The generalized antisymmetrized geminal-power (GAGP) function, shown to be the ground state for the oneparticle-hole propagator, can be computed using the rather simple properties of its reduced density matrices and the properties of unitary transformations. The practical procedure involves limited storage notwithstanding the rather large number of configurations with which the GAGP function can be associated. Using the stability properties previously derived for this function, we construct the self-consistent one-particle-hole propagator.

Correlation energy of doublet and triplet electronic states is formulated in terms of many-body diagrammatic perturbation theory through third order. Applications are presented for B${\mathrm{H}}_2$ and N${\mathrm{H}}_2$ radicals and the computed correlation energies are compared with data obtained with the same basis set from configuration-interaction treatments covering singly and doubly excited configurations. It is shown that the two approaches give correlation energies close in absolute value.

Ground-state energy $E$ of a weakly coupled Hamiltonian in two dimensions is analyzed in terms of the zeros of the inverse $T$ matrix, and an explicit series expression for $\ln \mathrm{}(-E)\mathrm{}$ is obtained.

Single-electron-capture cross sections have been measured for argon ions with initial charges $2\le q\le 12$ incident on an argon-gas target. The cross sections show little dependence on the incident ion energy in the range $1q-10q$ keV. A remarkable oscillating feature is seen for cross sections ${\sigma }_{q,q-1\mathrm{}}$ when $q\ge 7$. Particularly, ${\sigma }_{8,7}$ is smaller than ${\sigma }_{7,6}$ and ${\sigma }_{9,8}$, the ${\mathrm{Ar}}^{8+}$ electronic structure being Ne-like. Variation of the cross section is shown as function of the initial charge at constant energy.

The semiquantal treatment of ionization in $A-B\left(n\right)\mathrm{}$ collisions, based on encounters between the Rydberg electron $e$ and incident atom or molecule $A$, is derived from the full quantal impulse approximation. The useful transformation between the dynamical variables natural to these treatments is provided. Various levels of approximation are then deduced and necessary criteria for validity of application of the basic impulse expression to various types of $A-B\left(n\right)\mathrm{}$ processes—ionization, excitation, and quasielastic—in different energy regions are emphasized, including those associated with the additional assumption of "on-the-energy-shell" ($e-A$) encounters. It is pointed out for cases involving quasielastic collisions at thermal energies that models based on ($e-A$) encounters alone may not provide either a full or proper description of the underlying mechanism. A new treatment of (in) elastic transitions via ($A-B^{+}$) encounters at thermal energies and beyond is introduced and formulated. Preliminary assessment indicates that the proposed new mechanism is significant and could well be dominant in quasielastic $A-B\left(n\right)\mathrm{}$ processes.

The collision strengths for atom-atom collisions at high speeds are calculated in the first Born approximation. We studied four classes of collisions, distinguished depending upon whether each of the collision partners becomes excited or not. The results of numerical calculations of the collision strengths are presented for all neutral atoms with $Z\le 18$. The calculations are based on atomic form factors and incoherent scattering functions found in the literature. The relative contribution of each class of collision processes to the total collision cross section is examined in detail. In general, inelastic processes dominate for low-$Z$ atoms, while elastic scattering is more important for large $Z$. Other systematics of the collision strengths are comprehensively discussed. The relevant experimental literature has been surveyed and the results of this work for the three collision systems H-He, He-He, and H-Ar are compared with the data for electron-loss processes. Finally, suggestions are made for future work in measurements of atom-atom and ion-atom collision cross sections.

It is shown that all the previous procedures to include exchange effects in the elastic scattering of electrons by the ground-state hydrogen molecule within the framework of the independent-atom model are improper. The proper way to include exchange has been pointed out. The direct scattering amplitudes for the scattering of electrons by the hydrogenlike atom are obtained in the modified Glauber approximation and by the eikonal Born series method. Exchange scattering amplitude is calculated in the Ochkur approximation. The differential cross sections for the hydrogen molecule are then obtained in the independent-atom model. The results are in very good agreement with the absolute experimental data for impact energies $E\ge 100$ eV.

A method is described for calculating steady-state velocity distribution functions of charged test particles streaming through a one-dimensional slab under the influence of an applied electric field, at the same time undergoing binary collisions with a background gas. By way of combining the method of characteristics with the concept of successive collisions, the partial distribution functions $f_{\nu }$, related to the particles having undergone exactly $\nu$ collisions, can be successively calculated by integrating linear first-order ordinary differential equations. Their sum is the total distribution function satisfying the linear Boltzmann equation. Boundary conditions and strongly nonequilibrium situations can be handled in a natural way, and convergence is inferred from simple physical arguments. As an example of application, a boundary-value problem involving symmetric charge transfer is solved analytically, and a previous result is recovered in the appropriate limit.

The formation of Na ($\mathrm{nl}$) and $\mathrm{Na}_2^{}{}_{}{}^{+}$ in sodium vapor (∼${10}^{13}$ ${\mathrm{cm}}^{-3\mathrm{}}$) irradiated by a single-frequency (20-MHz bandwidth) cw dye laser tuned to one of the $D$ lines has been studied. The dependence of product signal on laser power density suggests that Na $3p$-Na $3p$ energy pooling collisions are responsible for these species. Rate constants for specific reaction channels and temperature dependences of rate constants are also reported.

An interative static-exchange single-center close-coupling procedure is applied to electron collisions with molecular ions. The method is taken mutatus mutandus from a procedure used previously to study electron neutral-molecule collisions. The procedure is found to be both stable and efficient for calculating static-exchange level wave functions and eigenphases. The method is applied to electron collisions with $\mathrm{H}_2^{}{}_{}{}^{+}$, C${\mathrm{H}}^{+}$, and $\mathrm{N}_2^{}{}_{}{}^{+}$. In addition, ro-vibrational-excitation cross sections for $e$ + $\mathrm{H}_2^{}{}_{}{}^{+}$ collisions in the adiabatic nuclei approximation and photoionization cross sections for ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$ are reported.

Earlier derivations of approximations for electron-atom scattering in a low-frequency laser field are generalized to account for the effectively strong interaction of the field with groups of nearly degenerate states of the atomic target. The basis of the derivation is a reformulation of the scattering problem, obtained with the aid of a gauge transformation, which allows one to extract the strong-field effects explicitly in the form of dressed-atom and dressed-electron states. The effects of the weakened residual interaction can then be included in perturbation theory. The result obtained by working to first order in this modified perturbation theory has the simplifying feature that it involves as input the scattering operator in the absence of the field. This first-order approximation is studied in some detail in the dipole approximation, with the final target state taken to be one of a pair of nearly degenerate states.

Equilibrium charge-state fractions for 0.3-10-keV D ions and atoms in cesium-, rubidium-, and sodium-vapor targets are reported. The ${\mathrm{D}}^{-}$ yield from charge transfer in a thick cesium-vapor target exceeds 30 percent at energies below 800 eV. The high ${\mathrm{D}}^{-}$ yield in cesium vapor is consistent with recent calculations of the cross sections ${\sigma }_{0-}$ and ${\sigma }_{-0\mathrm{}}$ at low energies; at energies above 2.5 keV, the ${\mathrm{D}}^{-}$ yield is consistent with our measurements of ${\sigma }_{0-}$ and ${\sigma }_{-0\mathrm{}}$. The ${\mathrm{D}}^{-}$ yield from charge transfer in rubidium vapor is similar to that for cesium vapor. For sodium vapor, however, there is a broad maximum of about 10 percent ${\mathrm{D}}^{-}$ yield at about 3 keV, with slight structure at lower energies, implying structure in one of the charge-transfer cross sections.

The stopping power of matter for alpha particles at extreme relativistic energies has been calculated by incorporating the charge form factor. A table is presented for aluminum, copper, and lead. It is found that at the highest energies considered here, inclusion of form factor reduces the mass stopping power by about 6-8% in comparison with that predicted by Bethe's relativistic formula.

The impact-parameter dependence of molecular-orbital (MO) x rays has been measured as a function of x-ray energy for collisions of 143-MeV Nb ions with Mo. Different shapes for the impact-parameter dependence are found as a function of x-ray energy and are attributed to transitions to vacancies in the $2p\sigma$ and $1s\sigma$ orbitals, $C1\mathrm{}$ and $C2\mathrm{}$ continuum, respectively. $C1\mathrm{}$ MO x-ray emission probabilities were calculated from separately determined $2p\sigma$ vacancy-production probabilities and agree well in magnitude and shape with the measured values.

Integrated and differential cross sections for the excitation of the $b{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state of ${\mathrm{H}}_2$, from the ground state, by electron impact, are presented. The energy range of interest is 10.5 to 40.0 eV. The close-coupling equations for this process are solved in five different exchange approximations: exact two-electron exchange terms, no orthogonality; exact two-electron exchange terms, orthogonality; semiclassical exchange terms, no orthogonality, with barrier term; semiclassical exchange terms, no orthogonality, no barrier term; and semiclassical exchange terms, orthogonality, with barrier term. The purpose is to judge the reliability of the semiclassical exchange approximation for electronic excitation of molecules by electron impact at intermediate energies. The results are compared with recent theoretical estimates for the same process.

An $S$-matrix treatment is given for potential scattering in the presence of a laser radiation field for the case when the collision time is much smaller than the radiation-field period. The resulting Born series has the same analytic structure as the field-free one, but with the free-particle energies and momenta renormalized to incorporate the effect of the field. Different expressions are derived for the transition probability giving the field-free result as a limit and the first laser field-dependent corrections to it. The present treatment clearly implies two distinct time scales: that of the variation of the radiation field, and that of the characteristic time of the quantum system involved in the scattering process. With respect to the first time scale, the collision event is assumed to take place instantaneously; on the contrary, the collision time must be sufficiently large with respect to the second time scale to neglect the effect of the switching on of the interaction. The proper limiting passages are stated to obtain from the Kroll and Watson low-frequency result one of the results derived within the present quasistatic-field approximation.

Total $L$ x-ray production cross sections of Y and Sn and $M$ x-ray production cross sections of Au and Bi for proton impact have been measured over the projectile-energy range 3.0-40 MeV and the ionization cross sections obtained for these shells are compared with calculations of the plane-wave Born approximation and the binary encounter approximation. The inner-shell ionizations by close and distant collisions are theoretically discussed in terms of the generalized oscillator strength and the contributions from these two kinds of collisions are separately estimated in the framework of the plane-wave Born approximation. Distant collisions in this energy region are not so effective as in the case of $K$-shell ionization, while at a very high energy the two kinds of collisions contribute nearly equally to the ionization. The experimental results show good agreement with the plane-wave Born approximation calculation except for the $M$-shell ionization of Bi.

A model calculation of cross sections for inner-shell ionization by electrons is described. This model is based on the classical binary-collision model and modified with the application of several sum rules. It is found that the model predicts quite accurately generalized oscillator strengths and cross sections for inner-shell ionization of atoms. A comparison is made with experiment and other theoretical results.

The Vainshtein-Presnyakov-Sobel'man approximation (VPSA) is extended for heavy projectiles and applied to calculating cross sections for direct excitation of atomic hydrogen by proton and ${\mathrm{He}}^{+}$ impact. The contribution of the projectile-target core interaction to the transition matrix element is included here for the first time. In addition an effective charge $\zeta$ is introduced to minimize the effect of neglecting certain terms in the Schrödinger equation of the collision system; this term-neglecting process is inherent to the VPSA. It is found that the projectile-target core interaction contribution is, as expected for heavy projectiles, small for calculating total cross sections but becomes significant for differential cross sections and increasing scattering angles. Inclusion of the effective charge raises the cross sections at lower-impact energies. The developed formulation is applied to excitation of atomic hydrogen to the $n=2,3,4,\mathrm{and} 5$ levels and comparison is made with the available experimental values for total and differential cross sections. The agreement is very good when the relative velocity is larger than $\sim 0.6v_0(v_0=\alpha c=2.188\mathrm{}\times {10}^{-8\mathrm{}} {\mathrm{cm}\mathrm{s}}^{-1\mathrm{}})$. The present results are also compared with the ones obtained by typical alternative theoretical approaches of varying sophistication.

The response of a collision-broadened gas sample to driving coherent radiation is studied theoretically, taking into account effects of coherent excitations of two or more atoms (or molecules). In analogy to the Bloch-type master equation for one-atom coherences, describing the motion of a single atom "dressed" by the relevant (incident and detected) field modes, a master equation is derived for two-atom coherences, including an effective interaction of the Bethe-Salpeter—type, accounting for the mutual interaction of the coherently driven pair. The master equation includes also all symmetrization effects owing to resonance exchange between identical atoms, and is limited to nonreactive gas atoms (or molecules) undergoing binary collisions, including otherwise all (internal and translational) relaxation effects. The self-energy kernels are expressed in a nonperturbative fashion, in terms of binary-collision scattering amplitudes, and include renormalization effects due to coincidence of radiative couplings with the collisions (optical and radiative collisions). The concept of two-atom coherences is generalized to higher coherence ranks by constructing a hierarchy of master equations, including vertex operators that upgrade or downgrade the coherence rank, as a prelude to a diagrammatic method for calculating continuous-wave spectra. This hierarchy is compared with prevalent Agarwal-type master equations, based on the Dicke pseudospin method, and used in the study of two-level atoms.