We consider the alteration of the normal Brownian motion of a seed particle brought about by the enhanced velocity fluctuations that exist near the threshold of a hydrodynamic instability. We utilize our results to quantitatively predict the fluctuation induced effects for the threshold region of the Bénard convective instability.

The eikonal amplitude is used in the framework of the adiabatic approximation to obtain the rotational excitations of homonuclear diatomic molecules by intermediate-energy electron impact. The formalism is simple and may be extended to collision processes in which heteronuclear molecules are used as the target, or positrons as projectiles. The results for the differential cross section of the $J=1\mathrm{}\to 3$ rotational excitation of hydrogen molecules by 40-eV electron impact are in qualitative agreement with the recent experimental findings.

Total scattering cross-section measurements for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ + ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ + ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are presented for velocities between 60 and 900 m/sec and 105 to 1000 m/sec, respectively. For ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ + ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, a Ramsauer-Townsend effect is resolved and $s$ and $d$ phase shifts are obtained. The behavior of the $s$ phase shift suggests that this system is not bound. For ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ + ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ a virtual state at 135 m/sec is resolved and some $p$ phase shifts are obtained. A fit to the data for both pairs indicates that mass-polarization effects are negligible.

A method is formulated for the straightforward evaluation of the Coulomb-Born and Coulomb-Born-Oppenheimer (CBO) cross sections for $1s$-$2s$ excitation of hydrogenlike ions by electron impact, without employing partial-wave analysis. The simplicity of the method makes it very economical for the calculation of electron-ion scattering cross sections at any energy. Some results for the $1s$-$2s$ excitation cross sections for hydrogenlike ions with $Z=2, 3, 6, 10, \mathrm{and} 50$ are presented. The high-energy CBO results for the $1s$-$2s$ excitation of ${\mathrm{He}}^{+}$ agree well with recent experimental findings.

Energies and eigenstates are obtained for the $n=2\mathrm{}$ and $n=3\mathrm{}$ levels of hydrogen atoms moving in strong magnetic fields. The Hamiltonian of the system includes the interaction with the Lorentz field, $\overrightarrow{E}=\overrightarrow{\mathrm{v}}\times \overrightarrow{B}$, as well as the magnetic interaction, $-\overrightarrow{\mu }·\overrightarrow{B}$. These results are utilized together with the Doppler shifts in order to obtain profiles and polarizations of the Balmer-$\alpha$ line in tokamak-like environments under the assumption that the velocity distributions are Maxwellian.

In this paper high-resolution $K$ x-ray spectra for boron (1 MeV) and neon (90 keV) projectiles moving in solid targets are reported. The x-ray transitions from the moving ions are found to be substantially broadened, compared to gas-target spectral lines. Estimates of the extent of broadening are presented, and physical mechanisms responsible for it are discussed.

The method of singlet-triplet anticrossing has been extended to the $n{}_{}{}^{1-3}{}_{}{}^{}D$ levels of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ with $n=3, 4, \mathrm{and} 5$. We measure both the zero-field singlet-triplet separation with a higher accuracy than optical measurements, and the antisymmetric part of the spin-orbit coupling between singlet and triplet states. The agreement with many-body perturbation calculations for singlet-triplet intervals and with the hydrogenic approximation for spin-orbit coupling is fairly good even for low-$n$ states. Values of singlet-triplet mixing in the $n=3-8\mathrm{} D$ states, derived directly from the experimental results, are significantly more accurate than previous experimental and theoretical values.

The beam-foil time-of-flight method has been used to investigate radiative lifetimes and transition rates involving $\Delta n=0\mathrm{}$ allowed transitions within the $L$ shell of highly ionized sulfur. The results for these transitions, which can be particularly correlation sensitive, are compared to current calculations based upon multiconfigurational models.

Moment-theory methods for the construction of photoabsorption and dispersion profiles from associated dipole spectral moments are described and applied to simple atoms and ions. A previously devised (Stieltjes) moment approach, which provides convergent histogram approximations to absorption and dispersion profiles, is refined and extended to the use of arbitrarily large numbers of spectral moments, and an improved (Tchebycheff) moment approach is introduced which gives profiles that are continuous in the photoionization region and exhibit the $\delta$-function-like behavior associated with discrete transitions at the appropriate frequencies. Recurrence relations for the polynomials orthogonal and quasiorthogonal with respect to the distributions are employed in solving the necessary moment problems involving large numbers of spectral moments. The methods are applied in illustrative calculations of absorption and dispersion profiles in one- and two-electron atoms and ions. In the case of one-electron atomic systems the necessary polynomial recurrence coefficients are obtained in closed form from the known spectral moments, allowing the construction of distributions which reproduce the known profiles with high accuracy, employing as many as 100 spectral moments. Variational calculations using large basis sets of square-integrable functions, including the special functions required to satisfy sum rules, provide accurate spectral moments for atomic helium and the negative hydrogen ion. A simple moment-extension procedure is devised to interpolate the associated recurrence coefficients to infinite order employing their known asymptotic values. The associated Stieltjes and Tchebycheff approximations to the absorption and dispersion profiles obtained in these cases are in excellent agreement with available measurements and previous accurate calculations employing discrete and continuum wave functions.

We present a systematic theoretical analysis of two-photon ionization of cesium in the perturbation-theory regime. Matrix elements from diverse sources, such as quantum-defect theory and model potentials, as well as from experimental oscillator strengths, have been used in the calculation. The results are discussed in the context of recent measurements. In addition to total generalized cross sections (gcs) for linearly polarized light, ratios of gcs for linear to circular polarization, as well as photoelectron spin polarization, have been calculated. The various sets of matrix elements give results which are consistent, given variations that should be expected from the diversity of the sources. The disagreement with experiment, however, persists.

The Stieltjes imaging method makes possible the computation of photoionization or photodetachment cross sections without use of electronic continuum wave functions. Several practical difficulties are encountered in applying this method to complex atoms. Modifications of the computational procedure are introduced here, allowing the efficient computation of high-order principal representations of oscillator-strength distributions of complex atoms without numerical instabilities inherent in previous methods. Illustrative calculations are reported for the ground states of He and B. Principal representations obtained by variational calculations for these two atoms are used to compute spectroscopic moments and Van der Waals constants, and to reconstruct the oscillator strengths of line spectra at observed excitation wavelengths. Good agreement is found with all available quantitative data. Difficulties in constructing the photoionization cross section from the computed principal representations are shown, analyzed, and tentatively resolved by separating the oscillator-strength distributions into physically distinct excitation series.

Extensive photoelectric measurements of the plasma-broadened line shapes of 42 neutral nitrogen lines have been carried out with a wall-stabilized arc. The arc current was varied from 20 to 100 A to achieve a variation in the axial electron density from about 5 × ${10}^{16}$ to 1.5 × ${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$. Most observations were made end-on, and the arc was operated in pure nitrogen as well as argon with a small admixture of nitrogen to avoid self-absorption problems, which mainly arose with the red and near-infrared lines. The electron density was determined from the well-known Stark half-width of the hydrogen $H_{\beta }$ line, for which purpose a trace of hydrogen was added to the plasma. Our principal results are as follows: (a) Good agreement with the recent theoretical work by Griem and co-workers has been obtained; (b) consistent with theoretical predictions, ion-broadening effects are not noticeable; (c) the Stark widths and shifts for different lines in a multiplet are identical within the experimental precision (≅ 3%) as predicted by the theory; and (d) measurements performed over a range of transitions involving different quantum states agree equally well with the theoretical data, indicating that the atomic-structure part of theory is very adequate.

The photodissociation processes of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ have been studied using photon wavelengths in the $\lambda \lambda 686-723$-Å region. The fluorescence radiation from the photofragments was dispersed in the $\lambda \lambda 3500-7000$-Å region and was identified as the Balmer series. The cross sections for the production of the Balmer series were measured and were used to infer the cross sections for the photodissociation of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ into atomic products in the $n\ge 3$ levels. The dependence of the cross sections for the production of excited atoms in the $n$ levels on the excess kinetic energy is, in general, similar to that in the $n=2\mathrm{}$ level calculated by Allison and Dalgarno. The photodissociation process is therefore attributed mainly to the direct photoexcitation of molecules from the ground state into continua. This suggestion is further strengthened by the fact that the ratio of the cross sections for production of atoms formed in the $n=4\mathrm{} \mathrm{and} 5$ levels agrees with that of the square of their transition moments calculated by Rothenburg and Davidson. However, the ratio of the cross sections between the $n=3\mathrm{} \mathrm{and} 4$ levels does not agree well with the same calculation. It is therefore inferred that the cross section for the production of atoms excited in the $n=3\mathrm{}$ level may be partially through predissociation processes. This observation is consistent with the theoretical prediction of Berry and Nielsen that photodissociation of ${\mathrm{H}}_2$ into $H\left(1s\right)+H(nl,n\ge 3)$ through predissociation is only important in the $n=3\mathrm{}$ channel.

We develop a new approximation method for determining resonance properties of atomic systems interacting with intense photon beams. This method, based on an improved iteration procedure, leads to analytic expressions for the atomic density matrix from which positions of the resonances are determined. Our iteration procedure is more rapidly convergent than the continued-fraction method, and already in its second step reproduces the Bloch-Siegert shift of the one-photon resonance within 1 ppm.

We have used a Doppler-tuned x-ray spectrometer to measure the energy of the 1564-eV photon emitted during the forbidden intercombination decay $\mathrm{}\left(1s2s2p\right)\mathrm{}{}_{}{}^4{}_{}{}^{}P_{\frac{5}{2}}^o{}_{}{}^{}\to \left(1\mathrm{}{s}^{2}2s\right){}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^e{}_{}{}^{}$ in ${\mathrm{Al}}^{+10\mathrm{}}$. Delayed x rays were observed coming from 25-, 50-, and 75-MeV Al ions a few nanoseconds after they passed through a ${20-\mathrm{\mu }\mathrm{g}/\mathrm{c}\mathrm{m}}^2$ carbon foil. Li-like and He-like $2p\to 1s$ transitions were observed, and the triplet and singlet He-like transitions were well enough resolved to permit their use as energy calibration lines. To verify that the 1564-eV photon was emitted by the $J=\frac{5}{2}$ component of the ${}_{}{}^4{}_{}{}^{}P$ term we measured its intensity as a function of time after excitation, and found a mean life that agrees with a previously published measurement. Both the measured excitation energy, 1563.65 ± 0.90 eV, and the measured mean life, 2.71 ± 0.14 nsec, agree with the theoretical values published by Cheng, Lin, and Johnson.

We have evaluated relativistic dipole oscillator line and momentum strengths for a number of elements in the Li and Be isoelectronic sequences. In the Li sequence, the transitions considered are $2s_{\frac{1}{2}}$-$2p_{\frac{1}{2},\frac{3}{2}}$, $2s_{\frac{1}{2}}$-$3p_{\frac{1}{2},\frac{3}{2}}$, $2p_{\frac{1}{2}}$-$3d_{\frac{3}{2}}$, and $2p_{\frac{3}{2}}$-$3d_{\frac{3}{2},\frac{5}{2}}$; in the Be sequence, $2s_{\frac{1}{2}}^2$-$2s_{\frac{1}{2}}2p_{\frac{1}{2},\frac{3}{2}}$. The two electromagnetic-field gauges which in the nonrelativistic limit give the length and velocity forms of the transition operator have been used. The heaviest element considered in both sequences was uranium. Relativistic wave functions were obtained using a multiconfiguration Dirac-Hartree-Fock calculation. Nonrelativistic calculations of similar accuracy were also carried out for comparative purposes. The results are discussed with a particular emphasis on how relativistic effects manifest themselves, and under what conditions.

We report the first observation of perturbed and unperturbed Rydberg progressions of atomic uranium. Highlying levels within 1000 ${\mathrm{cm}}^{-1\mathrm{}}$ of the ionization limit were accessed by time-resolved stepwise excitation using dye laser pulses tuned to resonant transitions. Atoms excited to these states were then photoionized by intense infrared radiation from a pulsed ${\mathrm{CO}}_2$ laser. The resultant photoion production was monitored. By delaying the infrared ionizing pulse, and thus discriminating against the shorter-lived valence states, we preferentially detected Rydberg levels with principal quantum numbers $n$ exceeding 60. Series convergence yields a value of the ionization limit of 6.1941 ± 0.0005 eV, in fair agreement with the value of 6.1912 ± 0.0025 eV obtained in photoionization studies. Ab initio calculations indicate that the unperturbed series belong to highly excited $5f^{3}7s^2\mathrm{np}$ and $\mathrm{nf}$ configurations.

The problem of calculating transition probabilities for an atom interacting with an intense radiation field is set up within the context of an effective Hamiltonian formalism. This has the virtue that resonance effects are properly accounted for at the outset; more generally, it provides a convenient framework for approximations. Through the restriction of the class of intermediate states to be included in the construction of the effective potential, a unitary (nonperturbative) model is obtained. A successive approximation procedure for determining the effective potential, which is based on continued-fraction representations, is described. While very likely intractable for the true problem, this successive approximation procedure can be implemented, for the model effective potential, with the aid of a generalized Rayleigh-Ritz procedure described here. The level-shift matrix is constructed from the effective potential; it determines the transition probabilities, linewidths, and energy-level displacements induced by the field. We derive variational expressions of the Kohn type for each of the elements of the model level-shift matrix.

We report a measurement of the $A^2\Sigma (v^{\prime }=0)$ radiative lifetime in silicon monofluoride. In this experiment, SiF radicals were produced by the microwave discharge of Si${\mathrm{F}}_4$. The ground-state SiF molecules were then excited to the $A^2\Sigma (v^{\prime }=0)$ state by a dye-laser pulse. The resultant fluorescence was recorded and its decay rate measured. The measured lifetime was 0.23 ± 0.02 μsec and was independent of Si${\mathrm{F}}_4$ pressure in the range 0.05 to 1.0 Torr.

We present a theoretical treatment of the coherent three-level beat signals occurring in the transient response of a Doppler-broadened molecular system with coupled closely spaced levels resonating with an intense monochromatic cw laser field. When the degenerate levels of the molecular system are suddenly split by means of an external Stark or Zeeman field, the transmitted laser radiation exhibits decaying beats at frequencies related to the level splitting or Raman frequency. This effect has been the subject of earlier theoretical analyses, but some relevant aspects such as the velocity integration, were not taken into account. A perturbation treatment, complete to third order in laser field strength, is used to calculate the velocity-integrated induced polarization and the corresponding reradiated field. The calculation takes into account both Raman-type processes, which lead to transient oscillations at the Raman frequency ${\omega }_{21}$, and population-saturation effects. In particular, population-induced transient oscillations at half the Raman frequency, $\frac{{\omega }_{21}}{2}$, are predicted. The relative importance of the various oscillations is analyzed as a function of the laser detuning and other parameters, including velocity-changing collisions. The relationship between the three-level beat signals and the well-known quantum-beat effect studied in fluorescence is explored.