For hydrogenlike atoms, it is shown on the basis of Kramers's semiclassical formula for the oscillator strength that the mean lifetime of an excited state with a principal quantum number $n$ behaves with respect to $n$ as $\frac{n^5}{\ln n}$. In comparison with the exact calculations, it is shown that the $\frac{n^5}{\ln n}$ law provides a better and more accurate scaling law than the commonly used empirical $n^{4.5}$ scaling law. It is shown that the lifetime of an excited state $T(n,l)\mathrm{}$, where $l$ is the angular momentum quantum number, increases for large $l$ as $l^2$. Previously, no law existed for the relationship between the lifetime and angular momentum. By writing $T(n,l)=c_{\mathrm{nl}}{\left(\mu Z^4\right)}^{-1\mathrm{}}{n}^3{l}^2$, where $\mu$ and $Z$ are the atomic reduced mass and effective charge acting on the running electron, the coefficients $c_{\mathrm{nl}}$ for low and intermediate values of $n$ and $l$, and their asymptotic values for large $n$ and $l$, are tabulated. Within a factor of 2.35 the lifetime of any excited state, except the $l=0\mathrm{}$ states, is given by the formula $0.847\times {10}^{-10\mathrm{}}{\mu }^{-1\mathrm{}}{Z}^{-4\mathrm{}}{n}^3{l}^2$ sec. Agreement is found with selected measured radiative lifetimes of excited helium and alkali-metal atoms. The spread in the experimental data is too large to allow deduction of a systematic deviation from the hydrogenic lifetimes.

This paper derives a number of sum rules for nonrelativistic three-body scattering. These rules are valid for any finite region $\Sigma$ in the six-dimensional coordinate space. They relate energy moments of the trace of the on-shell time-delay operator to the energy-weighted probability for finding the three-body bound-state wave functions in the region $\Sigma$. If $\Sigma$ is all of the six-dimensional space, the global form of the sum rules is obtained. In this form the rules constitute higher-order Levinson's theorems for the three-body problem. Finally, the sum rules are extended to allow the energy moments to have complex powers.

A local-density-functional model in momentum space enabling direct calculations of electron momentum densities for atomic systems is presented. This is based on the coordinate-space local-density-functional model of Parr et al. in conjunction with quasiclassical phase-space considerations. Within the model, electron-electron interaction and nuclear-electron attraction energies turn out to be simple local functionals of momentum density while kinetic energy has been treated exactly. The momentum densities obtained through this model have a simple algebraic form. Numerical investigations employing these densities reveal that reasonable estimates of various $〈p^n〉$ expectation values as compared to their Hartree-Fock counterparts can be obtained.

When a complete orthonormal square-integrable real basis set $\left\{{\chi }_n\right\}$ can be found in which a model one-dimensional Hamiltonian $H_0$ is represented by an infinite symmetric tridiagonal matrix, analysis of the spectrum of $H_0$ leads to a close analogy of Weyl's theory of the Schrödinger equation. With $H_0$ tridiagonal, the Schrödinger equation becomes a three-term recursion relation in $n$ instead of a differential equation. The Sturm-sequence polynomials $p_n\mathrm{}\left(E\right)\mathrm{}$ form the solution regular at $n=0\mathrm{}$, while a second, Weyl's solution $q_n\mathrm{}\left(E\right)\mathrm{}$, is irregular. Then the resolvent ${(E-H_0)}^{-1\mathrm{}}$ is proportional to ${p_n}_{<}{q_n}_{>}$. Furthermore, completeness implies the orthogonality of the $p_n$, and hence, that truncating to a finite basis generates a Gauss quadrature of the spectral density with abscissas at the eigen-values of the truncated $H_0$, and just as in Weyl's theory, approximating the spectral density as a Stieltjes integral. By truncating the representation of any additional potential to a finite matrix, the theory can be extended in analogy to $R$-matrix theory to potential and even multichannel scattering, yielding an explicit construction of the Fredholm determinant, whose zeros locate the resonances and bound states. In addition, such an analysis reveals, at least in the basis sets in which $H_0$ is tridiagonal, how other $L^2$-function methods such as stabilization, Stieltjes imaging, and coordinate rotation work and how accurate they are.

The $2{}_{}{}^1{}_{}{}^{}P$ and $2{}_{}{}^3{}_{}{}^{}P$ levels of two-electron S xv have been aligned by collision at 2 MeV/amu with carbon atoms in a foil. The degree of alignment is obtained by analysis of the normalized angular distribution of $K$ x-ray radiation measured in high resolution with a pivoted plane-crystal Bragg spectrometer. The mean cross-section ratio $\frac{{\sigma }_0}{{\sigma }_1}$ for population of the $m=0\mathrm{}$ sublevel relative to the $m=\pm 1$ sublevels of the $2P$ parent state is obtained by analysis of the $1{}_{}{}^1{}_{}{}^{}S-2\mathrm{}{}_{}{}^1{}_{}{}^{}P$ and $1{}_{}{}^1{}_{}{}^{}S-2\mathrm{}{}_{}{}^3{}_{}{}^{}P$ transition intensities. The result $\frac{{\sigma }_0}{{\sigma }_1}=1.79\mathrm{}\pm 0.1$ leads to the polarization fractions $P\left({}_{}{}^1{}_{}{}^{}P\right)=0.28\mathrm{}\pm 0.05$, and $P\left({}_{}{}^3{}_{}{}^{}P\right)=-0.16\mathrm{}\pm 0.03$, in good agreement with results obtained by an independent analysis, and in excellent agreement with coupled-states calculations of Reading et al. Comparison with other theories is also made.

Invoking simple considerations based on properties of the unitary transformations, we show that the proper use of the Kramers-Henneberger space-translation method in atomiccollision problems gives essentially the same results as the conventional treatments and removes the ambiguities reported in the literature. Laser-assisted electron—hydrogen-atom collisions are considered as an example.

The ${\sigma }_{-0\mathrm{}}$ cross section for ${\mathrm{F}}^{-}$ ions in rare-gas targets is found to be energy independent for helium and neon between 25 and 120 keV, and to increase with target mass and with beam energy for heavier gas targets. Extrapolation to existing lower-energy data suggests that in the few-keV energy region either double-electron detachment is equally as important as single-electron detachment, or that the single-electron-detachment cross section rises to a maximum and then decreases to our observed values.

Electron-capture cross sections for ${\mathrm{H}}^{+}$ plus alkali-metal atom (Na, K, Rb, and Cs) systems have been computed for projectile energies from 10 eV to 10 keV. An impactparameter perturbed-stationary-state theory using molecular states that incorporate electron translation factors was used to calculate the cross sections. The wave functions were generated by employing the pseudopotential method. These yield equilibrium parameters $R_e$ and $D_e$ for the $A{}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ molecular state that are in good agreement with ab initio results. Interaction energies are also presented for the Li${\mathrm{H}}^{+}$ system. Basis sets of up to eight molecular states were used to calculate the electron-capture cross sections from ground ($\mathrm{ns}$) as well as from the first excited ($\mathrm{np}$) states of the alkali-metal atoms. Results for electron capture from the ground-state alkali-metal atom are in good agreement with the recent experiments of Nagata. Electron capture from excited alkali-metal ($\mathrm{np}$) atoms does not yield enhanced cross sections relative to capture from the ground state and, in fact, shows decreased cross sections for the heavy alkali-metal atoms. Such behavior is contrary to predictions made using arguments based on the magnitude of the energy gap $\Delta E$ to the electron-capture product states.

Quantum-mechanical elucidation is applied to the semiclassical theory in the dynamicalstate representation previously proposed to deal analytically with the nonadiabatic rotationally induced transitions. A general path-integral formulation of the scattering matrix is given in terms of a product of two kinds of matrices. This enables us to treat a multistate curve-crossing problem involving both radial and rotational couplings. Discussions are made on the qualitative difference in collision-energy dependences of the ordinary Landau-Zener-type radial transitions and rotationally induced transitions.

We analyze the dependence of the rate of associative ionization of two radiatively excited atoms on the polarization properties of the exciting light. This provides a direct relation between the observed ion-production rate as a function of the polarization and the ionization rates for various combinations of the magnetic substates. We consider an atomic beam irradiated by a single laser beam, as well as an atomic vapor. The description applies to a recent experimental observation of a strong polarization dependence of the ionization rate in an atomic beam, and at the same time we suggest alternate experimental methods of analyzing the total cross sections of any inelastic or reactive binary collision of excited atoms as a function of the magnetic quantum numbers.

As part of an experiment to study atomic-field bremsstrahlung produced by electron bombardment of rare-gas atoms in the 4- to 10-keV energy range, we have determined the characteristic x-ray production cross section for the $K$ shell of argon and the $L$ shells of krypton and xenon. We compare our results for the inner-shell ionization cross section with the Bethe theory, the plane-wave Born approximation of McGuire, and the classical binary encounter theory as well as with previous experiments. Using the observed validity of classical scaling over this energy range, and the known average $K$-shell fluorescence yield for argon, we have determined the average $L$-shell fluorescence yield for xenon and krypton.

New results for the atomic-field bremsstrahlung for $Z=80\mathrm{}$ are presented which, along with an extension of previous results for $Z=10\mathrm{} \mathrm{to} 54$ to lower radiated-photon energies, can be compared with theory. The results are in very good agreement with theory and suggest that there is no evidence for the onset of two-photon processes for $Z=80\mathrm{}$.

For Hamiltonians with two potentials, differential cross sections are written as time-correlation functions of reference and distorted transition operators. Distorted eikonal differential cross sections are defined in terms of straight-line and reference classical trajectories. Both elastic and inelastic results are obtained. Expressions for the inelastic cross sections are presented in terms of time-ordered cosine and sine memory functions through the use of the Zwanzig-Feshbach projection-operator method.

Total cross sections for radiative charge transfer in collisions of ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{2+}{}_{}{}^{}$ ions with ground-state H atoms leading to ${\mathrm{He}}^{+}$ $1s$ and ${\mathrm{H}}^{+}$ ions have been calculated for a range of center-of-mass energies from 0.1 to 1000 eV. An adiabatic optical-potential formalism is used where the imaginary part of the potential-energy function is proportional to the Einstein $A$ coefficient for the molecular transition. Both quantum-mechanical and semiclassical JWKB calculations are performed. Predissociation resonances add structure to the cross section. The radiative contribution is shown to dominate the charge-transfer process for this system at low collision energies.

A simple two-state numerical model is used to illustrate the influence of strong low-energy ${\sigma }_g$ scattering on near-threshold excitation of the different vibrational modes of C${\mathrm{O}}_2$. In the case of 000→100 symmetric-stretch excitation, the model provides an extrapolation of a previously determined adiabatic-nuclei result down to threshold. For all modes, the "virtual-state" feature of the ${\sigma }_g$ scattering gives rise to strong enhancement of the excitation cross sections just above threshold. The calculated cross sections for all modes are reasonably consistent with low-energy beam and swarm measurements.

Electron-impact ionization cross sections have been calculated in a distorted-wave exchange approximation for seven ions in the argon isoelectronic sequence. For neutral argon, target configuration interaction and term dependence in the ejected-electron continuum were found to be significant influences on the cross section. Similarities of electron ionization and photoionization are discussed. An analytic fit is given which accurately reproduces the distorted-wave cross sections and rate coefficients of argonlike ions with $Z\ge 20$.

A method is proposed for obtaining coherent $\gamma$ radiation through the interaction between a relativistic electron beam and two interfering laser fields. The periodic structure associated with the interference fringes gives rise to coherent effects of the radiation emitted by stimulated inverse Compton scattering, if suitable conditions are fulfilled.

We calculate the energy spectrum of electrons detached from 0.5-MeV negative hydrogen ions in collision with helium targets using the plane-wave Born approximation. Three different models for continuum states of ${\mathrm{H}}^{-}$ are used to calculate electron-detachment doubly differential cross sections. The first model uses a single exponential function for the loosely bound electron of ${\mathrm{H}}^{-}$ and a plane wave for the detached electron. The second model is similar to the first one, but the final state is Gram-Schmidt orthogonalized. The third model includes the $s$-wave phase shifts obtained from Schwinger's variational principle. These phase shifts incorporate the radial correlations which are essential for the study of such low-energy continuum electrons. The doubly differential cross section obtained by the second and third models have a double-peak structure. These peaks are at energies different from the ones measured by Menendez and Duncan. Based on this calculation we observe that the ejected electrons are sensitive to the $s$-wave phase shifts and electron-electron correlations. This observation rejects the use of plane-wave models for the detached electrons and indicates the need for more accurate wave functions which incorporate radial and angular correlations.

Shell corrections to electronic stopping powers are obtained from a theory which utilizes different orbital mean excitation energies for the atomic shell and which determines the shell correction from knowledge of the atomic velocity distribution. When summed over all shells, and taking into account the "effective" occupation of the shells, the orbital mean excitation energies yield the total mean excitation energy $I$. Orbital mean excitation energies are much larger than $I$ for $K$ shells and less than $I$ for the outer valence shells. The atomic velocity distributions are obtained from numerical Hartree-Fock calculations. We report shell corrections for Al and Ar. We find very good agreement between other theoretical and experimental shell corrections and the present calculation. We find that the $L$ shell gives the dominant contribution to the shell corrections for low projectile velocities while $K$-shell corrections dominate for larger velocities. The total shell correction is relatively insensitive to the choice of the total mean excitation energy. We have also investigated the validity of expanding the shell correction in powers of $v^{-2\mathrm{}}$.

The electron excitation cross sections for $\mathrm{He} (1\mathrm{}{s}^2{}_{}{}^1{}_{}{}^{}S\to 2p^2{}_{}{}^3{}_{}{}^{}P)$, $\mathrm{Mg} (3\mathrm{}{s}^2{}_{}{}^1{}_{}{}^{}S\to 3p^2{}_{}{}^3{}_{}{}^{}P)$, and $\mathrm{Ca} (4\mathrm{}{s}^2{}_{}{}^1{}_{}{}^{}S\to 4p^2{}_{}{}^3{}_{}{}^{}P)$ have been calculated with the use of the Ochkur, Glauber, and a simplified Glauber approximation. The results are compared with the Born-Oppenheimer approximation and, in the case of helium, with available experimental data. The Glauber and simplified Glauber approximations are found to differ significantly from the Born-Oppenheimer approximation, especially in the high-energy limit.