The theory of the cascade level-crossing effect as formulated by Happer is evaluated for zero-nuclear-spin atomic systems and extended to include the case of a polarized initial state. We have used this theory to interpret our cascade-Hanle-effect results (zero-field level crossings) to obtain the lifetime of the two resonance levels, $1s_2\left({}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ and $1s_4\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$, of the $2p^{5}3s$ configuration of neon. The resonance lines 744 Å ($1s_4-{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$) and 736 Å ($1s_2-{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$) are produced in the cascade to the ground ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ state when a beam of metastable $1s_3\left({}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}\right)$ and $1s_5\left({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)$ neon atoms is excited by selected lines of the $2p^{5}3s-2p^{5}3p$ transition array. Our results are $\tau \left(1\mathrm{}{s}_2\right)=1.65\mathrm{}\pm 0.16$ nsec and $\tau \left(1\mathrm{}{s}_4\right)=20.5\mathrm{}\pm 1.5$ nsec.

We present the analysis of the x-ray spectrum between 9.5 and 17.0 Å of a laser-produced iron plasma. Wavelengths and relative intensities for 96 lines are measured. For the strongest part of the spectrum, above 13 Å, almost all of the observed lines are identified as radiation from ${\mathrm{Fe}}^{\mathrm{XVII}}$, ${\mathrm{Fe}}^{\mathrm{XVIII}}$, and ${\mathrm{Fe}}^{\mathrm{XIX}}$ ions. Measurements were made with a curved-crystal spectrograph. Calculations were full intermediate coupling, Hartree-Fock with relativistic corrections. Coulomb-approximation oscillator strengths were used to help in the line identification.

A new theory of autoionization is presented which makes no reference to decay channels and which treats the process as a bound-state problem. The starting point is a postulative definition, describing autoionizing—or resonance—states as time-stability maxima within the set of bound functions. The outcome of the mathematical formulation of the postulate is a variational expression for the mean-square deviation of energy. The resulting Euler expression is a nonlinear pseudoeigenvalue equation whose solutions include autoionizing as well as stationary bound states. A second equation, similar to the first, is derived, whose solutions correspond to most stable bound functions at any given energy. Using the second equation, it is possible to obtain a plot of lifetime versus energy—the time stability spectrum. The theory is applied to some ${}_{}{}^1{}_{}{}^{}S$ autoionizing states of He below the $n=2, 3, \mathrm{and} 4$ ionization thresholds. The present results are within error bounds of experimental measurements. Agreement with Feshbach-type calculations is also good.

The time evolution of a two-level system interacting with a classical monochromatic radiation field is calculated by Fourier transforming the equations of motion. This can be done exactly if one uses the convolution of the product of two Fourier transformations. The method produces recurrence relationships for the transforms. The time-dependent amplitudes of the states and the transition probability are evaluated by using two such recurrence relationships. The time-averaged probability shows characteristic resonances at odd multiples of the ratio of the natural frequency of the system to the frequency of the radiation field. The peaks of the resonances are displaced by the Bloch-Siegert shift. At these resonances the system is completely saturated with the flipping frequency dependent on the strength of the radiation field. The time dependence and the frequency spectrum of the dipole moment is determined at the main resonance and at the three-quantum resonance. The spectrum contains the zero-frequency terms which are responsible for the coherence resonances.

Propagation of short ($\lesssim T_2$, where $T_2$ is the phase relaxation time) light pulses through absorbing media consisting of two ensembles of two-level systems of slightly different transition frequency is considered here. It is shown that one group of absorbers can be totally excited (inverted) while the other is returned to ground state. The effect of inhomogeneous broadening is illustrated by examples of propagation (numerical simulation) of properly shaped pulses through media having a linewidth equal to 1/5 of the frequency separation between the two transitions. The initial proportion of the two-level mixture is: 5% of the element to be excited, 95% of the element to be kept in ground state. The selective excitation capabilities of a Gaussian pulse and a zero-area pulse are compared.

We have developed a self-consistent description, based on the semiclassical radiation theory of the propagation of a light pulse in a dye medium. The multilevel nature of the energy bands of a dye molecule and the solvent cage effect in a solution are taken into account. In the case of light pulses whose duration is much shorter than the solvent-solute relaxation time but much longer than the time of atomic phase memory, the latter being of the order of ${10}^{-12\mathrm{}}$ sec for dyes, we solve the coupled system of equations for the field and the medium by the perturbation procedure. The hole-burning effect is incorporated into the solution in a natural manner. This is especially clear in the direct transition approximation where all the intermediate transitions are neglected. A recent idea of pulse superposition, consisting in storing the energy of a pulse in the form of population inversion followed by stimulated emission triggered by another pulse, is further discussed. Contrary to the orginal model developed by one of us (S.L.C.), we show that no cw pumping is required. The feasibility of the pulse superposition is supported by some experimental results obtained by sending a train of 10-psec pulses through a glycerine solution of oxazine 1 perchlorate.

Diffusion cooling and heating of electrons in a neutral gas is shown to be related to steep-gradient, nonlinear diffusive effects imposed by the presence of boundaries. A variational method of solution of Boltzmann's equation is outlined and the effective electron diffusion coefficient is obtained as the minimum of a certain integral. Gas mixtures and inelastic collisions are considered using model cross sections.

The anisotropy of the electron distribution function of an afterglow plasma produced in a microwave discharge and confined in a magnetic mirror field is studied with the use of a mirror probe method. It is found that the observed distribution indicates the characteristics of the loss-cone distribution function.

Non-Markoffian effects in the Josephson-radiation linewidth are investigated by using the projection-operator formalism of Mori. The memory function as well as the frequency are calculated in perturbation theory. We develop formal expressions for these to order ${\lambda }^4$, $\lambda$ being a perturbation parameter, and discuss the simpler results valid to order ${\lambda }^2$.

Enhancements above the predicted spectrum for a thermal plasma have been reported at various multiples of 1/4 the plasma frequency in an $\alpha \lesssim 1$ plasma. We have investigated the spectrum of a $\theta$-pinch plasma over the range of parameters covering reported deviations. With a 2-≫ resolution we were able to fit thermal spectra to the observed spectra with a standard error of estimate, in most cases, of less than 2%. Using parameters very similar to those used in a recently published study where many deviations were reported, we were able to fit a thermal spectrum to our measured spectrum with a standard error of estimate of 4% and 0.66-≫ resolution.

A general theory of two-body reaction rates in a relativistic plasma is developed. The most notable results of this theory are exact expressions for total rates involving only a single integral over the cross section for the usual case of relativistic Maxwell-Boltzmann or Bose-Einstein momentum distributions. This simplification arises from the fact that in the relativistic as well as the nonrelativistic case, an effective combined-particle distribution function can be found analytically. These results are applied to calculate the rates for radiative Compton scattering, photon-photon pair creation, and pion production in proton-proton collisions.

The generalized off-shell scattering of pairs of constituent fermions embedded in an infinite system of identical particles having thermodynamic properties characterized by arbitrary values of the temperature and chemical potential, is examined using a temperature-dependent Green's-function formalism, which treats particle-particle and hole-hole excitations symmetrically. The important features which emerge are (i) the possible existence of bound-state pairs (of quasiparticles which are linear combinations of particle and hole states) which correspond to poles in the scattering amplitude at negative total energies depending parametrically on the properties of the medium and the total momentum of the interacting pair; (ii) a generalized unitarity condition from which one obtains a parametrization of the on-shell positive-energy scattering amplitude by a set of real effective phase shifts; (iii) that these phase shifts completely determine the large-separation asymptotic behavior of the scattering (positive energy) pair wave functions in a manner which is form equivalent to two-particle scattering in free space; and (iv) that the small- and large-momentum asymptotic limits of the phase shifts are related to the number of bound-state pairs in the medium via an analogous, but modified, form of Levinson's theorem for free scattering. The effects of these pairing singularities on the single-particle excitation spectrum, and hence on the thermodynamic behavior of the system are outlined.

Molecular-dynamics calculations are reported for systems of ions in which the contribution to the interionic forces arising from polarization is taken explicitly into account. Two models of polarization are considered: a modification of that used for alkali-halide molecules by Tosi and Doyama and a simplified version of the shell model of lattice dynamics. In each case the effects of polarization are superimposed on an underlying rigid-ion pair potential of the type proposed by Tosi and Fumi. Calculations of the phonon spectra show that use of either model leads to agreement with experimental data on solid NaCl, which is considerably better than that achieved with the Tosi-Fumi potential alone; good results are also obtained for solid KI. Calculations for molten KI based on the shell model show that the effect of polarization in the liquid state is to increase significantly the diffusion coefficients, particularly that of the positive ion, and decrease the shear viscosity, but the effect on electrical conductivity is almost negligible. These results are broadly consistent with the known adequacy of the rigid-ion-model to account for the transport coefficients of molten alkali halides. Polarization is also shown to lead to a reduction in the characteristic frequencies and a considerably increased damping of collective longitudinal-optic-type modes in the liquid. The effect on other collective modes is less pronounced.

Measurements of the intensity autocorrelation of light scattered from diffusing micropheres suspended in a normal fluid show that if the particle radii satisfy the condition $l\lesssim {\lambda }_0$ where ${\lambda }_0$ is the wavelength of the incident light, and if the suspension is polydisperse (a finite-width particle-size distribution), the experimental diffusion constant displays a dependence upon the scattered wave number $k$ which is qualitatively the same as that for a critical fluid system in the nonhydrodynamic ($k\xi \gtrsim 1$) regime. These experimental observations have led us to propose a model of a critical fluid in which the order-parameter fluctuations are considered as spherical molecular clusters, or droplets, performing Brownian motion in a normal host fluid. The droplets are assumed to have a Gaussian index of refraction spacial profile, and a particle-size distribution $N\left(l\right)\mathrm{}$ characterizing the suspension determined from the requirement that the scattered light intensity be of the modified Ornstein-Zernike form. In a first approximation, the droplets are assumed to diffuse without changing size for times of the order of the characteristic diffusion time. The intensity-autocorrelation function of light scattered by our model system of diffusing droplets is evaluated, and the effective Rayleigh linewidth is found to agree to within a constant factor of order 1 with the ansatz for the critical part of the Rayleigh linewidth chosen by Perl and Ferrell. The resulting line-shape function is nearly Lorentzian, except in the wings where experimental detection of a departure from Lorentzian behavior becomes extremely difficult. Our droplet-size distribution is very similar to that which results from the static droplet model of Fisher which has been applied successfully to describe static critical phenomena in fluids below the critical temperature. In the diffusing droplet model, the $k$ dependence of the diffusion constant extracted from light-scattering measurements on critical fluids is seen to be an artifact introduced by the light-scattering process, and introduces no new physical information concerning the critical fluid behavior which is not contained in the droplet-size distribution function.

Analysis of dielectric data along the coexistence curve in Xe shows that neither revised scaling nor corrections to scaling has a significant effect on the value of the critical exponent $\beta$. The data are best represented by a single $\beta$ value ($\beta =0.356$) over the entire range $2\times {10}^{-5\mathrm{}}<\left|t\right|<3\mathrm{}\times {10}^{-2\mathrm{}}$, but they are also compatible with a variation in $\beta$ from 0.356 at large $\mathrm{}\left|t\right|\mathrm{}$ to 0.340 at small $\mathrm{}\left|t\right|\mathrm{}$. However, these data are incompatible with the Ising $\beta$ value even when correction terms are included. Revised scaling effects are small, and available ${\rho }_d$ values are compatible with either a $\mathrm{}\left|t\right|\mathrm{}$ or a ${\mathrm{}\left|t\right|\mathrm{}}^{1-\alpha }$ variation.

A series of ${}_{}{}^{129}{}_{}{}^{}\mathrm{I}$ Mössbauer measurements have been completed on $4-n-\mathrm{hexoxybenzylidene}-4^{\prime }-{}_{}{}^{129}{}_{}{}^{}\mathrm{iodoaniline}$ dissolved in the liquid crystal $4-n-\mathrm{hexoxybenzylidine}-4^{\prime }-n-\mathrm{propylaniline}$. Ordered solute "monocrystals" were produced by orienting the samples in an external magnetic field. The sample exhibited three liquid-crystalline phases: nematic, smectic $A$, and smectic $H$. Analysis of the ${}_{}{}^{129}{}_{}{}^{}\mathrm{I}$ Mössbauer spectra gave a value of 50 ± 4° for the smectic-$H$ tilt angle.

A Landau theory of the smectic $B-E$ transition at constant volume is proposed. The coupling constants of this theory are then derived from a previously published microscopic theory. Coupling between the orientational order and the lattice-strain tensor is then introduced, and it is shown that this causes the $B-E$ transition to be first order. Elastic neutron scattering is discussed as an experimental test of the microscopic theory. Finally, interlayer interactions are included.

The important rates for a high-electron-density (≳ ${10}^{21}$ ${\mathrm{cm}}^{-3\mathrm{}}$) aluminium plasma containing ${\mathrm{A}1\mathrm{}}^{\mathrm{X}\mathrm{I}-\mathrm{X}\mathrm{I}\mathrm{V}}$ ions are presented as a function of electron temperature. The collisional excitation rates are calculated in the Coulomb-Born approximation. The effect of electron collisions upon the dielectronic recombination rates is included. The nonlinear set of statistical equilibrium equations for constant electron density and temperature plus the averaged radiation transport equations are solved to give the emitted power density in each line as a function of the angle to the normal to the face of the coin-shaped plasma. Comparison with observations from a laser-produced plasma gives a determination of the average electron density, electron temperature, and physical thickness of the plasma during the time and in the region of maximum radiation.

A two-parameter class of single-particle orbitals, giving rise to long-range order in the local (spatial and/or spin) density, is shown to satisfy the full Hartree-Fock (HF) equations for occupied states in the thermodynamic limit. For a $\delta$ interparticle potential, these states are stabler (have lower HF energy) than the usual plane-wave (or trivial) HF solutions, for sufficiently strong coupling and/or high density. Minimization of the energy with respect to the (new) free parameters leads to sometimes gradual (second-order transition) and sometimes abrupt (first-order transition) onset of order, accompanied by a "bifurcation" of the new energy state from the old. The existence of even lower-energy, nontrivial HF states is also mentioned. We discuss the relevance to neutron and nuclear matter, to the Pauling "close-packed spheron" model of nuclei, as well as to the electron-gas problem.

A kinetic model based on the Enskog transport equation is proposed as a description of time correlation functions in a dense hard-sphere fluid at arbitrary wavelengths and frequencies. The kinetic equation has the desired properties with respect to short-time behavior, transport coefficients, and thermodynamics. It is capable of describing the dynamic structure factor in liquid argon if the collision frequency were scaled with wavelength.