In this paper the theory of a single Rydberg series perturbed by an interloping state is examined. General analytic expressions are presented which apply both to the bound-state regions and to the autoionizing regions above the Rydberg ionization limit. The parameters are expressed in terms of configuration-interaction matrix elements, which can be calculated a priori. There is no restriction to weak-perturbation theory, and the wave function and all its associated properties, such as transition moments, can be extracted. Explicit calculations are presented for the $\mathrm{Cd}\left(5s nd\right){}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ series perturbed by the $\mathrm{Cd}\left(5\mathrm{}{p}^2\right){}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ valence state, and excellent results are obtained.

Several recent measurements of the fine-structure intervals in the $3{}_{}{}^3{}_{}{}^{}P$ state of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ are compared, and the best values are recommended: the $3{}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}-3\mathrm{}{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ interval is 8772.552(40) MHz (as given by Kramer and Pipkin), and the $3{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}-3\mathrm{}{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ interval is 658.67(9) MHz (which is a weighted average of results by Kramer and Pipkin, by Tam, and by Wieder and Lamb). Also examined are the presently available experimental data on lifetime and depolarization cross section of the $3{}_{}{}^3{}_{}{}^{}P$ state, and the current theoretical understanding of the fine structure of this state.

The hyperfine structure of the rubidium atom in the ground state has been studied by means of the relativistic many-body perturbation procedure. Relativistic effects are found to have an important influence on direct, exchange-core-polarization (ECP), and correlation effects, the enhancement over nonrelativistic results being, respectively, 20, 19, and 15%. Correlation effects are found to be significantly larger in magnitude as compared to ECP effects, the ratio of the two to the direct contribution being 0.32 and 0.19, respectively. This feature is opposite in nature to that in lithium and sodium, but represents a continuation of the trend found in going from lithium to sodium, and indicates that the relative importance of correlation will be even more pronounced in the heavier alkali metals, cesium and francium. The net theoretical value for the hyperfine constant was obtained as 3460±50 MHz, in satisfactory agreement with the experimental result of 3417 MHz. The physical reasons for the observed trends in the contributions from different mechanisms will be discussed, including some detailed features such as the relative contributions from different core shells to the ECP and correlation effects.

Analytical approximations to the solution of the Thomas-Fermi and Thomas-Fermi-Dirac-Weizsäcker equation for neutral systems are presented. The authors demonstrate in detail the quality of the solutions for one-center boundary conditions and provide an extension for two-center systems. Finally, the construction of effective single-particle potentials for diatomic systems based on the solutions obtained is discussed.

Solutions of the stationary two-center Schrödinger equation with effective Hartree-Fock-Slater-type potentials derived from the Thomas-Fermi (TF) or TF-Dirac-Weizsäcker models are presented for the systems N-N and Ne-Ne. The authors compare correlation diagrams with corresponding Hartree-Fock results and with the results of the variable-screening model of Eichler and Wille.

The authors obtain differential cross sections for ${\mathrm{He}}^{2+}$ impact on $\mathrm{He}\left(1\mathrm{}{s}^2\right)$ using a molecular treatment of the collision and the impact-parameter eikonal approximation. Small angles and low energies for which elastic and two-electron resonance transfer reactions occur are considered. The results are compared with the experimental data of Chen et al. Total cross sections are also given and compared with other theoretical and experimental results.

The $L$ x rays of Ho and Sm produced by proton and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ impacts were measured with a Si(Li) detector over the incident energy ranges $E_p=0.75-4.75\mathrm{}$ MeV and $E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}=1.5-9.3\mathrm{}$ MeV in the direction of 90° to the projectile. Ratios of x-ray-production cross sections for the $L\alpha$ and $L_l$ lines depend markedly on projectile energy but are independent of the projectile charge. It is shown that these experimental results are in good agreement with the plane-wave-Born-approximation calculation taking into account the effect of inner-shell alignment.

The total cross sections for charge transfer in ${\mathrm{Ne}}^{10+}$ + H, ${\mathrm{Si}}^{14+}$ + H, and ${\mathrm{Ca}}^{20+}$ + H collisions are calculated for ion impact energies of 0.025-2000, 0.025-5000, and 0.1-10 keV/amu, respectively, by means of a unitarized-distorted-wave-approximation method. A scaling rule is derived from the results to predict cross section data. The partial cross sections for electron transfer into the individual orbitals around the projectiles are also investigated. The results show that the most probable principal quantum number of the final state is almost independent to impact energy below 100 keV/amu, while with increasing impact energy above 100 keV/amu it decreases considerably. The strong effects of level crossing and momentum transfer are confirmed to appear in the distributions of final-state population over angular momentum quantum number.

The importance of imposing orthogonality constraints on the continuum wave functions calculated from model exchange potentials for electron collisions with the highly polar systems LiH and LiF is demonstrated. The $\Sigma$ and $\Pi$ resonance features in $e$-LiF collisions, found in earlier model-exchange calculations, disappear upon imposing orthogonality; no evidence for these features is observed in the exact static-exchange calculations.

The approach to electron capture previously developed by the authors is extended to describe the capture of hydrogenic $\mathrm{ls}$ electrons into arbitrary hydrogenic $n$,$l$ excited states of fast projectiles. A simple formula for $n$,$l$ distributions is derived. Capture occurs mainly into states around $n_{\mathrm{res}}\approx \frac{Z_p}{Z_t}$ ($Z_t$ and $Z_p$ are the target and projectile charges) and $l\approx n_{\mathrm{res}}-1\mathrm{}$. The $n$,$l$ distributions for ${\mathrm{O}}^{8+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to {\mathrm{O}}^{7+}\mathrm{}\left(\mathrm{nl}\right)+{\mathrm{H}}^{+}$ and for ${\mathrm{O}}^{8+}+\mathrm{He}\left(1\mathrm{}{s}^2\right)\to {\mathrm{O}}^{7+}\mathrm{}\left(\mathrm{nl}\right)+{\mathrm{He}}^{+}\mathrm{}\left(1s\right)\mathrm{}$ are graphically displayed as representative examples. For the reactions ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to \mathrm{H}\mathrm{}\left(\mathrm{nl}\right)+{\mathrm{H}}^{+}$ and ${\mathrm{H}}^{+}+\mathrm{He}\left(1\mathrm{}{s}^2\right)\to \mathrm{H}\mathrm{}\left(\mathrm{nl}\right)+{\mathrm{He}}^{+}\mathrm{}\left(1s\right)\mathrm{}$ ($nl=2s,2p,3s,3p,3d, \mathrm{and} 4s$), good agreement is obtained with experimental cross sections.

Electronic states of swift channeled ions are studied in terms of a time-dependent effective-Hamiltonian theory. These states are shifted in energy by the electric potential of the perturbed crystal, and transitions among them are induced coherently by the oscillation of the potential. Calculated energies for low-lying states of hydrogenic ions channeled in Au are in reasonable agreement with experimental resonant coherent-excitation spectra.

Quantum-mechanical calculations for differential cross sections and various transport cross sections describing the thermal-energy collisions of ${\mathrm{D}}^{+}$ with D and ${\mathrm{He}}^{2+}$ with He are presented. Lowest-order Viehland-Mason theory is used to calculate mobility of ${\mathrm{D}}^{+}$ in D. The zero-field mobility at 77, 303, and 10000 K is, in units of ${\mathrm{cm}}^2$${\mathrm{V}}^{-1\mathrm{}}$${\mathrm{s}}^{-1\mathrm{}}$, 10.5, 7.0, and 2.1, respectively.

Cluster properties of multiparticle scattering operators defined in terms of a separation variable are shown to be equivalent to cluster properties specified in terms of an angular variable. It is shown that these formulations lead to a formulation of cluster properties in terms of an angular momentum limit. Finally, using a spectral representation of the scattering operators derived from unitarity, the author shows that scattering operators satisfy cluster requirements if the eigenvectors in the spectral representation split into products of eigenvectors in the large-angular-momentum limit.

The theory of Chang and Fano is applied to electron scattering by polar molecules. For collision energy $E>\mathrm{}{E}_{min}$ the problem can be treated accurately without numerical radial integration; the solution is presented in a form suited to an $R$-matrix treatment of the molecular core. The value of $E_{min}$ (in a.u.) is determined through $D\frac{\mathrm{Bj}}{E_{min}}<\delta \ll 1$; when $\frac{E}{E_{min}}\approx \mathrm{a}\mathrm{few}$ eV, more extensive calculation is required beyond the bodyframe Born-Oppenheimer region. For this purpose a generalization of the Chang-Fano theory is developed. It consists of an adiabatic continuous transformation of frame, the frame used at each electron-molecule distance $r$ being determined directly by the dynamics of the problem. This procedure generates a coordination diagram for the known solutions to limiting cases, a diagram analogous to that used in quantum chemistry for connecting the united-atom and separated-atom limits of molecular-orbital theory. A new type of symmetry in the problem is made apparent. Preliminary discussion is made of the applicability of this method to more general problems of close coupling in the asymptotic region.

The excitation and deexcitation processes in slow collisions of highly excited (Rydberg) atoms with ground-state parent atoms are considered. A mechanism, based on the quasiresonant energy transfer within the electronic part of the colliding system, is proposed for these processes. Both direct and exchange reaction channels are included into the treatment. Expressions for the $n\to n^{\prime }$ transition probabilities are obtained in closed form. Probability and cross section calculations for some transitions and level decays in the ${\mathrm{H}}^{*}\mathrm{}\left(n\right)\mathrm{}$-H system are presented.

Contrary to the expectation from a compound-state model, observation shows that the detachment cross section increases with energy in the "adiabatic" region below 2 keV. The compound-state model is not appropriate because a strong $s$-wave component in the wave function allows the extra electron to run away as soon as its state becomes unbound. The detachment cross section increases with collision velocity because detachment is induced by a breakdown of the Born-Oppenheimer approximation, which shifts to larger separations of the nuclei as the collision velocity increases.

Neutron "optical activity" or the rotation of the neutron polarization is investigated in the scattering of polarized neutron beams from chiral molecules. A rotation exists to first order in the neutron-electron spin-orbit interaction for randomly oriented target molecules if a total angular momentum $\hslash ({\overrightarrow{\mathrm{j}}}_t+{\overrightarrow{\mathrm{s}}}_t)$ and an orbital angular momentum $h{\overrightarrow{\mathrm{j}}}_t^{*}$ are transferred coherently to a molecular rotator. The first is the angular momentum developed by incident and scattered waves and spinors through a region of interaction with the magnetic fields generated by electrons bound in the "twisted" potentials characteristic of a chiral molecule. The second is the angular momentum developed by incident and scattered waves through a region of interaction with a network of atomic nuclei having the same twist. The magnetic amplitude must be calculated in the first Born distorted-wave approximation. Distortion causes the magnitudes of the magnetic amplitudes to be distinct for $\Delta l=\pm 1$, $\Delta m=\pm 1$, and $\Delta l=\pm 1$, $\Delta m=0\mathrm{}$ partial-wave transitions induced by the magnetic forces, thus preventing their cancellation on rotationally averaging the cross section. This distortion is produced by the nuclear background; thus the rotation is of order $\frac{m_N}{m_e}$ (neutron-to-electron mass ratio) larger than previous estimates based on the use of the second Born plane-wave magnetic amplitude for forward scattering. However, the present rotation exists only at nonzero scattering angles. This is the first example of a rotation of the neutron polarization which is nonvanishing to first order in a spin-orbit interaction. Its strength makes it an important effect in the use of neutrons to probe molecular structure. We check our result by finding the limit of scattering from spin-independent forces. Here the rotation vanishes, and the incoherent limit for the transfer $\hslash {\overrightarrow{\mathrm{j}}}_t=\hslash {\overrightarrow{\mathrm{j}}}_t^{*}$ obtains. This limit is well known from the Fano-Dill or Temkin-Sullivan theory of orbital-angular-momentum transfer to a rotator.

The laser-rf double-resonance technique has been used to obtain 1-ppm measurements of the largest hyperfine intervals in the ground ($5d6s^2{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}$) and first excited ($5d6s^2{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$) atomic levels of 0.09% abundant ${}_{}{}^{138}{}_{}{}^{}\mathrm{La}$ with a beam of unenriched lanthanum. The hfs ratios $\frac{A^{138}}{A^{139}}$ and $\frac{B^{138}}{B^{139}}$ are thereby obtained. The former shows a 0.36% hyperfine anomaly with respect to the NMR ratio of the nuclear $g$ factors. The uncertainty in the new value $\frac{B^{138}}{B^{139}}=+2.27\mathrm{}\pm 0.04$ arises from uncertainties in interpreting the hyperfine-anomaly effects observed. The ${}_{}{}^{138,139}{}_{}{}^{}\mathrm{La}$ isotope shift is evaluated for both of the lines studied.

A semiclassical treatment of collision-induced three-photon ionization of atoms with a near two-photon resonance is presented. The system is described by an effective two-level system. The wavelength dependence of the ionization yield does not obey a power law. When the first excited state is far from resonance, and with a $\frac{C_6}{R^6}$ interatomic potential, a first-order correction to the expected $-\frac{3}{2}$ power law obeys a - ½ power law. This three-photon process promises to be an extremely sensitive method for the study of collisional effects in the far wing of two-photon $S-S$ and $S-D$ transitions, and without the requirement of high densities.

Inverse bremsstrahlung is one of the important mechanisms for heating plasmas with lasers. In the intense fields required for laser fusion, processes involving multiphoton effects are very important. This paper reviews and compares the different approaches used to quantify the effect of intense fields on the inverse-bremsstrahlung absorption rate. The quantum-mechanical treatment of this problem requires summation of the contribution of large numbers of photons. Numerical problems associated with this summation have made direct evaluation difficult. In this paper the authors describe a method, applicable to many potentials of interest, for transforming the sum over a large number of complicated terms into a rapidly converging sum. Numerical results for both classical and quantum treatments are presented and compared, and the errors introduced by several approximations are quantified.