The line shape and strength of two-photon absorption in an atomic vapor are studied both theoretically and experimentally for the case of absorption of unequal-frequency photons. Special attention is given to the situation in which the intermediate state is resonant or nearly resonant. It is shown that for the resonant case, maximum absorption rates and Doppler-free spectra are simultaneously obtained. Either counterpropagating or copropagating beams can be used. With counterpropagating beams the two-photon linewidths are quite insensitive to power broadening of the intermediate state. With copropagating beams the two-photon spectra can also reveal the intermediate-state structure with a resolution determined mainly by the intermediate-state lifetime (nearly as well as can be done using any spectroscopic technique). The theoretical analysis provides a closed-form solution for the line shape and strength of the two-photon spectrum. In general the line shape is composed of two features. One is Doppler broadened and predominates when the intermediate state is nonresonant. The second feature is Doppler free, and it predominates with a resonant intermediate state. Detailed comparisons of experimental measurements of the line shape and strength of two-photon absorption in Na vapor are made with the theory and found to be in excellent agreement. Signal strengths for the onresonance case are 6 × ${10}^9$ larger than the case of equal-frequency photons with no loss in resolution.

Multiphoton ionization of neon in the case of a 16-photon resonance with the $3p^{\prime }{\left[\frac{1}{2}\right]}_1$ intermediate level is studied using a neodymium-glass laser. Experiments show that when the electric field $E$ ranges from 2.2 × ${10}^7$ to 3.5 × ${10}^7$ V/cm, the number of collected charges takes a maximum value at 2.9 × ${10}^7$ V/cm. A theoretical study on the basis of the formalisms due to Keldysh and Zon etal predicts that, when an intermediate resonant level is considered, this maximum can be observed by the use of a laser beam of sufficiently large spectral width. This is the case in our experiment. The number of ionization events decreases when the resonance is destroyed, i.e., when the Stark shift of the level becomes larger than the spectral width of the laser, which, at 16 photons, is of the order of 100 Å. Good agreement between experiment and theory allows us to determine the polarizability of the resonant $3p^{\prime }{\left[\frac{1}{2}\right]}_1$ level of neon which is found to be 21.8 ${\mathrm{\AA }}^3$. We have also determined an experimental cross section of multiphoton ionization of neon at $\lambda =1.06\mathrm{}$ μm.

When the dipole-dipole interaction energy of two polar molecules is comparable to their thermal energy during a binary collision, there is a net orientation of the two dipoles towards each other. The impact theory for the inversion bands of ${\mathrm{NH}}_3$ and ${\mathrm{ND}}_3$ is investigated in order to assess the implications of such orienting collisions. This is done by retaining cross sections which involve odd powers of the interaction Hamiltonian and results in a simple modification of the formula for the band shapes due to Ben-Reuven. A strict procedure for comparing the theory with experiment is described and applied to available data for ${\mathrm{NH}}_3$.

The single-mode laser model as formulated by Haken and co-workers is considered. Within the approximation which takes into account only the interaction (at all orders in the coupling constant) between the mode and the single atoms, this model leads to a linear time-evolution equation for the Glauber quasiprobability distribution $P(\beta ,{\beta }^{*},t)$ of the field mode, containing derivatives of all orders in $\beta$ and ${\beta }^{*}$. This equation is solved exactly in the stationary situation. Thus the quantum effects due to the terms with derivatives of order higher than the second one are fully taken into account. It is shown that these terms have a shrinking effect on the stationary distribution above threshold, counteracting the broadening effect due to the second-derivative term. The photon and photoelectron distributions are given. Exact relations are deduced, which allow the calculation of all the moments of the steady-state distribution from the first one. This distribution is compared with the stationary solutions of Risken's equation, of P. Mandel's equation, and with the stationary distribution deduced by Weidlich, Risken, and Haken. The connection with the single-mode laser theory of Scully and Lamb is analyzed in the high-intensity region. The complete Scully-Lamb master equation is translated into the Glauber representation, yielding a linear equation for $P(\beta ,{\beta }^{*},t)$ containing derivatives of all orders in $\beta$ and ${\beta }^{*}$. Suitably connecting the parameters $A$, $B$, and $C$ of the Scully-Lamb equation with the parameters of the model of Haken and co-workers, it is shown that there is perfect agreement between the strong-signal Scully-Lamb steady-state distribution and that of Weidlich, Risken, and Haken for all values of the pump parameter.

The fluctuation properties of a cw dye laser, pumped by an argon-ion laser, have been investigated by photon-counting and two-time correlation measurements. The results show significant departures from the usual single-mode laser theory in the region of threshold and below. However, there are indications that the departures may be due to extraneous rather than intrinsic effects, and when these effects are subtracted out, the results are in substantial agreement with the predictions of the usual theory.

One-dimensional wave propagation in a slightly dissipative random medium is studied by applying a probabilistic theory developed in a previous work, which showed the presence of the cutoff mode in a random medium and its detailed characteristics, the cutoff mode being an exponentially increasing or decreasing standing wave without energy flow. The medium loss is assumed to be constant and small enough so that the mode is regarded as the cutoff mode perturbed by the dissipation. Including in the analysis an imaginary constant describing either attenuation or amplification of the medium indicates the need of correct choice of the branches in solving the dispersion equation, which was overlooked in the loss-free case. The local power-reflection coefficient of the cutoff mode, which in the loss-free case equals unity, meaning no energy flow, is shown to become a stationary process in the lossy medium. The average increment of the logarithmic amplitude is increased by the loss, but the fluctuations in the phase and amplitude are decreased because of the medium attenuation screening the effect of multiple scattering. The average phase shift is unchanged by the loss in the lowest-order approximation. Computer simulations for the lossy random medium are made to obtain those statistical characteristics, which are compared with the theory in good agreement.

Coherent excitation of an atomic excited state occurs during the propagation of near-resonant light pulses and is responsible for the induced polarization. Simultaneously, incoherent excitation occurs due to the relaxation processes described by the absorption coefficient. Here, the theory for the coherent and incoherent excitation is initially presented in terms of the traditional vector model. While a complete understanding of the two-level system is provided by the vector model, it is shown to be incomplete when the problem of directly monitoring the coherent and incoherent excitation is considered. This is because this latter problem involves more than two levels. For this more complicated multilevel problem, adiabatic states are introduced to gain further understanding. The adiabatic states are the stationary states of the atom in the presence of the near-resonant laser field; they help to explain the intimate connection between the coherent excitation and the two-photon resonance. Experimental measurements of the coherent and incoherent excitation associated with near-resonant pulse propagation in Rb vapor are presented. The double-resonance technique used a relatively strong pulsed dye laser tuned near the $5S_{\frac{1}{2}}\leftrightarrow 5P_{\frac{1}{2}}$ transition (7948 ÅA) of Rb to produce the coherent and incoherent excitation, and a weak, tunable cw dye laser tuned in the region of the $5P_{\frac{1}{2}}\leftrightarrow 6D_{\frac{3}{2}}$ transition (6206 ÅA) to monitor this excitation. In agreement with theory, the experimental results demonstrate that coherent excitation is responsible for two-photon absorption, while the incoherent excitation corresponds to one-photon absorption to the $5P_{\frac{1}{2}}$ state.

The problem of monitoring an excited state by a probe beam resonant with the transition to a second excited state is examined in the case in which the first excited state is adiabatically excited off resonance. It is shown that dispersive effects are to be expected, and their magnitude is estimated.

The thermodynamic properties of one-component ionic plasmas in a responding (polarized) background of fully degenerate electrons are calculated over a wide range of temperatures and densities. The weak and intermediate screening regimes are treated by two complementary methods which take the one-component plasma in a rigid background as a starting point. Thermodynamic perturbation theory is used in the weakly screened ionic plasma typical of white-dwarf matter; this leads to simple, analytic expressions for the thermodynamic properties. Relativistic effects in the very dense electron gas are considered explicitly. A variational method, based on the Gibbs-Bogolyubov inequality, and the physical idea of an effective charge reduction of the ions, yields satisfactory results in the intermediate screening regime typical of the deep interior of Jupiter. Our results are in good agreement with the available Monte Carlo data and represent a significant improvement over previous calculations based on a hard-sphere reference system.

We present the results of a systematic study of threshold instabilities in a Wien bridge oscillator. The dynamical circuit equations can be cast into a time-dependent Ginzburg-Landau form where the order parameter is the complex zero-dimensional amplitude of the oscillatory voltage. In this context we have been able to simulate behavior which in classical theory is characteristic of first-order, second-order, and tricritical phase transitions, and have measured the associated threshold properties.

Electronic transport is considered in dense fully ionized hydrogen. The equivalence of the Boltzmann-Ziman approach with the more deductive Kubo formalism for weak electron-ion interactions is established. The ionic structure factors obtained from recent and improved Monte Carlo simulation of the classical one-component plasma are used to obtain the linear time-independent transport coefficients. The effects of inelastic electron scattering from the ionic density fluctuations are taken into account. The electrical and thermal conductivities, the conductive opacity, the bulk viscosity, and the thermoelectric power at different densities and temperatures are tabulated. These results are compared with previous calculations.

The low-frequency microfield arising from homogeneous, anisotropic, partially developed turbulence is represented by a Gaussian distribution, and is introduced into a generalized computation of the hydrogen $\mathrm{Ly}\alpha$ line. The electrons are taken to be thermal, and they provide their usual impact broadening in the line center, while their effect is neglected in the wings. Analytical approximations, valid either in the line center or in the wings, are obtained for the polarized profiles emitted both parallel and perpendicular to the turbulence axis. This axis is simulated by a fictitious magnetic field $\overrightarrow{B}$ which is allowed to vanish at the end of the calculations. The line profiles are characterized by the anisotropy parameter ${\eta }^2=\frac{2〈E_{\parallel }^2〉}{〈E_{\perp }^2〉}$ where $〈E_{\parallel }^2〉$ and $〈E_{\perp }^2〉$ are the mean square electric field components parallel and perpendicular to the turbulence axis of the microfield, respectively.

The Kirkwood-Buff formula has been extended to include three-body interactions by differentiation of the partition function with respect to the area. Assuming a step-function density profile (Fowler) and the superposition approximation (Kirkwood) for the triplet correlation function, the nonadditivity correction ${\gamma }_3$ to the surface tension is expressed as a septuple integral whose integrand contains the three-body interaction potential $u_{123}$ and the radial distribution function of the liquid $g\left(r\right)\mathrm{}$. We use the triple-dipole interaction (Axilrod-Teller) for $u_{123}$ and the neutron diffraction data of Yarnell etal for liquid Ar at 85°K to represent $g\left(r\right)\mathrm{}$. It is necessary to make several changes of variable and inversions of the order of integration in order to transform the integral into a sextuple integral which can be programmed without incurring large errors due to cancellation. The result for Ar at 85°K is ${\gamma }_3=-4.5\mathrm{}$ erg/${\mathrm{cm}}^2$, which is not negligible when compared with the experimental surface tension (13.1 erg/${\mathrm{cm}}^2$). When ${\gamma }_3$ is combined with ${\gamma }_2$ [the surface tension computed in the Kirkwood-Buff-Fowler approximation from realistic pair potentials for Ar using the same $g\left(r\right)\mathrm{}$ data], the total surface tension is significantly smaller than the experimental value.

The velocity autocorrelation function in a hard-sphere fluid is calculated by including corrections to the Boltzmann-Enskog theory due to correlated binary (ring) collisions. The memory function describing these processes is reduced to a form suitable for numerical computation by assuming the dominant contributions are due to couplings between hydrodynamic modes. A simple approximation is introduced to account for the effects of nonhydrodynamic modes. Using the interpolation formulas recently suggested by Resibois, we have computed the memory function, the velocity autocorrelation function, and the self-diffusion coefficient $D$. The diffusion coefficient shows the enhancement effect relative to the Enskog diffusion coefficient that was first observed by computer molecular-dynamics calculations. Our results also show a rapid decrease in $D$ in the high-density region. A comparison of the present work with the analysis of Resibois is made, and further refinements are suggested.

The plasmon scattering by electrons in the simultaneous presence of laser and magnetic fields is discussed. A kinetic equation is derived, and the rate of change of the plasmon population is calculated. For laser radiation propagating parallel to the magnetic field it is found that multiphoton processes are dominant when the laser frequency is near the electron cyclotron frequency. Furthermore, the damping rate is found to decrease exponentially as the laser frequency approaches the electron cyclotron frequency.

Perturbation-numerical calculations have been performed using nonrelativistic Hartree-Fock-Slater wave functions to obtain the Sternheimer quadrupole antishielding factor ${\gamma }_{\infty }$ for all the tetrapositive ions in the actinide series ($90\le Z\le 103$). For these ions, the nonrelativistic ${\gamma }_{\infty }$ values seem to be constant at ∼-95. It is estimated that the relativistic effects would increase the $\left|{\gamma }_{\infty }\right|$ value by ∼ 65%.

This paper presents results of calculations of the Hartree-Fock first-order frequency-dependent properties of argon. Numerical results are given for the linear polarizability, refractive index, Verdet coefficients, and first electric dipole transition frequency. In addition, Van der Waal's coefficients between pairs of Hartree-Fock rare-gas atoms are presented.

Mode-coupling equations for the anomalous shear viscosity which incorporate vertex corrections are used to calculate the critical exponent for this transport coefficient. These corrections are shown to have an important effect on the magnitude of this exponent.

We present the results of a computer experiment designed to investigate the effect of chirp on the amplitude of the solitons produced in resonant media by incident coherent optical pulses. Comparison is made to the predictions derived from higher conservation laws.

A number of previously derived rigorous upper and lower stationary bound formulas are tested using as an example the expectation value of the operator $\frac{(r_1^2+r_2^2)}{2}$ for the ground state of helium.