Theoretical values of the oscillator strengths of the resonance transition of atoms of the zinc isoelectronic sequence are in satisfactory agreement with each other, but differ substantially from the measured values. Recent relativistic random-phase-approximation calculations on this sequence treated the inner-shell electrons as a frozen core. We investigate here the effect of relaxing the core by taking account of the perturbations of the $3d$ electrons and compare the results with the measured values. Inclusion of the $3d$-subshell correlation effects somewhat improves agreement with experiment, but a significant difference remains.

The broadening and shift of two-photon $S-S$ transitions (e.g., in alkali-metal atoms perturbed by rare gases) are shown to be readily calculable. These calculations employ (a) newly available expressions for alkalimetal-rare-gas long-range potential coefficients $C_6$, $C_8$, and $C_{10}$; and (b) the (herein discussed) appropriate form of impact theory (particularly simple since only a single potential curve is involved and inelastic processes are not usually important). It is demonstrated in particular that the influence of $C_8$ and $C_{10}$ terms on the broadening and shift is significant though not dominant. Comparison with recent experimental data on the Na-rare-gas pairs shows reasonable agreement for the heavy rare gases.

We present a theory of quantum beats in photoionization from a coherent superposition of $D_{\frac{3}{2},5.2\mathrm{}}$ levels in alkali-metal atoms. The semiclassical density-matrix formalism is used to describe both the excitation of the $D_{\frac{3}{2},\frac{5}{2}}$ levels by a two-photon resonant pulse and the subsequent photoionization by a delayed probe pulse. Quantum beats occur in the ionization signal as a function of the delay of the probe pulse. The depth of modulation is determined for different light polarizations.

The fine-structure splittings of $\mathrm{nd}{}_{}{}^2{}_{}{}^{}D\mathrm{}(n=5-7\mathrm{})\mathrm{}$ and $\mathrm{nf}{}_{}{}^2{}_{}{}^{}F\mathrm{}(n=4-6\mathrm{})\mathrm{}$ levels in singly-ionized magnesium have been determined by means of fast-beam, level-crossing, and anticrossing spectroscopy. The inverted ${}_{}{}^2{}_{}{}^{}D$ fine-structure splittings are found to be approximately 8% smaller than predicted by recent theoretical calculations based upon many-body theory. The ${}_{}{}^2{}_{}{}^{}F$ fine-structure splittings are found to be approximately 3%-7% smaller than the theoretical values for the corresponding hydrogenic levels.

Given the shape of a potential barrier $V\left(x\right)\mathrm{}$, there is an explicit expression in the WKB approximation for the transmission coefficient for penetration of the barrier. The problem considered in this paper is to find the inverse relation, determining $V\left(x\right)\mathrm{}$ from the transmission coefficient. It is shown that the width of the barrier at energy $E$ can be determined if the transmission coefficient is known for energies between $E$ and $V_{max}$, the barrier maximum. Other properties of the turning points can be deduced for potentials which can be written in terms of a parameter $\lambda$ as $V\left(x\right)=V_0\mathrm{}\left(x\right)-\lambda \phi \mathrm{}\left(x\right)\mathrm{}$, if the dependence of transmission coefficient on $\lambda$ is known. For the specific case of field emission, one can find the potential $V\left(x\right)\mathrm{}$ from the energy and field dependence of the transmission coefficient.

Tunable-cw-dye-laser spectroscopy of an atomic-beam sample, combined with interferometric wavelength measurements, has been applied to the measurement of energy levels, hyperfine structure, and lifetimes of ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$i. We find $E\left[{\mathrm{}\left(6p\right)\mathrm{}}^3{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right]=33\mathrm{}164.7000\left(7\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $E\left[{\mathrm{}\left(6p\right)\mathrm{}}^{2}7s{}_{}{}^4{}_{}{}^{}P_{\frac{5}{2}}^{}{}_{}{}^{}\right]=48\mathrm{}489.7593\left(8\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, and $E\left[{\mathrm{}\left(6p\right)\mathrm{}}^{2}7s{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right]=49\mathrm{}460.8014\left(8\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. The hyperfine coupling constants $A$, $B$, are for the ${\mathrm{}\left(6p\right)\mathrm{}}^{2}7s{}_{}{}^4{}_{}{}^{}P_{\frac{5}{2}}^{}{}_{}{}^{}$ level $(A, B)=[3717.4(5), -137.8\mathrm{}(5.0\left)\right]$ MHz and for the ${\mathrm{}\left(6p\right)\mathrm{}}^{2}7s{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ level $(A, B)=[2830.6(5), -132.6\mathrm{}(4.6\left)\right]$ MHz. The lifetimes are determined to (5.25±0.30) and (5.18±0.20) ns, respectively.

A laser perturbation method is used to determine the relaxation rates of levels $n=3, 4, 5$ of atomic hydrogen as a function of pressure and current intensity in a glow discharge. Quenching is due to spontaneous emission of radiation towards lower levels and to inelastic collisions with ${\mathrm{H}}_2$ molecules in the ground and quasimetastable states with thermally averaged cross sections of about 1.5×${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$.

The $7{}_{}{}^1{}_{}{}^{}S-9\mathrm{}{}_{}{}^1{}_{}{}^{}P$ energy separation of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ has been measured by the method of laser magnetic resonance in electron-beam-excited ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The measurements have also provided Zeeman tuning coefficients for terms up to fourth order in the field $B$. Motional-Stark-effect (MSE)-dominated line shapes are observed at most fields. These line shapes are analyzed, and their Doppler-free portions used to obtain a value for the energy separation with a precision exceeding 1 ppm ($\Delta E_o=980.7979\mathrm{}\pm 0.0002$ ${\mathrm{cm}}^{-1\mathrm{}}$). Arguments are presented that show the importance of the MSE in magnetically confined hot plasmas and in certain collapsed stars possessing high magnetic fields.

The asymptotic ($h\to 0$) limit of Dirac's single-electron theory is discussed with the magnetic field strength formally regarded as a quantity of order $\frac{1}{h}$. The main new result is that the phase function for the asymptotic series is to be calculated from the relativistic Hamilton-Jacobi equation with the orientation energy of the magnetic moment added to the electron's rest mass. This is the mechanism by means of which Hamilton's equations contain the Stern-Gerlach force when the phase function is interpreted as a classical generating function. An attempt is made to clarify the physical significance of this result.

The covariant photon interaction between electrons is reviewed briefly. Its potential function in configuration space is obtained unambiguously in a covariant perturbation calculation. Several different forms are presented, and their applications in atomic physics are discussed. In addition, the general matrix elements of various potential functions are given in terms of radial integrals, suitable for numerical computations.

We derive an equation of motion of the Bloch-vector tipping angle and the area theorem in the presence of relaxation. We derive relaxation-dependent shifts in the equilibrium $n\pi$ areas. Part of these shifts depends on a weighted time integral of the sine of the area, and hence these shifts remove the propagation degeneracy of pulses having equal areas but different shapes.

We discuss a mean-field quantum-mechanical model which describes the dynamics of a homogeneously broadened system of two-level atoms contained in a pencil-shaped resonant cavity and driven by a coherent resonant field $E_I$. The model is treated in the semiclassical approximation. The model is justified on the basis of Maxwell-Bloch equations with two coherently coupled directions of propagation, with boundary conditions for the fields taken into account. Above a suitable critical density of atoms the system exhibits a bistable behavior including both the stationary situation and the transient, both the light transmitted in the forward direction and the fluorescent light. Bistability is shown to be a consequence of atomic cooperation. We give a simple description of optical bistability leading to new predictions for the transient behavior of the transmitted light and for the spectrum of the fluorescent light. The damping constant which characterizes the rate of appraoch to the stationary situation exhibits a hysteresis cycle. In the low-transmission regime the approach is monotonic, whereas in the highly transmitting situation the approach is oscillatory. One finds a critical slowing down in correspondence with the values ${E_I}^{\mathrm{}(+)\mathrm{}}$, ${E_I}^{\mathrm{}(-)\mathrm{}}$ of the incident field where the transmitted field (as well as the total fluorescence intensity, the rate of approach to the stationary state, etc.) changes discontinuously. On the basis of the regression hypothesis we give a qualitative description of the spectrum of the fluorescent light. This is shown to undergo hysteresis and discontinuous changes at the same values $E_I^{\mathrm{}(+)\mathrm{}}$, $E_I^{\mathrm{}(-)\mathrm{}}$ of the incident field. Below the critical density of atoms one recovers the usual picture of resonance fluorescence, with a continuous transition from a single-line spectrum to a three-peaked structure when the Rabi frequency becomes equal to the natural linewidth. Above the critical density the triplet appears only when the Rabi frequency becomes equal to the cooperative linewidth of pure super-fluorescence (i.e., for $E_I=E_I^{\mathrm{}(+)\mathrm{}}$). Moreover, it appears discontinuously: when $E_I$ crosses the value $E_I^{\mathrm{}(+)\mathrm{}}$ the spectrum changes from a single narrow line to a triplet with well-separated sidebands.

We consider the time-evolution equation for the Glauber distribution function of the field emitted by a laser with saturable absorber and investigate the role of the terms with derivatives of order higher than second. It is found that the main effect of these terms is the following: When the relative saturability of the passive atoms with respect to the active atoms is very high, the (first-order-like) transition is much sharper than predicted by the Fokker-Planck equation.

The stability criteria in the pumping and lasing states in a cw solid-state laser are investigated using the semiclassical theory of the multimode laser. The model admits of one (trivial) steady state corresponding to thermal equilibrium, for which an $N$-body principle of minimum-entropy production may be obtained the entropy production serving as a Lyapounov function in this case. The other (multiple) steady states are far from thermal equilibrium. It is possible to construct an $N$-body Lyapounov function in the general, multimode case for these states within the framework of the rate approximation. Near equilibrium, the linear thermodynamics of the multimode laser are developed with the entropy production.

Autocorrelations due to natural phase and amplitude fluctuations of the laser field were investigated in the threshold region of a 633-nm He-Ne single-mode laser by use of an interferometric autodyne method. The measured time-dependent autocorrelation function shows deviations from an exponential decay that can be described by a formal fine structure predicted by the theoretical Van der Pol laser model. As a consequence, the natural laser spectrum is not exactly Lorentz shaped. The natural linewidth shows the expected general reciprocal power dependence and an additional factor-of-2 narrowing above threshold, in full agreement with the theory.

The Stark-broadened profiles of singly ionized silicon lines of multiplet $1(3s3p^2{}_{}{}^2{}_{}{}^{}D-3\mathrm{}{s}^{2}4p{}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{})$ and multiplet $m(3\mathrm{}{s}^{2}4s{}_{}{}^2{}_{}{}^{}S-3\mathrm{}{s}^{2}4p{}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{})$ have been measured by three methods, namely, photoelectrical scanning, fast scanning with a Fabry-Perot spectrometer, and using an optical multichannel analyzer. An electromagnetically driven shock tube was used to generate a high-density helium plasma containing small silicon and hydrogen admixtures and having an electron density $N_e\approx 1\times {10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$ and temperature $\mathrm{kT}\approx 1.5$ eV. The measured half widths of the lines in the two multiplets are in ∼10% agreement with the widths estimated from a semiclassical calculation, while semiempirical and quantum-mechanical calculations give widths by as much as a factor of 2 below the measured widths.

The mode-coupling theory has been worked out to calculate the longitudinal and transverse current-fluctuation spectra, the dynamical structure factor, and the dynamical as well as the static transport coefficients of liquid rubidium. The results are compared with experimental data. A detailed comparison of the excitation spectra of liquid rubidium with those of liquid argon is presented.

In a Hamiltonian system of three degrees of freedom we have found a large stochastic region (the "big sea"), some other stochastic regions, apparently separated from the above ("small seas"), and some ordered regions. In the ordered regions the maximal Lyapunov characteristic number vanishes, while it has finite values in the stochastic regions. However, these values are different in the big sea and the small seas. Three formal integrals were constructed and they were truncated at orders 2,3,...,11. The numerical values of the truncated integrals along several orbits were calculated. The variations of all three integrals decrease with order in the ordered region, while they remain large in the big sea. In a small sea two integrals have large relative variations, while one integral seems to be well conserved. This indicates that in the ordered region there are two integrals, in the big sea none, and in the small seas one integral beyond the energy.

The pressure of a classical simple fluid, assumed to be represented by a Lennard-Jones 6-12 potential function, is computed as a function of density at a temperature approximately midway between the triple- and critical-point temperatures. The method employs a parametric integral equation to compute radial distribution functions for a reference potential and these functions are then used in a first-order perturbation equation to obtain the Helmholtz function for the system, and consequently the pressure. The Lennard-Jones potential function is separated into the sum of two parts, a reference potential and a perturbing potential which includes a parameter which varies the "strength" of the perturbation. In this paper we are particularly interested in how the final results depend upon the perturbation parameter: that is, upon how the potential function is separated. We find that there is some dependence of the final answer upon how the potential is separated, but that there is a range of the parameter for which the results are reasonably constant and show good agreement with "exact" calculations.

We build up a method which permits us to investigate the propagation of a traveling wave in different cases (homogeneous or inhomogeneous plasmas, relativistic or nonrelativistic approximations). In the inhomogeneous-plasma case, our results show that, near the critical surface, the wave amplitude spatial dependence is greatly modified when the wave becomes relativistic.