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The authors have performed systematic quantal calculations of Ar-Ar elastic scattering events using accurate pair potentials. Specifically, they have calculated a large number of partial wave phaseshifts, total cross sections and resonance energies over a range covering most of the glory region. The cross sections from two accurate potentials are compared over one glory oscillation and over a region including several shape resonances. The resonance energies obtained from these two potentials also are compared. The authors discuss the inappropriateness of using Levinson's theorem to define the absolute scale of the phaseshifts for realistic atomic potentials. As an alternative, the authors define an 'absolute phaseshift' that explicitly accounts for the difference in phase between the true wavefunction and its free particle counterpart.

Cross sections and polarizations of impact radiation have been calculated for 2s to 2p excitation of Li in collisions with He and Ne, and for 3s to 3p excitation of Na in collisions with He and Ne, for the (centre-of-mass) energy ranges ECM=0.2-100 keV (Li/Na-He), ECM=0.7-100 keV (Li-Ne) and ECM=1-100 keV (Na-Ne). The calculations have been based on three-state one-centre expansions of the electronic states, 2s, 2p0 and 2p+or-1 in the case of Li-He/Ne collisions, and 3s, 3p0 and 3p+or-1 in the case of Na-He/Ne collisions. For Li-He/Ne collisions a study of excitation cross sections and of polarizations of emissions calculated for two Baylis model potentials, two Bottcher-type model potentials and a Hartree-Fock frozen-core potential is reported. For Na-He/Ne collisions the results obtained by the Baylis model potential are reported.

The results of a combined experimental and theoretical investigation of the excitation processes in Li-He collisions in the 1-100 keV energy range are presented. Experimentally the emission cross sections have been measured for the two lowest members of each of the 22S-n2P, 22P-n2S and 22P-n2D Li I Rydberg series, which are the strongest optical transitions observed. Due to the long lifetimes of the higher excited levels of the projectile the problem of radiation equilibrium in the collision cell requires attention. Theoretically, the collision has been treated as a quasi-one-electron system and close-coupling solutions to the impact-parameter equations have been obtained, using the (2s, 2p0, 2p+or-1, 3s, 3p0, 3p+or-1, 3d0, 3d+or-1, 3d+or-2) basis. A Hartree-Fock frozen-core potential has been used to describe the direct electrostatic interaction between the Li valence electron and the helium atom.

We extend the linear response-like derivation of the generalized Navier-Stokes equation to non-Newtonian flows with rate of strain-dependent transport coefficients. We derive a time correlation function expression for the viscosity tensor and point out possible ambiguities in the operational definitions of viscosity coefficients. Our analysis is specific to a suspension of polar, rod-like ferromagnetic particles. A commentary is included about the approximations that lead from the time correlation function and the molecular definition of the viscosity tensor to the standard, Brownian dynamics model used in the theoretical rheology of suspensions. Some theoretical difficulties and logical inconsistencies are pointed out. Preliminary results for the transport coefficients of dilute suspension of magnetic rod-like particles are presented.

An extension of the linear transport laws is derived from first principles of statistical mechanics. The resulting transport laws include both relaxation and nonlinear terms. It is found when these terms are included the Onsager reciprocal relations are no longer valid. Therefore, the development gives the limit of validity of the Onsager relations, as well as expressing the transport coefficients as correlation functions of the dynamical variables. In order to show the validity of the procedure used, a functional integral is derived as a first-order approximation for the transition probability. This integral when evaluated verifies the assumption of Onsager and Machlup for the transition probability for the linear transport laws.

For pt.I see ibid., vol.8, p.460 (1975). Cross sections for the transfer ionization process, He++Mg to He+Mg2++e, have been calculated using several different approximations for the wavefunction of the initial electronic state. The first was a frozen-orbital calculation using molecular orbitals associated with the neutral diatomic species HeMg. The second was a quasi-stabilization calculation involving configuration interaction among several frozen-orbital-type states. The final calculation used the hole-state model of Schwartz (1970) and of Bagus and Schaefer (1971). A critical analysis is made of these three methods and estimates provided for their conditions of applicability. Specifically, the results lead us to question whether the hole-state model is appropriate at all to this system.

A two-electron model of direct excitation in Li-Na collisions is developed, based upon one-electron eigenstates of the separated atoms. A valence-bond-type two-electron atomic basis, antisymmetrised and modified by the translational phase factors, is used in the expansion of the electronic scattering state. The time-dependent Schrodinger equation is solved by the impact parameter method assuming a rectilinear trajectory and constant relative velocity of the alkali cores. Solutions of the resulting close-coupled equations have been obtained in the high-energy limit which defines a model with complete neglect of exchange contributions. Various sets of basis functions, Li(2s/2p)Na(3s/3p), involving single and/or double (simultaneous) excitation of the alkali atoms have been used. The aim was to obtain first estimates of Li(2p) and Na(3p) excitation cross sections and polarisations as functions of collision energy and to probe the details of the direct-excitation mechanism. The single-excitation predictions match recent experimental cross sections at 50-60 keV centre-of-mass energy. The double-excitation contributions are significant but the present calculations tend to overemphasize their importance. Excitation out of the collision plane, an allowed two-electron excitation process, is important at centre-of-mass energies above 100 keV.

For pt.I see ibid., vol.11, no.13, p.2377 (1978). Regional wavefunctions of the type proposed by Rudge have been used to construct estimates of the integral and differential cross sections for the parity-unfavoured 1Sg to 3Pg and 1Sg to 1,3Du transitions of helium. Both single- and multi-configurational ground-state wavefunctions are tested. Results obtained by using the Born-Oppenheimer approximation are found to be quite insensitive to the choice of ground-state wavefunction. Cross sections computed in this way are similar to previous Born-Oppenheimer results based on conventional continuous wavefunctions for the target states. However, calculations based on the Rudge variation principle are found to depend very sensitively on the choice of target wavefunction and to exhibit several other unexpected characteristics.

Integral and differential cross sections for the parity-unfavoured excitations of the 3Pg and 1,3Du states of helium have been calculated using the Born-Oppenheimer approximation for the scattering amplitude and a variety of estimates for the ground-state wavefunction of the helium atom. These cross sections are found to be much more sensitive to the choice of target wavefunction than single-excitation cross sections which previously have been investigated. Thus, the integral cross section for excitation of the 3Pg state is only half as large when calculated with a 35-term CI helium ground-state wavefunction as with a Hartree-Fock function.

For pt.I see ibid., vol.9, p/L403 (1976). In part I the authors incorrectly stated the asymptotic conditions on the wavefunctions of the classical trajectory theory and also erred in describing the consequences of time-reversal invariance of the choice of integration constants (and limits of integration) associated with the phases of these wavefunctions. These errors are corrected and it is shown that there are many phase factors which yield integral and differential cross sections that are identical with those calculated on the basis of the Bates and McCarroll (1958, 1962) 'travelling-wave phase factors'.

The rheological properties of dilute solutions of rod-like macromolecules are treated on the basis of a new model of macroparticle dynamics. Calculations are presented of the rigidity modulus, the shear viscosity, and the first and second normal stresses.

A theoretical investigation has been conducted to the exothermic transfer ionization reaction, He++Mg to He+Mg2++e-. The mechanisms assumed is autoionization of the diatomic ion HeMg+. To compute the potential energy curves and autoionization width descriptive of this process, Hartree-Fock single-configuration electronic wave-functions have been constructed for the initial discrete state, He+-Mg, and for the final continuum state, He-Mg+2-e-. As the internuclear separation varies from 3 to 5 bohr, the lifetime for autoionization grows from 8.75*10-14 to 3.2*10-13 s. The cross section for transfer ionization has been computed according to Miller's classical trajectory theory of Penning ionization. This cross section reaches a maximum value of 12.9 a02 for a collision energy equal to 1 hartree. Because of the inadequacy of our approximate potential energy function for the initial state, the theoretical cross section the authors have computed here is believed to be unreliable for energies less than this value.

Excitation probabilities P(b,E) and the coherence parameters, lambda (b,E) and chi (b,E) have been calculated for 2S to 2P excitation of Be+(2s) and Mg+(3s) ions in collisions with ground-state He and Ne atom targets in the energy range ECM=0.5-100 keV and the impact parameter range b=0.1-5.0 au. Each ion-atom pair has been treated as a quasi-one-electron three-particle system consisting of the valence electron of the ion, the closed-shell ion core, and the closed-shell rare-gas atom. Close-coupled equations, based upon a rectilinear trajectory, have been solved for the amplitudes associated with a three-state (ns, np0, np1) one-centre expansion of the electronic wavefunction. A Hellmann-type pseudopotential has been used for the electron-ion core interaction; for the electron-rare-gas interaction an electrostatic model was chosen. The theory predicts that high energies and/or large impact parameters lambda will tend to zero and chi to tau /2. For finite energies (impact parameters) the function lambda (b) ( lambda (E)) exhibits pronounced oscillations which correlate with rapid changes (phase jump mod Delta chi mod approximately= pi ) of the phase angle chi (b) ( chi (E)).

The authors present an investigation of collisional excitations in systems characterised by the presence of two valence electrons localised outside closed shells in the energy range 1-300 keV. Two types of systems have been studied: (i) systems such as Mg-rare gases with both valence electrons localised on the projectile, and (ii) systems such as Li, K-Na with one valence electron localised on the projectile and one on the target. Experimentally, the total emission cross sections and polarisations have been measured for the Mg I 31S-31P, 33P-43S, s3P-33D, 33P-3p2 3P, Li I 22S-22P, Na I 32S-32P and K I 42S-42P transitions. The content metastable Mg(3s3p3P) atoms in the applied neutral Mg beams has been determined by means of an optical method based on the Wigner spin conservation rule in low-energy atomic collisions. The Mg(3s2)-He collision has been examined theoretically using a Hartree-Fock frozen-core potential to describe the interaction between the Mg valence electrons and the He atom.

A new derivation is presented of the properties of the travelling wave phase factors which are important in the semi-classical theory of high energy charge exchange processes. In the case of a rectilinear, constant velocity trajectory the phases obtained are those required by the Galilean invariance of the non-relativistic Schrodinger operator. For an arbitrary trajectory this invariance is not maintained and so there appear in the Schrodinger operator compensating terms which cannot be transformed away by a change of phase.

The memory function formulation of the time‐dependent Schrodinger equation is used to analyze the internal state problem associated with the decoupled motions or impact parameter approximation to binary collisional events. The exact, time‐orderd memory functions are then replaced with their time‐disordered counterparts. This generates a unitary approximation to the collision problem as well as simple, easily interpretable formulas for the transition probabilities. Two specific examples are considered in detail, namely, (i) the three‐state resonant transfer model and (ii) a ’’paired‐states’’ model for the dynamics of a many‐state problem.

Collision-induced coherent S to D excitation is investigated. A polarisation analysis of the subsequent D to P transition by the photon-particle coincidence method is not sufficient to completely determine the excitation amplitudes for the D state. Two distinct solutions are obtained. The electron distributions associated with these two are mirror images of one another in the plane determined by the normal to the scattering plane and the direction of maximum intensity of linearly polarised light, as measured from the direction of the normal. The Li(2s to 3d) excitation induced by collisions with helium is studied both theoretically and experimentally in the keV energy range. The measurements confirm the existence of a theoretically predicted low-energy structure in the circular polarisation. The results are interpreted by generalising concepts previously developed for S to P excitation in quasi-one-electron systems.

Using the interaction picture, formal time dependent solutions of the Zwanzig-Feshbach projection operator method are derived which involve a nonunitary time-ordered memory operator. The familiar approximation which leads to a decoupling of the translational and internal motions in terms of a classical trajectory is derived by a systematic procedure which emphasises the generators of observable (operator) motion rather than the generators of wavefunction motion. Two-state approximations to this decoupled system are considered. These depend upon different approximations to the memory operator. Neglect of the memory operator together with the use of the stationary phase method produces the Landau-Zener approximation. Two extensions of this approximation are considered which depend upon different time disordered approximations to the two-state memory operator. Treating the continuum as a single state gives the bound-to-continuum analogues of these approximations.

Cross sections and polarization of emission have been calculated for the excitation of ground-state ions in collision with rare gas atom targets in the energy range ECM=1-100 keV. Each ion-atom pair has been treated as a quasi-one-electron system, the interaction of the valence electron of the ion with the closed-shell ion core and with the rare gas atom being represented by semi-empirical model potentials. Close-coupling solutions to the impact-parameter equations have been obtained. The calculations for Be+ excitation are based upon the three states of the ion valence shell, 2s, 2p0 and 2p1, and those for Mg+ excitation upon the six states of the ion valence shell, 3s, 3p0, 3p1, 3d0, 3d1 and 3d2, and the energetically similar 4s state. Characteristic features of the predicted excitation cross sections and the polarization of emission are in agreement with the experimental results of Andersen et al. (1976).

Calculations are reported of matrix elements of the Baylis-Gombas model potential for Li-He and Li-Ne interactions. Included are comparisons of two computational approaches, one based upon a numerical double-integration procedure, the other an analytical, approximative method. The special emphasis of the calculation is the sensitivity of matrix elements that are important for collision-induced electronic transitions to the precise choice of the Baylis model parameter r0. Also reported and compared to the Baylis results are calculations of Li-He/Ne matrix elements for a Hartree-Fock frozen-core model potential and for two Bottcher-type model potentials.

General formulas have been derived for the molecular friction coefficients of a dilute gas. The velocity and temperature dependencies of these coefficients are examined in detail for several choices of the pair interaction potential. Also we have considered the frictional loss of kinetic energy and, for one special case, the dissipation of molecular internal angular momentum. The concepts of free path length and collision frequency are extended to nonrigid molecular models.

The ions Ar2+, Ne2+, and He2+ are formed in a mass spectrometer operated at high pressures (up to 300 μ) by the bimolecular excited atom reaction R*+R=R2++e, and Ar2+ and Ne2+ are formed by the termolecular ion‐molecule reaction R++2R=R2++R. In helium, while He2+ is formed by a third‐order process, there is doubt that an ionic reaction is involved.Ratios of the rates (cross‐sections) for excitation leading to R2+ formation and ionization are found to be 5.5×10—2, 1.0×10—2, and 6.4×10—2 for argon, neon, and helium. The measurements were made at nominal electron voltages (EV) of 15, 20, and 22 v, respectively, which correspond to maximum excitation. Values of 1.4×10—2 and 0.45×10—2 were also obtained at EV=70 v for argon and neon.The experiments yield only the product of the bimolecular rate constant and the lifetime of the R* reactant atom (krτu), and the values of this product obtained at EV=15, 20, and 22 v are for argon, neon, and helium 3.6×10—16, 11.6×10—16, and 0.58×10—16 cc/molecule. At EV=70 v valu...

The equations of change for the statistical distribution functions involved in the kinetic theory are examined for molecular species which interact with arbitrary central forces. It is shown that the notion of inverse encounters follows in a straightforward fashion from the fundamental Liouville equation. The analysis also establishes that it is not the usual singlet distribution function, but a particular modification thereof, which should satisfy an equation of the Boltzmann variety. Three body collision processes are briefly examined and the extension of the method to the domain of chemical kinetics discussed.

Classical continuum theory is generalized to provide a systematic procedure for treating in successively greater detail the macroscopic manifestations of subcontinuum events without sacrificing the convenience of the field approach. The point of departure from traditional theory is the general angular momentum principle for continua. Internal angular momentum is associated with configurational and kinematic structure of the continuum ‘particle' and that structure is represented by moment expansions in polyadic polarization densities. Each step in the theoretical development is analyzed both in terms of the statistical mechanics of polyatomic media and from the standpoint of continuum physics. Accurate accounting of content and flux is found to require introducing the concepts of proper densities and currents. Among topics examined in detail are asymmetric states of stress, equations of change for dynamical variables, and equilibrium conditions in structured continua, including alinement of internal angular momentum with the principle axes of local mass distributions.

The methods of Prigogine and Resibois are used to construct a description of classical two‐body scattering events which bears a close formal analogy to that of time‐dependent quantum‐scattering theory. It is shown how the distribution in phase space evolves after long times into a steady‐state scattering form, from which expressions for cross sections and transition rates are obtained by means similar to those of the quantum‐mechanical treatment. These expressions are shown to be equivalent to the conventional classical formulas but offer in principle alternative means of evaluation.