Absolute and relative cross sections were obtained for the charge-transfer reaction ${\mathrm{He}}^{+}\mathrm{}\left(1S\right)+{\mathrm{Ne}}^{*}\to {\mathrm{He}}^{‡}+{\mathrm{Ne}}^{+}$. The Ne* represents a composite of $\mathrm{Ne}\left(3s{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)$ and $\mathrm{Ne}\left(3s{}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}\right)$, and the He‡ represents various excited states of He. The studies were made by a merging-beams technique for a relative kinetic energy $W$ of the reactants from 0.1 to 500 eV. The data indicate that the reaction is directed with most of the product ${\mathrm{Ne}}^{+}$ scattered in the direction of the reactant Ne*. The cross section monotonically increases with $W$. The threshold for the reaction is near 0.1 eV. A modified Demkov approach is used to calculate cross sections, which agree very roughly with the experimental values above $W\approx 3$ eV. At lower $W$ the agreement is poor.

Coupled-state calculations of proton—hydrogen-atom scattering using a scaled hydrogenic basis set have been performed, and the results are reported on in this paper. Thirty-five basis functions, centered about each proton, were included in the expansion of the electron wave function. Cross sections for direct excitation and charge transfer to the $n=1, 2, \mathrm{and} 3$ levels, and for ionization, have been calculated. The results for ionization indicate that charge transfer to the continuum dominates over direct ionization at proton energies below about 60 keV. The charge distribution has been plotted as a function of time at an energy of 40 keV and impact parameter of 1.5 a.u.; the plot illustrates the considerable distortion of the electron cloud caused by the passing proton.

The method of polarized orbitals is modified to treat low-energy scattering of electrons from highly polarizable systems, specifically alkali-metal atoms. The modification is carried out in the particular context of the $e$-Li system, but the procedure is general; it consists of modifying the polarized orbital, so that when used in the otherwise orthodox form of the method, it gives (i) the correct electron affinity of the negative ion (in this case ${\mathrm{Li}}^{-}$), (ii) the proper (i.e., Levinson-Swan) number of nodes of the associated zero-energy scattering orbital, and (iii) the correct polarizability. A procedure is devised whereby the scattering length can be calculated from the (known) electron affinity without solving the bound-state equation. Using this procedure we adduce a ${}_{}{}^1{}_{}{}^{}S$ scattering length of $8.69a_0$. (The ${}_{}{}^3{}_{}{}^{}S$ scattering length is $-9.22\mathrm{}{a}_0$.) The above modifications can also be carried out in the (lesser) exchange adiabatic approximation. However, they lead to qualitatively incorrect ${}_{}{}^3{}_{}{}^{}S$ phase shifts. The modified polarized-orbital phase shifts are qualitatively similar to close-coupling and elaborate variational calculations. Quantitative differences from the latter calculations, however, remain; they are manifested most noticeably in the very-low-energy total and differential spin-flip cross sections.

New $K$-shell ionization cross sections are presented for symmetric and near-symmetric heavy-ion-atom single collisions $Z_1\to Z_2$, with $16\le (Z_1, Z_2)\le 54$ and $0.4\le E_1\le 225$ MeV. For $0.6\lesssim Q\lesssim 1$, where $Q=\frac{Z_L}{Z_H}$, all data are unified by a simple scaling law, parametrized through the united-atom $2p_{\frac{1}{2}}$ binding energy. Existing models for $K$-vacancy production are shown to be inadequate.

Single-electron capture and ionization cross sections have been calculated for collisions of ${\mathrm{He}}^{2+}$ with Li over the relative collision velocity range 0.1-10.0 × ${10}^8$ cm/sec. For low collision velocities (i.e., $v=0.1-0.6\mathrm{}\times {10}^8$ cm/sec), a molecular approach has been used to determine the electron-capture cross section. Ab initio potential-energy curves and coupling matrix elements have been computed for the ${\mathrm{}\left(\mathrm{HeLi}\right)\mathrm{}}^{2+}$ system and used in a cross-section evaluation based on the perturbed-stationary-state method. For the low velocities, the electron-capture reaction ${\mathrm{He}}^{2+}+\mathrm{Li}\to {\mathrm{He}}^{+}\mathrm{}\left(3l\right)+{\mathrm{Li}}^{+}$ is found to dominate the collision process, and proceeds with a large cross section $\sigma \approx {10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$, thus providing the possibility for population inversion and the subsequent emission of Lyman-$\alpha$ (304 Å) and Lyman-$\beta$ (256 Å) soft-x-ray photons. At the higher velocities (i.e., $v=1.4-10.0\mathrm{}\times {10}^8$ cm/sec), a classical-trajectory Monte Carlo method has been used to estimate both the electron-capture and ionization cross sections. At 2.2 × ${10}^8$ cm/sec, both cross sections are found to be equal, while one ionization dominates the collisions process at higher velocities and electron-capture dominates at lower velocities.

The contributions of bound-state excitations and continuum ionizations to the total inelastic (sum-rule) cross section are examined in Born approximation. The results of an investigation of this problem for the case of one-electron ions colliding with neutral atoms are presented. Emphasis in this work is placed on the general features of these types of cross sections and on the relative contributions of excitation and ionization to the total Born cross section. In addition, extensive numerical results for the parameters which determine the cross sections for electron loss, and for excitation to bound states, are given for one-electron ions having atomic numbers up to 30 colliding with He, N, and Ar target atoms. It is shown that for the asymptotic (high-velocity) Born cross sections, excitation never contributes more than a certain fraction of the total sum-rule inelastic cross section, and this fraction has a bound which is determined by the dipole limit of the transition amplitudes for the incident ion. This bound is given by $\frac{M_{\mathrm{ex}}^2}{M_{\mathrm{tot}}^2}$, where $M_{\mathrm{tot}}^2$ is the -1 energy moment of the dipole-oscillator-strength distribution and $M_{\mathrm{ex}}^2$ is the contribution to this moment from transitions to bound excited states. This result is independent of the target atom involved in the collision. Since $\frac{M_{\mathrm{ex}}^2}{M_{\mathrm{tot}}^2}$ does not depend on the atomic number for one-electron ions, this bound is also independent of the incident-ion atomic number in this case. As a consequence, ionization never contributes less to the sum-rule cross sections than the fraction $(1-\frac{M_{\mathrm{ex}}^2}{M_{\mathrm{tot}}^2})=\frac{M_{\mathrm{ion}}^2}{M_{\mathrm{tot}}^2}$. The more general problem, which involves multielectron ions (or atoms) colliding with atoms, is discussed from several viewpoints, and similar results are suggested for that case. In particular, separate upper bounds on the Born-excitation cross section, and lower bounds on the Born electron-loss cross section, are proposed which are all expressed as fractions of the total inelastic-scattering Born cross section.

Nonadiabatic couplings for ionizing transitions in two-center one-electron systems are computed, using switching functions to take account of electron translation effects. The remarkable sensitivity of these couplings to the switching function parameters is used to determine a well-defined "optimum" choice for the switching function, which is shown to depend only on the characteristics of the initial discrete molecular state involved. Both number and range of the corrected couplings are very much smaller than those for the perturbed stationary states couplings. The switching function parameters are given and examples of corrected and uncorrected results compared. Some implications regarding the use of switching functions in general close-coupling problems are discussed.

The charge-transfer process ${\mathrm{O}}^{8+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to {\mathrm{O}}^{7+}+{\mathrm{H}}^{+}$ is considered for ${\mathrm{O}}^{8+}$ impact energies from 0.025 to 200 keV/amu, using the atomic base $S$ matrix formulation represented by time-dependent bases which denote moving atomic orbitals. In the evaluation of the $S$ matrix, models of two extreme types, the unitarized model and the absorption model, are introduced. The numerical results show that there is only a small difference between the cross sections obtained using the respective models for impact energies above 0.5 keV/amu, while the cross section due to the unitarized model becomes smaller than one-half of that obtained with the absorption model at an impact energy of 0.05 keV/amu. The data are also compared with other calculations of the same process. For the investigation of the validity of our formula, the unitarized formula is also applied to the processes ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to \mathrm{H}+{\mathrm{H}}^{+}$ and ${\mathrm{He}}^{2+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to {\mathrm{He}}^{+}+{\mathrm{H}}^{+}$. The results are in good agreement with the experimental data.

It was long ago suggested by Thomas that the charge-transfer cross section in the neighborhood of forward scattering was dominated by a double-scattering process. Thomas's analysis, which was almost completely classical, might well suggest that, in a proper quantum-mechanical study, the second Born contribution would dominate over the first, and this was ultimately found to be the case. Unfortunately, the problem which Thomas considered was charge transfer to any bound state of an incident proton from a hydrogen atom in its ground state, a problem which cannot truly be studied classically. Thomas found that the cross section behaved as $r^{-\frac{7}{2}}$, where $r$ is the initial electron-target-proton separation, and simply replaced $r^{-\frac{7}{2}}$ by $a_0^{-\frac{7}{2}}$, where $a_0$ is the Bohr radius. The result he obtained is identical in form to that obtained in the second Born approximation, but the coefficient is smaller by about a factor of ten. The more consistent procedure of replacing $r^{-\frac{7}{2}}$ by its expectation value gives $\infty$ for the $1s$ ground state, (or indeed for any state with orbital angular momentum quantum number $l=0\mathrm{}$). We show that for capture from a high-Rydberg state, that is, a state with principal quantum number $n\gg 1$, the classical picture is not only meaningful for $l\ne 0$, but, for $l$ sufficiently large, becomes exact.

The electron-density distribution in solids differs from that of a free atom. The main difference is in the peripheral region, where the electron density is greater than that of a free atom and is fairly constant. At low ion velocity, below $3-4v_0$, where $v_0=\frac{c}{137}$, this is the region which absorbs most of the transferred energy. A simple model for computation of the electronic energy loss in solids, which takes those facts into account and uses the Lindhard-Winther formalism, is developed, and is compared with other existing models. The agreement between computational and experimental results is better than that of other models, especially around the maximum of the $S_e\mathrm{}\left(v\right)\mathrm{}$ curve and below. Some of the differences between various experimental results can be explained within the framework of this model.

A self-consistent field theory for one-positron, many-electron systems derived by Schrader [Phys. Rev. A 1, 1070 (1970)] is solved in first order for positron-hydrogen and -helium elastic scattering below the positronium formation threshold. The perturbation is the positron-electron interaction, and the zeroth-order target, in the case of helium, is the Hartree-Fock atom. The first-order target equation is solved variationally. Unlike the polarized-orbital method of Callaway-Temkin, no further simplifying approximations are made here for $s$-wave phase shifts except the use of a finite basis in which to expand the perturbed electronic orbitals, and in the case of helium the neglect of a certain small and intractable integral at an intermediate stage of the calculation. In addition, for non-$s$-wave phase shifts we follow much previous work and neglect contributions of an excited target. Our approach is fully nonadiabatic, and is contrived in such a way that the zeroth-order target equation contains the positronic Laplacian operator. The nonadiabatic polarization potential thus generated by the positron differs significantly from that in other more approximate nonadiabatic theories. The positronic scattering phase shifts of the $s$, $p$, and $d$ waves are calculated and compared to the best available results from other methods. Our calculated phase shifts for the hydrogen target lie midway between those for a static target and the exact results, thus revealing a serious lack of accuracy for any first-order method, at least when applied to systems similar to hydrogen. Our results for helium are more accurate but still not satisfactory. Our results thus cast doubt on the validity of many earlier calculations in which the polarization potential obtained from a first-order perturbation calculation is adjusted to improve the resulting phase shifts.

Relative spectral-line intensities of beam-foil-excited magnesium projectiles have been measured versus the projectile energy (100-900 keV) with carbon foils tilted 0°, 30°, and 45°. The photon intensities depend upon the foil tilt angle. Charge-state distributions measured for ${\mathrm{H}}^{+}$, ${\mathrm{C}}^{+}$, ${\mathrm{N}}^{+}$, ${\mathrm{O}}^{+}$, ${\mathrm{Na}}^{+}$, ${\mathrm{Mg}}^{+}$, ${\mathrm{S}}^{+}$, and ${\mathrm{Kr}}^{+}$ transmitted through carbon foils tilted 0°, 30°, and 45° (100-400 keV) were found not to be influenced by the tilt angle in contrast to the optical results. Charge-state distributions for C and S, which have not been reported earlier, are in agreement with a recently proposed independent-electron model for charge-state distributions and beam-foil populations.

I examine the exchange scattering of an electron from a hydrogenlike atom in the high-energy limit. Although I use the word "electron," the discussion is not restricted to interactions that are pure Coulombic, and the emphasis is on the determination and interpretation of the dominant mechanisms for exchange. I find, in agreement with earlier conclusions, that the second Born term is, except in special circumstances, more important than the first Born term. I present the results of calculations of the differential cross sections for $1s\to 1s$ and $1s\to 2s$ exchange scattering of an electron from a hydrogen atom at impact energies of 500 eV and 1 keV; these results illustrate the degree to which the second Born term dominates over the first. At zero scattering angle, the differential cross section for $1s\to 2s$ exchange is found to be two orders of magnitude larger when calculated within the second Born approximation rather than within the first Born (Ochkur) approximation.

The author has developed a technique for testing various charge-transfer approximation schemes for consistency with the requirements of the Kohn variational principle for the amplitude to guarantee that the amplitude is correct to second order in the scattering wave functions. Applied to Born-type approximations for charge transfer it allows the selection of particular groupings of first-, second-, and higher-Born-type terms that obey the consistency requirement, and hence yield more reliable approximations to the amplitude.

The velocity dependence of both the Penning and associative ionization cross sections ${\sigma }_{\mathrm{PI}}$ and ${\sigma }_{\mathrm{AI}}$ for the $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)+\mathrm{H}$ interacting system as well as total ionization cross section ${\sigma }_{\mathrm{TI}}$ is measured for the relative velocity range 1900-5300 m/sec (0.015-0.10 eV energy range) in a crossed-beam experiment by a time-of-flight technique. Characteristic cross-section ratios $\frac{{\sigma }_{\mathrm{AI}}}{{\sigma }_{\mathrm{TI}}}$ and the relative magnitudes of the cross sections ${\sigma }_{\mathrm{AI}}$, ${\sigma }_{\mathrm{PI}}$, and ${\sigma }_{\mathrm{TI}}$ are reported. The experimental results concerning the total ionization cross section are in very good agreement with previous theoretical work, but the experimental values of the ratio $\frac{{\sigma }_{\mathrm{AI}}}{{\sigma }_{\mathrm{TI}}}$ are found to be higher than theoretical values, especially at low energies. A numerical solution of the Schrödinger equation with a complex potential is performed to interpret both the results on the $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)+\mathrm{H}$ system and our previously published results on the $\mathrm{He}\left(2\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)+\mathrm{H}$ system. A truncated width is used for the calculation of the associative cross sections. It is observed that an exponentially shaped autoionization width $\Gamma \mathrm{}\left(R\right)={\mathrm{Ae}}^{-\frac{R}{B}}$ is satisfactory and that the width for the $\mathrm{He}\left(2\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)+\mathrm{H}$ system is nearly equal to the width for the $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)+\mathrm{H}$ system.

The velocity dependence of both the Penning and rearrangement ionization cross sections ${\sigma }_{\mathrm{PI}}$ and ${\sigma }_{\mathrm{RI}}$ for ${\mathrm{H}}_2^{+}$ and He${\mathrm{H}}^{+}$ ion production, as well as total ionization cross section ${\sigma }_{\mathrm{TI}}$, resulting from the collisions of He ($2{}_{}{}^1{}_{}{}^{}S$) and He ($2{}_{}{}^3{}_{}{}^{}S$) with ${\mathrm{H}}_2$ is measured over the relative-velocity range 2400-5300 m/sec (0.04-0.20 eV energy range) in a crossed-beam experiment by a time-of-flight technique. Characteristic cross-section ratios $\frac{{\sigma }_{\mathrm{RI}}}{{\sigma }_{\mathrm{TI}}}$ and the relative magnitude of the cross sections ${\sigma }_{\mathrm{RI}}$, ${\sigma }_{\mathrm{PI}}$, and ${\sigma }_{\mathrm{TI}}$ are reported. Comparison with some recent theoretical calculations is made; we observe a fair agreement in the triplet case except for ${\sigma }_{\mathrm{RI}}$, but a strong difference in the singlet case.

In an electron-beam plasma selective excitation by pulsed-dye-laser pumping has been used to study excitation transfer by electronic collisions. In particular, rate coefficients for the transitions $4{}_{}{}^1{}_{}{}^{}P\to 4{}_{}{}^1{}_{}{}^{}S$ and $3{}_{}{}^1{}_{}{}^{}P\to 3{}_{}{}^1{}_{}{}^{}S$ have been derived as well as the total deexcitation rate coefficient by $\Delta n\ne 0$ collisions of the $4{}_{}{}^1{}_{}{}^{}P$ and $4{}_{}{}^3{}_{}{}^{}D$ levels. The agreement with theoretical values is within the experimental uncertainties. The effective excitation transfer between the $n=4\mathrm{}$ singlet and triplet levels is higher than expected by about two orders of magnitude.

The properties of the two-state approximation are considered from the point of view of atomic collision theory in the limit of large and small values of a characteristic collision time $T$. For large $T$ (the adiabatic limit) asymptotically exact expressions are obtained for the elastic-scattering phase shifts and for the nonadiabatic transition probability due to the pseudocrossing of terms. This approximation is carried out under fairly general assumptions about the Hamiltonian, enabling us to consider such processes as transitions between $\Sigma -\Pi$ terms caused by rotation of an internuclear axis. Such general problems of the adiabatic approximation as the applicability of adiabatic perturbation theory, the introduction of a dynamical basis, and the properties of the electronic wave functions in the pseudocrossing region are discussed. For small $T$ (the sudden-peturbation limit) the evolution operator to zeroth and first order in $T$ is calculated. We introduce a general and unambiguous definition of an adiabatic basis as a basis of eigenvectors of the evolution matrix to zeroth order in $T$.

We consider a very simple approximation, in which the splitting of the energy of a $P$ state in a united atom into $\Sigma$ and $\Pi$ quasimolecular terms for small internuclear distances $R$ depends quadratically on $R$, and the colliding atoms pass one another along a straight or a hyperbolic trajectory. In this case the transition probability for a given scattering angle or impact parameter depends on only one parameter—the Massey parameter. This probability is computed numerically along with the elastic scattering phase shifts. Approximate formulas are obtained for both the adiabatic limit (in which the parameter is large and the flight is slow) and the sudden-perturbation limit for which the parameter is small, the flight is fast, and the process reduces to a sudden rotation of the internuclear axis. We also obtain, in the adiabatic case, the first term in the expansion of the factor in front of the exponential. In the intermediate range of the parameter, simple analytic approximations, ensuring transition to the limiting cases, are proposed. Analytic expressions for the total transition cross sections are obtained in the limits of large and small collision velocities. The results of the calculations are applicable to $\Sigma -\Pi$ transitions of electrons and holes in both outer and inner shells for close collisions in a broad energy range, where, owing to a scale transformation, all cases reduce to one. Reasonable agreement is found with other more complicated calculations for the collisions of specific atoms.

We present a method for calculating the continuum wave function in electron-molecule scattering for an $N\times N$ discrete-basis-set representation of the potential. The method is based on the $T$-matrix method introduced by Rescigno, McCurdy, and McKoy. In this work, the wave function is used in a prescription for the variationally corrected partial-wave $K$ matrix analogous to Kohn's variational formula for the scattering amplitude in three dimensions. Results presented for $e^{-}$-${\mathrm{H}}_2$ scattering in the static-exchange approximation are in good agreement with other accurate calculations.