In an effort to obtain simple but reliable methods for analyzing and predicting differential cross sections for photoemission from the outermost $p$ orbitals of rare-gas atoms, we have compared predictions of the following theories of the atom: (i) the local-density theories of Slater ($X\alpha$) and of Hohenberg, Kohn, and Sham, (ii) the pseudopotential method, (iii) Hartree-Fock theory as evaluated by Kennedy and Manson, and (iv) Amusia's random-phase approximation with exchange (RPAE). We show that the local-density theories, although simple, generally fail to produce reliable differential cross sections; the more complicated Hartree-Fock method is no more reliable; the a priori RPAE method is most reliable, but tedious; and the phenomenological pseudopotential method offers a good combination of reliability and simplicity. The muffintin approximation widely used in molecular and condensed-matter physics is examined, and found to be adequate.

Using relativistic and nonrelativistic Hartree-Fock methods we have calculated some $E1\mathrm{}$ and $M2\mathrm{}$ transition probabilities for $2p^{5}3d\to 2p^6+\gamma$ and $2p^{5}3s\to 2p^6+\gamma$ in the Ne isoelectronic sequence. The heaviest ion considered is U. The relativistic effects on both the photon energies and the transition amplitudes are discussed. A comparison of our calculated $M2\mathrm{}$ lifetimes with experimental results for the $2p^{5}3s-2p^6$ transition in Ne-like Cu shows significant differences, while the calculated $E1\mathrm{}$ lifetimes for Ne-like Cl indicates good agreement with experiment.

The time-independent approach to scattering in a laser field is used as the basis for a derivation of a low-frequency approximation, in which field-free scattering amplitudes enter into the determination of transition amplitudes in the presence of an intense radiation field. The scatterer is here represented by a local, short-range potential. For the case of a linearly polarized single-mode field, the result reproduces that obtained earlier by Kroll and Watson, who based their analysis on a semiclassical description. In the present derivation a plane-wave field of arbitrary polarization is treated; the field may consist of a superposition of low-frequency modes, the propagation direction being the same for each mode. In preparation for the derivation of the low-frequency approximation, a general analysis is given of the properties of the asymptotic states which describe the propagation of a charged particle in the field. This analysis should also be useful in other applications of the scattering formalism.

The short-time behavior of atomic multiphoton-ionization profiles is investigated using simplified models of the field and the atom. The importance of including many levels in the model atom, of spontaneous emission, and of pulse shape are studied in detail. It is shown that the first two of these have little influence on the qualitative behavior of the short-time behavior of the resonance profile, but that the third, the pulse shape, is critical in determining the time evolution of the resonance profile.

The linear-Stark-effect approximation is employed to investigate the effects of electric fields on autoionizing doubly excited atomic states corresponding to relatively large values of the outer-electron principal quantum number $n$. By assuming that a statistical distribution of the inner-electron magnetic sublevels has been established, simple expressions are derived which relate the autoionization and radiative transition rates in the presence of an electric field to the respective field-free rates. It is pointed out that the multiphoton laser excitation of the doubly excited states can give rise to a nonstatistical distribution of the magnetic sublevels and to complex interference terms involving transition amplitudes associated with different values of the outer-electron angular momentum quantum number $l$. The results of calculations are presented for the autoionization and radiative-transition rates which play the most important role in the dielectronic recombination of the Li-like ${\mathrm{Fe}}^{+23\mathrm{}}$ ion through the $2p\to 2s$ inner-electron transition, where the contributions from large-$n$ values are particularly important. In these calculations it is assumed that the magnetic sublevels are statistically populated and only the simple expressions for the transition rates are employed. The effects of the electric field on the dominant (inner-electron) radiative decay rate can be neglected, but the electric field mixing of the outer-electron $l$ substates substantially increases the autoionization rates from the higher-$l$ sublevels.

This paper reports a theoretical treatment of the line shape for two-photon transitions. The time-dependent perturbation-theory treatment is equally appropriate for a fast atomic beam interacting with a microwave field in a waveguide, and for laser excitation of a thermal beam. Two important features of the physical systems are successfully incorporated into the theory. First, the amplitude of the external field to which the atoms are exposed varies in time; the envelope function affects the resonance linewidth and power shift. Second, the theory includes the natural decay of the atomic states; the decay amplitude produces a novel "lifetime shift," which displaces the two-photon resonance from its expected location, even in the limit of weak external fields. This paper gives detailed predictions for shifts and other distortions caused by nonidealities of the experimental apparatus used for the measurement of the $3{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-3\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$ transition in atomic hydrogen.

This paper reports a double-quantum radiofrequency measurement of the $3{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-3\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$ fine-structure interval in hydrogen. The measurement was carried out in zero magnetic field with a fast hydrogen beam. The measured value for the $3{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-3\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$ interval is 4013.204(78) MHz. This is in good agreement with the theoretical value.

The permutation symmetry of the dielectric susceptibilities is shown to be a direct consequence of CPT invariance and crossing symmetry of quantum electrodynamics.

The collisional dephasing of the Na $13d-13f$ transition by Ne and CO has been investigated using the Ramsey method of separated radio-frequency fields. Upper limits for the dephasing cross sections are determined which are far smaller than the geometric size of the excited Na atoms. This leads to the conclusion that the separation of the potential cruves of the Na $13d-X$ and $13f-X$ states is nearly constant as a function of internuclear separation.

Second- and third-order nonlinear optical polarizabilities for a number of small molecules—${\mathrm{H}}_2$, ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, CO, NO, C${\mathrm{O}}_2$, ${\mathrm{H}}_2$O, ${\mathrm{H}}_2$S, N${\mathrm{H}}_3$, S${\mathrm{F}}_6$, (C${\mathrm{H}}_3$)${}_2{}^{}{}_{}{}^{}\mathrm{O}$, and C${\mathrm{H}}_3$OH—are derived from measurements of the temperature dependence of dc-electric-field-induced optical second-harmonic generation in the gas phase. Agreement with related measurements (where available) is generally adequate, but the results of theoretical calculations taken from the literature are in poor agreement with the experimental data. Consideration of the present results for ${\mathrm{H}}_2$O together with liquid-phase measurements by Levine and Bethea offers a means of investigating intermolecular interactions in liquid water. The bond-additivity approximation applied to ${\mathrm{H}}_2$O, (C${\mathrm{H}}_3$)${}_2{}^{}{}_{}{}^{}\mathrm{O}$, and C${\mathrm{H}}_3$OH yields surprisingly good fits of the dipole moment, linear polarizabilities, and second- and third-order nonlinear polarizabilities to experimental data.

We study the statistical mechanics of a one-dimensional classical system with the purely repulsive interaction $v\left(x\right)=C\exp (-\gamma \mathrm{}|x\left|\right)$. Emphasis is laid upon an exact treatment of the long-range character of the interaction. We give explicit analytical expressions for the equation of state as well as for the correlation function. The almost crystalline nature of the system shows up in the low-temperature region.

The perturbation theory for classical processes developed by Martin, Siggia, and Rose is clarified and extended so that it applies to systems prepared in arbitrary initial states and driven by arbitrary random forces. The necessary modifications are achieved by introducing additional bare vertices. The range of validity of the original scheme (including slight modifications) is discussed. Finally, a short comparison with other approaches to perturbation theory is given.

Localized electron states in the rare-gas fluids are investigated using a density-functional formalism for the interacting fluid and a contact potential for the electron-atom interaction. The results are in qualitative agreement with previous theories which use simpler models of the fluid in that no localized states are found in dilute helium gas, neon gas, argon, krypton, and xenon, while localized states are found in dense helium gas and in liquid neon near the liquid-gas coexistance curve. There are, however, large quantitative differences between the present results and those of the other theories. In particular, it is predicted that the localized states in neon will become unstable at sufficiently large liquid densities which are still below the density at which the liquid-solid transition occurs. The effectiveness of the localized states as a mechanism for vapor nucleation in liquid neon is investigated as is the possibility that the liquid density profile is not monotonic in the vicinity of the localized electron. No oscillatory behavior of the density profile is found.

We have determined the order-parameter correlation function near the critical mixing point of 3-methylpentane-nitroethane by measuring the intensity of scattered light as a function of temperature. The data cover a range ${10}^{-6\mathrm{}}<t<\mathrm{}2.7\mathrm{}\times {10}^{-3\mathrm{}}$ in the reduced temperature $t=\frac{(T-T_c)}{T_c}$, which corresponds to a range $0.18<k\xi <25\mathrm{}$, where $k$ is the wave number and $\xi$ is the correlation length. The critical exponents deduced from the experimental data agree within combined errors with the values calculated theoretically for the Landau-Ginzburg-Wilson model. However, the data cannot be reconciled with the exponent values deduced from high-temperature series expansions for the three-dimensional Ising model.

It has been conjectured, for the Boltzmann equation, that an arbitrary initial state tends first to relax towards a state characterized by the similarity solution. We present here a simple model where the possible validity of the statement can be studied numerically. The results of extensive numerical computation for the first time give support for the validity of this conjecture.

The pair correlation function and the correlation-energy density of two-dimensional electron liquids are calculated on the basis of Salpeter's Debye-chain cluster expansion. When the two-dimensional plasma parameter $\epsilon =2\mathrm{}\pi n{e}^4{T}^{-2\mathrm{}}$ is small, the expansion to first order gives the known first four terms of the correlation energy to the order of ${\epsilon }^2\ln \epsilon$. It is shown that experimental results in the domain $\epsilon \lesssim 0.5$ can be reproduced by taking into account the first- and the second-order terms in this expansion.

When fluctuations of the director and density are taken into account, the second-order nematic—smectic-$C$ transition predicted by mean-field theory is found to become first-order. A dimensionless parameter, which is a measure of the response of director fluctuations to fluctuations in the density, enters the calculation. We investigate the transition for two limiting values of this parameter. In one case we recover the analysis of Swift. In the other we find a transition related to that found by Halperin, Lubensky, and Ma for the nematic—smectic-$A$ transition. We briefly discuss the nature of the director correlation function in the ordered state.

Expressions for the fourth-frequency-moment sum rule for the longitudinal and the transverse current-correlation function are obtained in the form which can be easily computed for all momentum transfers. This is made possible by carrying out analytically three of the four angular integrations involved in the three-body contribution to these moments. Numerical results for the moments are presented for some values of the plasma parameter of interest. These results are used to interpret the recent molecular-dynamics data on the dynamical structure factor using the Mori formalism. It is found that a renormalized free-particle memory function provides an overall good description of molecular-dynamics results for the dynamical structure factor over entire range of plasma parameter.

We describe a method which enables us to calculate both the orientational and the angular-velocity autocorrelation functions of an asymmetric top driven by white noise. The results are valid for both short and long times, and provide inertial corrections to the classical result of Perrin. They are applied to the calculation of complex polarizabilities for asymmetric-top molecules and the correlation times associated with the dipolar broadening of nuclear magnetic resonance lines. We take the angular-velocity vector to be the stationary solution of the Euler-Langevin equation, and obtain it in the form of a perturbation series. The random angular velocity drives the random orientational motion, and we use methods of stochastic differential equations to obtain an equation of motion for the aftereffect function. This cannot be solved in general by direct integration, and we use the method of averaging to obtain the aftereffect function in a form which is asymptotically correct both for large and small times.

It is shown that for an isolated resonance in a multichannel problem the sum of the eigenphases ${\delta }_n$ satisfies the usual formula appropriate for the elastic phase shift: ${\Sigma }_n{\delta }_n={\Delta }^0+invtan\left[\frac{\Gamma }{2(E_0-E)}\right]$. The parameter $\Gamma$ is the total width of the resonance.