Photoelectron angular distributions for the valence $p$ shells of the rare gases have been measured up to a photon energy of 40.8 eV (48.4 eV for Ne) using resonance radiation from a hollow-cathode discharge lamp. This work extends the range of existing absolute measurements on Ne, Kr, and Xe. Comparison with HartreeFock and RPAE (random-phase approximation with exchange) calculations indicates excellent agreement for Ne. However, the present results, particularly for Xe, add to earlier evidence that data for Ar, Kr, and Xe show systematic deviations from theory, especially at the higher photoelectron kinetic energies. For Kr and Xe, we report asymmetry parameters separately for processes leading to the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2},\frac{1}{2}}^{}{}_{}{}^{}$ spin-orbit states of the residual ion. The Xe results indicate that ${\beta }_{\frac{3}{2}}-{\beta }_{\frac{1}{2}}$ is positive for $\lambda \ge 461$ Å, but changes sign in the range $\lambda \sim 350-400$ Å. At 304 Å, ${\beta }_{\frac{3}{2}}-{\beta }_{\frac{1}{2}}=-0.30\mathrm{}$, which agrees with a recent calculation based on the Dirac-Slater model.

Dynamical laws describing the space-time development of the response functions and second-order correlation functions of the electromagnetic fields in a linear dielectric medium are presented in the form of a number of differential and integral equations. The boundary conditions on the response functions are expressed as extinction theorems, which are particularly useful for systems involving rough surfaces and metallic gratings. Higher-order correlation functions are shown to be related to the linear-response functions in a manner analogous to the moment theorem for Gaussian random processes. A modified form of the fluctuation-dissipation theorem is obtained and is used to calculate free-space blackbody fluctuations in a moving frame. Fluctuations in a moving dielectric are obtained from the transformation of fields under Lorentz transformation. Contact with the earlier works of Mehta and Wolf, Eberly and Kujawski, and the recent work of Baltes and co-workers on blackbody radiation is made wherever possible. Finally, the correlation functions in a moving frame are used to discuss the relaxation of a moving atom. The discussion in the last section is for the case of free space.

A quantum-theoretic treatment of Lippmann fringes is given using the response-function formalism of part I of this series of papers. It is shown that the field emitted by the excited atom in the presence of a dielectric mirror possesses first-order coherence, and the absorption of such a field by the unexcited atom leads to the interference fringes. The nature of the emitted field is also examined from the point of view of excitation of surface modes. The causal character of the absorption process is also briefly commented upon.

High-resolution line-broadening studies have been made of C${\mathrm{O}}_2$ in collision with a wide variety of foreign gas perturbers. These measurements have been made by observation of the narrow saturated resonance in the 4.3-μm fluorescence emitted from a low-pressure C${\mathrm{O}}_2$ gas which is subjected to a saturating standing-wave electric field from a C${\mathrm{O}}_2$ oscillator operating on a 9.6- or 10.6-μm transition. The collision partners which have been investigated are C${\mathrm{O}}_2$, ${\mathrm{N}}_2$O, ${\mathrm{N}}_2$, NO, CO, ${\mathrm{O}}_2$, ${\mathrm{H}}_2$, ${\mathrm{D}}_2$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, Ne, Ar, Kr, Xe, N${\mathrm{H}}_3$, and C${\mathrm{H}}_4$. A semiclassical theory of the 4.3-μm saturated resonance is developed which accounts for the effects of phase-interrupting collisions, beam transit time, and optical intensity. The observation of a previously unobserved downward curvature of the C${\mathrm{O}}_2$ linewidth data at low pressure is attributed to the influence of the transit-time effect. The experimentally determined pressure-broadening coefficients include the important correction for the contribution of power broadening. These power-corrected results for C${\mathrm{O}}_2$, ${\mathrm{N}}_2$, and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ have been used to predict successfully the observed gain characteristics of high-pressure (> 1 atm) C${\mathrm{O}}_2$ amplifiers, as observed in other studies. We have also appraised our observed broadening coefficients in the context of the pressure-broadening theory developed by Murphy and Boggs in order to characterize quantitatively the intermolecular interactions. The comparison of theory and experiment indicates the need for an explicit incorporation of vibration perturbations in the theoretical analysis, particularly when vibrational resonance is present.

Calculations by Macek have shown that the ${\mathrm{H}}^{-}$ photoabsorption cross section should be affected by a shape resonance at 1129.5 Å. This experiment is an attempt to observe the resonance in emission according to the reaction $e+\mathrm{H}\to {\left[{\mathrm{H}}^{-}\right]}^{*}\to {\mathrm{H}}^{-}+h\nu$. The plasma is in a condition of local thermodynamic equilibrium and is generated by a stationary wall-stabilized hydrogen arc. With an axis temperature of 14000 K and 1 atm pressure, the ${\mathrm{H}}^{-}$ free-bound continuum contributes only about 2% of the total radiation which is dominated in the 1130-Å region by the Ly-$\alpha$ wing. However, the peak of the shape resonance, according to Macek, should have a cross section about 25 times greater than the continuous free-bound cross section; therefore, it should appear as a very noticeable 50% structure superimposed on the Ly-$\alpha$ wing. Except for some small features which are attributed to weak molecular emission, there is no obvious indication of the shape resonance in either deuterium or hydrogen spectra between 1105 and 1135 Å. It is estimated that the minimum feature which could have been detected at 1129 Å was about 2% of the total signal.

The effects of plasma electric microfields on linelike optical features arising from atomic levels above the ionization threshold are investigated within the framework of the quasistatic and single-frequency dynamical field theories of spectral-line broadening. The $2p^2{}_{}{}^3{}_{}{}^{}P\to 1s2p{}_{}{}^3{}_{}{}^{}P$ and $2s2p{}_{}{}^3{}_{}{}^{}P\to 1s2s{}_{}{}^3{}_{}{}^{}S$ transitions in helium and heliumlike ions are treated as illustrations. The mixing of the doubly excited levels in the perturbing microfields produces Stark broadening of the emission lines and induces autoionization of the $2p^2{}_{}{}^3{}_{}{}^{}P$ level, which, unlike the $2s2p{}_{}{}^3{}_{}{}^{}P$ level, is metastable against autoionization in the field-free environment. Determination of the complete Stark-broadening profiles in thermal plasmas is complicated by the need to include the effects of both the (quasistatic) ion and the (dynamical) electron fields. Under nonequilibrium conditions, where electric fields from either electron or ion plasma waves can far exceed nearby particle fields, the calculation and interpretation of the line shapes may be simplified and could provide a diagnostic probe of the wave-field properties.

This paper presents a theoretical study of laser-induced breakdown in argon. It is shown that the Ramsauer minimum in the momentum-transfer cross section of argon causes the mean electron energy in the discharge to be rather small. Thus, in the case of large laser quanta, the process of breakdown must be treated quantum mechanically. In order to calculate breakdown parameters for this case, a computer simulation based upon elementary quantum processes occurring in the laser radiation field is presented. Using this method, the electron multiplication coefficient in the discharge is calculated for several values of laser quanta energies. In the case of large laser quanta, the multiplication coefficient in argon is found to be higher than is predicted by the classical theory. It is shown that helium, not having a Ramsauer minimum, does not reveal a similar feature. Comparing our theoretical results with those of experiments from the literature, information is obtained on the role photoionization from upper excited levels of argon plays in the breakdown process.

The general applicability of molecular methods for studying hyperfine pressure shifts (HPS) in a hydrogen atom caused by Ar and He noble-gas buffers has been tested thoroughly by carrying out extensive multiconfigurational self-consistent-field (MCSCF) and single-configuration self-consistent-field (SCF) calculations on ArH and HeH diatomic systems. Calculations show that for a He atom, a light noble-gas buffer, single-configuration SCF molecular wave functions are sufficiently good in reproducing the HPS result quantitatively, although qualitatively the weak, long-range polarization features are not described. However, for a heavier noble-gas buffer, such as the Ar atom, the long-range polarization effects are the strong and dominant features in the ArH binary interaction. Because of a lack of a sufficient number of proper functions for describing the long-range polarization features, the single-configuration SCF molecular wave functions do not reproduce the long-range polarization effects adequately. For ArH, therefore, MCSCF molecular wave functions, constructed with a choice of configurations which describe the dominant polarizations, are employed to reproduce the HPS result quantitatively and the long-range features qualitatively. HPS results computed by using MCSCF molecular wave functions are in excellent agreement with the experimental result.

The photoionization of lithium from threshold to 50 eV above threshold is calculated via the method of polarized orbitals. The method is applied in as orthodox a manner as possible; this means that total wave functions are constructed as by Temkin and Lamkin using only the static dipole part of the perturbation of core electrons by the outer part of the external electron. According to other previously given prescriptions, both initial (bound) and final (continuum) wave functions are so polarized, only the length form of the matrix is calculated, and bilinear terms from the polarization contributions are retained (although their effect in this calculation is small). The results themselves are essentially identical to those of a recent diagrammatic calculation of Chang and Poe (in the region below 5 eV where they have calculated), and as such they differ in certain significant components from exchange adiabatic and extended polarization results of Matese and LaBahn (although their over-all result is similar). Discussion of these points is included. The $s$- and $p$-wave $e$-${\mathrm{Li}}^{+}$ phase shifts, which are derived as by-products of this calculation, are also presented and compared to other phase-shift calculations.

The amplification of a coherent optical pulse is analyzed by employing an inverse scattering method. In the extreme Doppler limit, one obtains an analytical expression that exhibits the expected evolution toward a $\pi$ pulse with pulse amplification and compression. In the sharp-line limit, one obtains justification for previous usage of a similarity solution to describe $\pi$-pulse propagation in an amplifier. The analysis is carried out for an initial pulse profile (truncated hyperbolic secant) which yields a sufficiently simple scattering problem that the Marchenko equation of inverse scattering theory may be solved analytically.

An inverse scattering transform method is presented for wave-wave scattering problems such as the Raman effect, distributed parametric amplifiers, and wave-wave interactions in plasmas. This transform method can be viewed as a nonlinear generalization of the Fourier-transform technique; and, in the form presented here, it describes the dynamics of the scattering medium.

Using the linear equations associated with the inverse scattering transform, the Bäcklund transformation equations for the wave-wave scattering problem are found. This again shows the exact correspondence between the equations of the inverse scattering transform and the equations for Bäcklund transformation.

We discuss from first principles the cooperative decay of a system of two-level atoms, initially prepared in an uncorrelated excited state with population inversion $N$, and we give the conditions under which the superfluorescence effect occurs. Describing the atomic system in terms of collective variables, we derive a master equation for the reduced atomic density operator, which gives rise both to a damping and to a time-dependent frequency shift in the dynamics of collective modes. The coupled equations of motion are solved with a self-consistent approach. It is found that the system goes through a nonexponential decay if the maximum length of the active volume is smaller than a "cooperation range" and larger than a "threshold length," in agreement with the one-mode theory. The radiation burst has a time width proportional to $N^{-1\mathrm{}}$, and its intensity is proportional to $N^2$. Specializing to a pencil-shaped volume, we find that only two atomic modes need to be considered; in this case, the average emitted radiation is all condensed in the two diffraction patterns of the opposite axial modes.

We consider a system of $N$ two-level atoms initially in the ground state and interacting with a small [$〈n(t=0\mathrm{})\mathrm{}〉\ll N$] coherent radiation field. The field is assumed to be monochromatic, and its wavelength is taken to be much larger than the dimensions of the region of the $N$ atoms. The statistical properties of both the atomic system and the radiation field are studied as functions of time. Using the Holstein-Primakoff transformation, it is shown that the initial coherence of the system tends to disappear after the energy of the system has been exchanged between atoms and field a number of times approximately given by $\frac{N}{〈n(t=0\mathrm{})\mathrm{}〉}$.

Inelastic light scattering has been used to study nonhydrodynamic behavior in the helium-xenon binary gas mixture with xenon dilute. Because of the large atomic mass and light-scattering cross section of xenon relative to helium, the contribution of xenon may be separated from the total scattered light spectrum. The spectrum of light scattered by xenon is studied as a function of helium pressure. At low helium pressure, xenon atoms are in free flight over the length $\frac{2\pi }{K}$, where $K$ is the scattering vector. The resulting scattered light spectrum is Gaussian. At high helium pressure, xenon atoms diffuse over the length $\frac{2\pi }{K}$ and the spectrum is Lorentzian. Quantitative study of the Gaussian-Lorentzian transition shows the Fokker-Planck model to be appropriate to describe the xenon-helium collision. Brillouin splitting and linewidth measurements are used to demonstrate the existence of nonhydrodynamic relaxation processes associated with momentum and temperature equilibration of the two species in a disparate mass mixture where the heavy component is dilute.

The rate of energy absorption by inverse bremsstrahlung of a plasma in an oscillating electric field is calculated. An expression for this rate is obtained that is valid for all ranges of the electron-plasma temperature and density and the electric field flux intensity and polarization. Analytical formulas are obtained for high-flux intensities where the rate is independent of the electron-velocity-distribution function.

Optical interferometric measurements which determine the equation of state of xenon in the neighborhood of the critical point are described. Analysis of Fraunhofer interference patterns from a thin slab of fluid yields data pairs: optical phase ${\psi }_{+}=\rho -{\kappa }_T\mu$ and isothermal compressibility ${\kappa }_T$, along isotherms in the temperature range $-{10}^{-4\mathrm{}}<\epsilon <{10}^{-4\mathrm{}}$, where $\epsilon =\frac{(T-T_c)}{T_c}$. Experimental data are analyzed in terms of a new parametric transformation of thermodynamic variables, based on the static scaling hypothesis of Widom, which requires that $\frac{d\ln {\psi }_{+}}{d\ln {\kappa }_T}=-\left(\frac{\beta }{\gamma }\right)W\left(\theta \right)$, where $\theta =\epsilon {\kappa }_T^{\frac{1}{\gamma }}$. On the critical isotherm, $\epsilon =0\mathrm{}$, we expect that $\ln {\psi }_{+}=\mathrm{const}-\left(\frac{\beta }{\gamma }\right)\ln {\kappa }_T$. This accords with observation and yields a sharp determination of $T_c$ which is decoupled from other parameters. The data are well represented by the bilinear form $W\left(\theta \right)=\frac{(1-\frac{\theta }{{\theta }_x})}{(1-\frac{\theta }{{\theta }_0})}$ where $\theta ={\theta }_0$ on the critical isochore and ${\theta }_x$ on the coexistence boundary. This is integrated to yield the parametric equation of state ${\psi }_{+}=Y_0^{\beta }{R}^{\beta }{(1-\frac{\theta }{{\theta }_0})}^{\beta \Delta }$, where $R={\kappa }_T^{-\frac{1}{\gamma }}$. A six-parameter fit to 1200 data points yields $T_c=T_c\left(\mathrm{lab}\right)\pm 0.0001°\mathrm{C}$, $\beta =0.3583\mathrm{}\pm 0.0002$, $\gamma =1.2296\mathrm{}\pm 0.0005$, ${\theta }_0=0.1101\mathrm{}\pm 0.0003$, $Y_0^{\beta }=0.4203\mathrm{}\pm 0.0004$, and $\Delta =3.869\mathrm{}\pm 0.001$. This implies $\beta \Delta =1.386\mathrm{}\pm 0.001$, which differs significantly from the value $\beta \Delta =\frac{3}{2}$ implied by a five-parameter transformation suggested by Ho and Litster. The coexistence curve is measured in the range ${10}^{-5\mathrm{}}<\left|\epsilon \right|<\mathrm{}5\mathrm{}\times {10}^{-2\mathrm{}}$, and fitted by the power law $\frac{({\rho }_L-{\rho }_G}{{\rho }_c}=B{(-\epsilon )}^{\beta }$, with the result $\beta =0.344\mathrm{}\pm 0.003$ and $B=3.51\mathrm{}\pm 0.05$. Systematic deviations indicate that $\beta$ increases for large $\left|\epsilon \right|$. A fit with the form $\frac{({\rho }_L-{\rho }_G)}{{\rho }_c}=B{(-\epsilon )}^{\beta }+A{(-\epsilon )}^{{\beta }^{\prime }}$ yields significant improvement, with $\beta =0.332\mathrm{}\pm 0.001$, $B=3.042\mathrm{}\pm 0.03$, ${\beta }^{\prime }=0.61\mathrm{}\pm 0.02$, and $A=0.93\mathrm{}\pm 0.04$. The disagreement between this $\beta$ and the $\beta$ obtained from fitting the Fraunhofer data will be discussed in the text. The coefficient of isothermal compressibility on the critical isochore $P_c{K}_T$ is measured in the range $2.7\times {10}^{-5\mathrm{}}<\epsilon <4\mathrm{}\times {10}^{-2\mathrm{}}$, and fitted by the equation ${\kappa }_T=P_c{K}_T=\Gamma {\epsilon }^{-\gamma }$. Over the measured range, the data indicate $\gamma =1.260\mathrm{}\pm 0.002$ and $\Gamma =0.056\mathrm{}\pm 0.001$. There is evidence that $\gamma$ depends on the range of fit, and we find $\gamma =1.232\mathrm{}\pm 0.006$ for $\epsilon <{10}^{-3\mathrm{}}$, which agrees well with the $\gamma$ determined from the near-critical Fraunhofer data.

An isolated one-dimensional self-gravitating system consisting of $N$ plane parallel sheets with uniform density is taken as a model problem for the study of the stochasticity of dynamical systems when the number of degrees of freedom increases. It appears that the proportion of the measure of the "ergodic" domain with respect to the whole volume of the phase space increases very rapidly with the number of degrees of freedom.

We study the kinetics of photons coupled to an electron gas by Compton collisions. We show that, for the limiting cases of linear and nonlinear evolutions, an initial narrow spectrum exhibits the same tendency of shifting towards the red frequencies. Concerning the Bose condensation of the photon gas which is predicted by standard thermodynamic arguments when the total number $A$ of photons exceeds some critical value $A_c$, we show that the nonlinear kinetic evolution leads to a condensationlike phenomena. This condensation, which always appears when $A>\mathrm{}{A}_c$, can also occur when $A<\mathrm{}{A}_c$ for sufficiently large and sharply peaked initial photon distributions. Such long-lived quasi-equilibrium states can be called "metastably condensed."

Parametric interactions between four electromagnetic waves subjected to a linear phase-matching condition have been considered in a plasma. The relativistic equation of motion of a single electron has been used. The evolution of two signal waves in time by two powerful pump fields has been studied. The largest contributions to frequency shifts and growth rates are found to come from the relativistic correction source. Moreover, in some cases of frequencies very large compared to the characteristic plasma frequency, a part of the relativistic effects totally cancels the other nonlinear effects. When the beat frequency of two of the waves equals the characteristic plasma frequency and in the neighborhood of this condition, the contributions from the nonrelativistic nonlinear sources are found to dominate. The frequency shifts and growth rates for high laser powers are considerable.