Multichannel photoionization calculations using the relativistic random-phase approximation for the outer shells in the rare gases, neon, argon, krypton, and xenon, are presented. Total cross sections and partial cross sections for $\mathrm{ns}$ subshells are determined and compared with experiment and with alternative calculations at low energies. Branching ratios of ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}:{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ cross sections which are sensitive to relativistic and correlation effects are presented and compared with experiment. Angular distribution asymmetry parameters $\beta$ determined for each subshell are found and compared with experiment; the differences between $\beta$ values for ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ subshells in krypton and xenon emphasize the importance of relativistic effects in outer subshells of heavy elements. Values of $\beta$ are given for outermost $s$ electrons which show large relativistic effects near the "Cooper minima" of the corresponding partial cross sections. Eigenphases from the multichannel analysis are presented for argon to illustrate mathematical features of the present calculation.

Argon $K\alpha$ x-ray satellites produced by ion collisions were measured with a crystal spectrometer. N ions with energies in the range of 4.7-7.8 MeV/amu were used to bombard argon contained in a gas cell. The average number $〈l〉$ of $L$-shell vacancies formed in single-$K$-vacancy-producing collisions decreases monotonically with an increase in the energy of bombarding ions and follows well the scaling law obtained by Schmiedekamp et al. on the basis of an increased binding effect.

The authors investigate the saturation and Stark splitting of an atomic transition in (i) a phase-diffusion field and (ii) a chaotic field of arbitrary bandwidth. The theory takes into account the infinite sequence of field-correlation functions. It is shown that a chaotic field is less effective than a phase-diffusion field in saturating a single- or multiphoton transition. This is contrary to the weak-field case, where the intensity fluctuations and the associated photon bunching make the chaotic field more effective in exciting a multiphoton transition. It is also shown that the Stark splitting of an atomic transition, as observed in double resonance, is influenced dramatically by the intensity fluctuations in the chaotic field.

The electric field gradient along the molecular axis at the nucleus in ${\mathrm{D}}_2$ has been calculated at $R=1.4\mathrm{}$ a.u. by means of the Kołos-Wolniewicz 54-term Born-Oppenheimer wave function. The result is a confirmation of the Reid-Vaida value. A nonadiabatic calculation using a 540-term wave function (explicitly containing the vibronic component) also confirms the earlier value of the electric field gradient and necessarily, therefore, the predicted quadrupole moment of the deuteron (i.e., $Q=0.2860\mathrm{}\pm 0.0015$ ${\mathrm{fm}}^2$).

The intensities of $L$-shell Auger and Coster-Kronig transitions in heavy atoms have been calculated relativistically. A detailed comparison is made with measured Auger spectra of Pt and U. The pertinent transition energies were computed from relativistic wave functions with inclusion of the Breit interaction, self-energy, a vacuum-polarization correction, and complete atomic relaxation. Multiplet splitting is found to distribute Auger electrons from certain transitions among several lines. The analysis leads to reassignment of a number of lines in the measured spectra. Lines originally identified as $L_2-L_3{N}_i$ in the U spectrum are shown to arise from $M_{4,5}$ Auger transitions instead. The effect of relativity on $L_3-MM$ Auger-transition intensity ratios is studied; in some cases, these ratios are found to be affected by as much as 50% by the inclusion of relativity, while in others the ratios change little. This variation in response can be traced to the different factors through which relativity influences radiationless transition probabilities.

A family of nonlinear variants of the Schrödinger equation was defined by Bialynicki-Birula and Mycielski by adding terms of the form $F\left({\left|\psi \right|}^2\right)$ to the Hamiltonian. It is proposed that this family be tested by observing whether a phase shift occurs when an absorber is moved from one point to another along the path of one of the coherent split beams in a neutron interferometer. If $F$ is $b$ times a logarithmic function, which is the most important case, a null result with apparatus now available would impose an upper bound on $b$ of 1.5×${10}^{-12\mathrm{}}$ eV, more than two orders of magnitude smaller than the bound estimated by the above authors on the basis of the Lamb-shift measurement.

Expressions for the kinetic energy $T$ (and incidentally also for the exchange energy $E_x$) of a ground-state inhomogeneous electron gas as a functional of the electron density $n\left(\overrightarrow{\mathrm{r}}\right)$, and for $n\left(\overrightarrow{\mathrm{r}}\right)$ as a functional of the one-electron potential $V\left(\overrightarrow{\mathrm{r}}\right)$, are readily generalized to the case of two unequal spin densities $n_{\uparrow }\left(\overrightarrow{\mathrm{r}}\right)$ and $n_{\downarrow }\left(\overrightarrow{\mathrm{r}}\right)$. As an example the authors consider the expansions of $T$ up to fourth order in the gradients of $n$, and of $n$ up to fourth order in the gradients of $V$. These expansions are tested for the extreme case of one- and two-electron atoms. It is found that (i) The $n\left[V\right]\mathrm{}$ expansion contains serious pathologies, while the $T\left[n\right]\mathrm{}$ expansion leads to much more reasonable results when applied to either the exact density $n\left(\overrightarrow{\mathrm{r}}\right)$ or to an $n\left(\overrightarrow{\mathrm{r}}\right)$ obtained by minimization of the approximate total-energy functional $E\left[n\right]\mathrm{}$. (ii) Good approximations to $E$ and $n\left(\overrightarrow{\mathrm{r}}\right)$ in one-electron atoms are obtained only when the complete spin polarization of a single electron is taken into account via $T[n_{\uparrow }, n_{\downarrow }]$. (iii) Within a variational calculation, the inclusion of second- and fourth-order gradient corrections to the zeroth-order (Thomas-Fermi) approximation for $T$ leads to systematic improvements in the analytic behavior of $n\left(\overrightarrow{\mathrm{r}}\right)$ near the nucleus. The authors also compare the local-exchange approximation with the local-exchange-correlation approximation in one- and two-electron atoms, and find that correlation should not be neglected.

The Fano-Macek alignment and orientation parameters have been measured for the foil-excited $3p{}_{}{}^3{}_{}{}^{}P$ state in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ i as a function of foil tilt angle at an incident ion energy of 200 keV. The measurements were made by quantum-beat amplitude analysis of both linearly and circularly polarized light. The angular dependence of the alignment and orientation are significantly different from that reported for the $3p{}_{}{}^1{}_{}{}^{}P$ state.

Absolute cross sections have been measured for $1s^{2}2s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-1\mathrm{}{s}^{2}2p{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2},\frac{3}{2}}^{}{}_{}{}^{}$ excitation of lithiumlike ${\mathrm{N}}^{4+}$ by electron impact. For this process, which has a threshold at 10 eV, relative cross sections measured at several energies between 4 and 52 eV were normalized to a single absolute measurement taken at 15.5 eV. Similar data for Li-like ${\mathrm{C}}^{3+}$ have been previously reported and are presented for comparison. In both cases, allowing for the experimental electron energy spread, the measurements agree within experimental uncertainties with published Coulomb-Born and close-coupling calculations over the entire experimental energy range. Rate coefficients as a function of electron temperature are also presented for the ${\mathrm{N}}^{4+}$ transition.

An improved impulse approximation is used to investigate the ionization collisions between two excited one-electron atoms at high energies. It is shown that the cross sections can easily be estimated by using the quantities calculated in the case of the collisions between two excited hydrogen atoms.

The identities of Hiller, Sucher, and Feinberg for the evaluation of bound-state matrix elements of $\delta$-function operators, such as $\delta \left({\overrightarrow{r}}_i\right)$ and $\delta \left({\overrightarrow{r}}_{\mathrm{ij}}\right)$, are extended to scattering states. It is shown how technical difficulties encountered in the application of the scattering-state identities can be overcome, including infrared singularities which arise if Coulomb forces are present and the velocity of the incident particle is small. Both the scattering and bound-state identities are generalized to include spin-dependent contact interactions and spin-dependent Hamiltonians. The possibility of using the identities to improve the accuracy of calculations of interest for diverse physical phenomena, ranging from positron annihilation to hyperfine structure, is stressed.

The method of Hiller, Sucher, and Feinberg for the evaluation of matrix elements of $\delta$-function operators between bound-state wave functions has been extended to scattering states in another paper. The resulting identities can be used to improve the calculation of positron annihilation cross sections whenever an approximate positron-atom scattering wave function is known. In this paper the advantages of the method are illustrated first with the static model for $e^{+}$-H scattering and then with the more realistic polarized-orbital approximation.

Using the generalized oscillator-strength formulation of the Born approximation, the author calculated electron ionization cross sections for all significant subshells of every fourth atom with $55\le Z\le 102$, and for Hg. The calculations used approximate Herman-Skillman wave functions and eigenvalues. The cross sections were put in scaled form, depending essentially on ionization energy only. The scaled cross sections were used with experimental energies to calculate the cross sections for Cs, ${\mathrm{Cs}}^{+}$, Ba, ${\mathrm{Ba}}^{+}$, Au, Hg, Tl, ${\mathrm{Tl}}^{+}$, and Pb. The cross sections so calculated were in good agreement with the measurements. Both inner-shell ionization and excitation followed by autoionization were prominent contributors to the cross section. The scaling procedure was used to calculate the electron ionization cross section of the noble-gas metastable levels, and there is excellent agreement with measured valves for Ne and A. The scaling procedure was used to calculate cross sections for the sequential ionization ${\mathrm{Ni}}^{+1\mathrm{}}$-${\mathrm{Ni}}^{+14\mathrm{}}$ and ${\mathrm{Au}}^{+3\mathrm{}}$-${\mathrm{Au}}^{+14\mathrm{}}$, which were compared with corss sections obtained from the semiempirical expression of Lotz. Good agreement was found for the Ni ions, but there was poor agreement for the Au ions. Lotz's expression is a factor of 3 smaller than our scaled cross section for the $4d$, $4f$, and $5d$ subshells. It is suggested that the absence of measurements on these subshells precluded correct parametrization in the semiempirical expression of Lotz.

The problem of scattering by a local potential in the presence of an intense radiation field is studied for the case where the potential is Coulombic at great distances. The effect of the Coulomb tail on the asymptotic dynamics is accounted for here through a modification of the form of the wave functions which describe the time evolution of the system in initial and final states. This is in analogy with previous treatments of field-free Coulomb scattering. Starting from the time-dependent picture, the author obtains a time-independent formulation of the problem and then applies it to the derivation of a low-frequency approximation. In the simplest version of this approximation the transition amplitude is represented as the product of a known fielddependent factor (a Bessel function) and the physical field-free scattering amplitude, thus generalizing an earlier result of this type derived for the case of a short-range potential.

The theory of Coulomb ionization of $L$ shells by low-velocity heavy charged particles whose atomic number is small compared to the atomic number of the target atom is extended to projectiles with velocities comparable to or larger than the $L$-shell orbital velocities. At large impact parameters projectiles polarize the shell, and at small impact parameters they increase the binding energies of the electrons to be excited. The polarization effect is incorporated in accordance with the perturbed stationary-state (PSS) approximation. The effect of the repulsion between the projectile and the target nucleus is accounted for by a Coulomb-deflection factor (C). This CPSS theory is developed further to include relativistic effects (R) of the target wave function through a procedure that reproduces the results of numerical calculations for heavy target atoms. With electron capture by the projectiles as an additional channel of ionization, the CPSSR theory is compared with experiment.

The Coulomb-deflection factor, defined as the ratio of the Coulomb to plane-wave Born cross sections, is derived for slow but classically moving ions, and found to be in agreement with the data for $K$-shell ionization. When the half distance of closest approach in a head-on collision, $d$, is comparable to the important impact parameters ($\sim \frac{1}{q_0}$, where $q_0$ is the minimum momentum transfer), this factor simplifies to $\exp (-\pi d{q}_0)$ as it has been employed in the inner-shell-ionization theory. When the impact parameters are small on the scale of the projectile de Broglie wavelength, as they are in nuclear phenomena, the Coulomb-deflection factor tends to $\exp (-2\mathrm{}\pi d{q}_0)$. An extension of our results to screened Coulomb repulsion gives good agreement with the semiclassical calculations and the data for $K$-shell excitation in ${\mathrm{Ne}}^{+}$-Ne collisions.

Results are presented for rotational and vibrational-rotational excitation of ${\mathrm{H}}_2$ by electron impact in the static-exchange approximation. We use the $T$-matrix discrete basis set method introduced by Rescigno, McCurdy, and McKoy. Our approach for vibrational excitation involves solving the fixed-nuclei scattering problem at several internuclear separations. We compare our results with the experimental data of Linder and Schmidt and with other calculated results.

Strengths and Stark-effect widths of the Sni and Snii lines prominent between 3200 and 7900 Å are measured with a spectroscopic shock tube. Absolute strengths of 17 ionic lines are obtained with estimated (22-50)% accuracy and conform to appropriate quantum-mechanical sum rules. Relative transition probabilities for nine prominent neutral tin lines, normalized to radiative-lifetime data, are compared with other experiments and theoretical predictions. Parameters for Stark-effect broadening are measured over a range of plasma electron densities. Broadening data [with accuracies of (15-35)%] for one neutral and ten ionic lines of tin are compared to theoretical predictions.

This paper summarizes a long series of experiments that have been done on Rydberg states of Rb. The basic experimental technique that has been used is atomic-beam laser spectroscopy which allows both low-resolution and high-resolution studies. Excitation of Rydberg states is provided by single-photon absorption from a suitably frequency-doubled rhodamine $6G$ tunable laser. Detection is done by field ionization and ion counting. These techniques have allowed us to study the critical ionizing field, which has been found to follow classical, hydrogenic behavior closely. Rydberg states of Rb have been observed from $n=28\mathrm{}$ up to $n>\mathrm{}100\mathrm{}$. High-resolution spectroscopic studies have led to measurement of the fine structure for $\mathrm{np}$ levels located between $n=28\mathrm{}$ and $n=60\mathrm{}$, as well as the isotope shift of the ground state, $\delta \nu =(172\mathrm{}\pm 15)$ MHz. Anomalies in the intensity ratio of the doublet $5s-np$ transitions have been observed and interpreted as relativistic effects. Perturbations by weak and strong dc electric field are reported. In the case of weak electric fields it is possible to evaluate the polarizability. In the case of strong dc electric fields, new phenomena have been observed and analyzed. We also find experimental evidence of selective photoionization in the presence of an appropriate dc electric field, which could have some applications in laser isotope separation. Finally, we give the preliminary results of an experiment on the effect of a strong nonresonant electromagnetic field on high-lying Rydberg states.

Stark patterns of high-lying excited states of rubidium (Rydberg states $n\sim 48$) in electric fields from 0 to 20 V/cm have been studied both experimentally and theoretically. Recordings have been obtained with high-resolution laser techniques. Theoretical interpretation takes into account a great number of close-lying levels in the diagonalization process. In order to reproduce the positions as well as the intensities of the one-photon transitions from the ground state, it is necessary to use for $s$, $p$, and $d$ levels the wave functions calculated from a central potential specific to the Rb spectrum.