave cavity method has been employed to study the decay of electron density in low gas pressures of very pure xenon. The main electron loss process in the late afterglow is via ambipolar diffusion affected by diffusion cooling of electrons. Extrapolation to zero pressure yields a value of (054 ± 003) cm2 v-1 s-1 for the mobility of Xe+ diffusing in xenon at 295 °K, in good agreement with previous work. A value of 246 × 10-14 cm2 is deduced for the diffusion cross section, in reasonable agreement with a theoretically calculated value.

The lifetime and effective quenching cross section of the 6 2P[formula omitted] state of thallium

The lifetime of the 6 2 P 3 2 metastable state of thallium has been measured at 15 different thallium densities and temperatures in the after-glow of a pulsed r-f discharge. The effective self-quenching cross section for the 6 2 P 3 2 -6 2 P 1 2 transition is 5·4±0·5 x 10 -16 cm 2, and the diffusion cross section for the 6 2 P 3 2 state is 100±30 x 10 -16 cm 2.

Application of Wagner's pellet method in investigating the mechanism of formation of heterophasic two-layer scales on alloys

Investigations were carried out on a model system Ag-Zn-S and consisted of determinations of kinetic data, and distribution of the chemical potential of silver in the scale, as well as the amount of inward diffusion of sulfur in the formation of two-layer scales on binary alloys. The chemical potential of silver was measured with AgI as a solid electrolyte and the diffusion of sulfur with the aid of the radioactive isotope35S. The inner layer consisted of pellets of Ag2S+ZnS mixtures having different degrees of dispersion and of mixtures of Ag2S and powdered foam glass. The investigations were carried out on the following systems: Ag-Ag2S-S; Ag-Ag2S+ ZnS-Ag2S-S; Ag-Ag2S+ glass-Ag2S-S; (Ag-Zn)-Ag2S-S. It was established that the ability of dispersed ZnS to decrease the rate can be explained on the basis of a decreasing cross section for the outward diffusion of silver ions in the inner layer. This phase makes the plastic flow of the scale toward the core very difficult. As a result of this, the secondary dissociation processes destroy the compactness of the scale over the whole cross section and favor the inward diffusion of sulfur. The chemical potential varies linearly across each layer.

Rotational Excitation of Polar Molecules by Electrons

Rotational excitation of polar molecules is calculated in the approximation that the electron transit time is short compared with rotational periods with the result of an ${E}^{\ensuremath{-}1}$ behavior of the cross section. Diffusion cross sections are calculated for $\ensuremath{\Delta}l=0,1,2$. Significant corrections to the Born approximation are obtained for large dipole moments. The range (in energy) of applicability of the result is discussed in terms of the energy dependence of the corrections, and a novel energy dependence of these corrections is encountered and explained.

Diffusion ofHe(2S13)in Helium Gas;2S13−1S01Interaction Potentials at Long Range

The existence at intermediate separations of a repulsive barrier in the interaction potentials between a $\mathrm{He}(2^{3}S_{1})$ metastable atom and a $\mathrm{He}(1^{1}S_{0})$ ground-state atom has been well established both experimentally and theoretically. The present investigation deals with the quantitative nature of this repulsive interaction for large internuclear separations. The diffusion coefficient, and thus the diffusion cross section, for $\mathrm{He}(2^{3}S_{1})$ atoms in helium gas has been measured over the temperature range from 1 to 300\ifmmode^\circ\else\textdegree\fi{}K by means of a pulsed afterglow technique. The diffusion cross sections so determined are 82, 58, 46, and 34 (${10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$) \ifmmode\pm\else\textpm\fi{}5% at 4.2, 20, 77, and 300\ifmmode^\circ\else\textdegree\fi{}K, respectively. For purposes of comparison, diffusion cross sections were also calculated quantum mechanically using adjustable long-range potentials of a form consistent with previous theoretical calculations. A comparison of the calculated and measured diffusion cross sections clearly indicates that the previous theoretically determined interaction potentials are much too strongly repulsive at large internuclear separations. Accordingly the parameters in the adjustable potentials were varied until agreement with the experimental diffusion cross sections was obtained. The adjusted interaction potentials were then used to calculate total and excitation transfer cross sections, and the results are shown to be in excellent agreement with previous and independent experimental measurements.

The mobility of He+ ions in He

The total, charge-transfer, diffusion and viscosity cross sections for He+ in He are calculated using numerically integrated phase shifts and term by term summations. The calculated mobility is in harmony with recent measurements. The corrections to the usual mobility expression are evaluated and found to be negligible. The average behaviour of the total cross section is satisfactorily described by the Schiff-Landau-Lifshitz approximation.

Diffuse Elastic Neutron Cross Section for an Impurity in a Heisenberg Antiferromagnet

Spin-wave theory of a Heisenberg antiferromagnet predicts a zero-point spin deviation η from the assumed ground state, namely, the Néel state. Measurements of η using NMR in a number of compounds give values substantially smaller than that given by spin-wave theory. The object of this paper is to present the theory necessary to allow the measurement of η by magnetic scattering of thermal neutrons from an antiferromagnet containing a weak concentration c of nonmagnetic impurities. The diffuse elastic cross section for such a system is dσ/dΩ=(γe2/2mc2)2(1−̂z2)Nc(1−c)F2(κ) 〈Sz〉2 | Q(κ−τ) | 2,where 〈Sz〉 is the thermal average of the unperturbed host spins, Q(κ) the Fourier transform of the deviations in the z components of spin from 〈Sz〉 due to an impurity and all other symbols have their usual meaning. It is evident that η may be measured provided Q(κ) is known. We have calculated Q(0) for a body centered antiferromagnet of arbitrary spin in the linear spin-wave approximation. This has been achieved using thermal Green functions which also permits the dynamics of the system to be investigated.

Spin-wave theory of impurity states in a Heisenberg antiferromagnet II. Negative impurity-host exchange coupling

In a previous paper we discussed the energy modes of a magnetic impurity with positive impurity-host exchange in an antiferromagnet. This was achieved by deriving the appropriate thermal two-time Green functions from which both the impurity states and inelastic neutron cross section were calculated. In this paper we follow essentially the same scheme to discuss the case of a negative impurity-host exchange coupling. The p-, d- and f-type modes remain the same but only one s-like mode occurs as opposed to two in the previous case. We give the energies and widths of this s mode for a wide range of the perturbation parameters. The diffuse inelastic neutron cross section is also calculated. This has exactly the same form as for an `antiferromagnetic impurity' in a ferromagnet but does not have the same energy behaviour because of the difference in the spin-wave spectra of the ferromagnetic and antiferromagnetic hosts.

Theory of the night-time F-layer

The behaviour of the night-time F-layer, as it appears from the quantities h m , Y m and N m (height of the F-layer maximum, layer thickness and maximum electron concentration), can be interpreted by electron losses, ambipolar diffusion and plasma drifts caused by electric fields in W-E and in N-S direction. The electric fields must be of the order of 5–10 V/km, if the loss coefficient and the ambipolar diffusion constant are chosen in accordance with laboratory measurements of the reaction rate for O + + N 2 → NO + + N and of the diffusion cross section for O + in O. The theoretical method which gives these results proceeds from the time-dependent continuity equation and the appropriate equations of motion for the electrons, ions and neutral particles which form a system of coupled partial differential equations. This system is solved numerically by means of an electronic computer.

Form of Inelastic Transport Cross Sections

Abstract

Classical scattering of an atom from an asymmetric molecule

Using the methods of classical mechanics, we have calculated the cross sections for inelastic scattering of an atom 4He, in collisions with a diatomic rigid rotator HT. The molecule has an asymmetric mass distribution, and as a consequence, a rotating potential model was introduced. This involves a potential field spherically symmetrical about the geometrical midpoint of the molecule which rotates around its centre of mass. The results show large deviations from the cross sections obtained with a simple spherical potential. These deviations depend strongly on the orientation and the angular momentum J of the molecule. An analysis of the effect of the space orientation of J reveals a considerable polarization of the deviations of the cross sections. A reasonable approximation to an orientation averaged cross section can be obtained by taking the positions of J perpendicular to the collision plane as representative, which permits simplification to a two-dimensional collision calculation. There is a positive increase in the diffusion cross section which can be as much as 20% for low relative velocities and high angular momentum values. It is possible to calculate the probability for change of the rotational state, showing how correctly a calculation based on classical mechanics can describe a quantum phenomenon. The new calculations predict an increase in the transition probabilities from 10 -3 to about 5·10 -2. This is in accordance with the value expected from experiments.

Distribution of magnetization in mixed magnetic systems: III. Magnetic impurity

In two previous papers the distribution of magnetization about a non-magnetic impurity in a Heisenberg ferromagnetic or antiferromagnetic host was considered in the molecular field approximation. The present paper is concerned with a magnetic impurity within essentially the same theory. The magnetic moments associated with the impurity and its first neighbours are calculated as functions of temperature and impurity-host exchange coupling for arbitrary impurity and host spins. Numerical results are presented for several systems. The moments calculated for a simple cubic lattice with a spin ½ impurity and host are compared with the corresponding results from a Green function calculation by Wolfram and Hall. The spatial extent of the moment disturbance on the host is investigated. The elastic diffuse neutron cross section for the system is fully discussed as a function of impurity-host exchange coupling, reduced temperature and scattering vector.

Определение отношения коэффициентов диффузии и подвижности электронов в случае благородных газов

Taking elastic scattering into consideration, but neglecting inelastic collision, with the application of the Boltzmann transport equation the equilibrum distribution function of electrons has been calculated with a view to determine the energy dependence of the diffusion cross section. In the knowledge of the equilibrium distribution function the ratioD/μ of diffusion coefficient to mobility was determined. In the case of very low electric field strength the calculated equilibrium distribution function gives the Maxwell-Boltzmann distribution andD/μ=kT/e. With increasing electric field strength the equilibrium distribution function passes through an intermediate distribution and finally gives the distribution calculated byMorse, Allis andLamar. The ratioD/μ increases with the electric field strength. With the assumption of a diffusion cross section independent from energy in the case of higher electric field strengths the ratio increases linearly with the field strength. The results have been applied to the calculation of the dependence of the ratioD/μ on electric field strength for helium and neon gases. The results have been compared with measured data.

Comparison of Low-Energy Total and Momentum-Transfer Scattering Cross Sections for Electrons on Helium and Argon

Modified effective-range theory has allowed an unambiguous extrapolation of recent total electron-atom and -molecule scattering cross sections to zero energy. This extrapolation completely determines the differential scattering cross section and therefore the momentum transfer or diffusion cross section for the range of applicability of the effective-range theory. Calculations of momentum-transfer cross sections derived from the total cross-section data of Golden and Bandel for the cases of He and Ar are presented and discussed. It is shown that diffusion cross sections obtained by unfolding swarm experiment data are inconsistent with diffusion cross sections obtained from total cross-section data using effective-range theory.

Effect of Resonant Charge Exchange on Heat Conduction in Plasmas

Estimates are made of cross sections for symmetric resonant charge exchange between ions differing by one electronic charge. At thermal energies and electron densities of interest, these cross sections are negligible compared to the elastic screened Coulomb cross section for diffusion. It is concluded that resonant charge exchange between ions cannot affect heat conduction in plasmas by controlling the rate of diffusive transport of ionization energy, in contrast to ion-neutral exchange in partially ionized gases.