Space-curvature-induced theoretical modifications in the interaction between atoms and external electromagnetic fields have been investigated in the framework of a ‘‘curved-orbital’’ model: The traditional Euclidean space is replaced by a geometrically simple curved space, i.e., the spherical three-space of radius R. The required solutions of Maxwell’s equations on the hypersphere have been obtained in closed form. A novel procedure has been devised in order to obtain analytical expressions of the curved-space Dirac hydrogenic pseudoradial integrals in terms of the Dirac energy parameter ε=1+${\alpha }^2$$E_{\mathrm{nk}}$ and of the Dirac quantum number k${=\left(\mathrm{-}1\right)}^{j+l+1/2\mathrm{}}$(j+1/2). The hydrogenic Zeeman and Stark effects have been studied in detail and analytical expressions of the curvature-induced contributions to the Landé g factor and to the Stark matrix elements have been given in terms of ε and k. This curved-space model, which will, we hope, provide the basis for an easy extension to the many-electron cases, gives the usual flat-space results in the limit as the radius R of the space increases to infinity.

Effect of laser intensity on the line shape of and the rate for resonant two-photon autoionization of ${\mathrm{H}}_2$ through the lowest doubly excited autoionizing state of ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{}{}_{}{}^{}$ (1${\mathrm{\sigma }}_{\mathrm{u}}^2$) symmetry has been studied using the resolvent-operator technique, the different vibrational levels of the B ${\mathrm{}}^1$${\Sigma }_u$ state of ${\mathrm{H}}_2$ being the intermediate resonances. The autoionization line shape and rate have been found to depend on the intensity and on the choice of (i) the vibrational level of the intermediate resonance, (ii) the vibrational level of the final ${\mathrm{H}}_2$${\mathrm{}}^{+}$ ion, and (iii) the nuclear continuum of the autoionizing state. It is shown that an experimental study of the process is feasible within the currently available laboratory laser resources.

The photodissociation cross sections corresponding to absorption from the ground electronic state X ${\mathrm{}}^1$${\Sigma }_g^{+}$ of ${\mathrm{H}}_2$ into the continua of B ${\mathrm{}}^1$${\Sigma }_u^{+}$, C ${\mathrm{}}^1$${\Pi }_u$, and B’ ${\mathrm{}}^1$${\Sigma }_u^{+}$ systems were calculated using accurate ab initio potential-energy and dipole-moment values. Noticeable discrepancies were found with previous calculations. Adiabatic corrections and centrifugal distortion were taken into account.

The total cross section for the photodissociation of ${\mathrm{H}}_2$ into H(1S)+H(n=2) between 85.0 and 77.0 nm has been measured using synchrotron radiation at high resolution (0.005-nm bandwidth). This continuum is made up of three contributions from B, B’ ${}^1$${\Sigma }_u^{+}$, and C ${\mathrm{}}^1$${\Pi }_u$. The B’ photodissociation cross section is obtained directly at some excitation wavelengths from analysis of predissociation Fano profiles. The data are compared to computed values. The contribution of predissociated levels to the production of H(n=2)+H(1S) atoms for white-light excitation is found to be more than two times more efficient than the direct photodissociation.

A new procedure for the construction of effective dipole-oscillator-strength distributions is proposed. The effective distributions satisfy not only the usual sum rules, but also have the correct asymptotic behavior and satisfy a ‘‘modified’’ oscillator-strength sum rule. The distributions may be used to evaluate logarithmic mean excitation energies. The application of the effective distributions toward the calculation of the high-energy photoionization cross section is also discussed. Calculations on atomic hydrogen have been performed which indicate the technique is an efficient method for the computation of the excitation energies. Finally, the technique is applied to atomic helium and the negative hydrogen ion.

We analyze instabilities in mixed absorptive and dispersive optical bistability in the rate-equation approximation and the mean-field and good-cavity limits. Our starting point is a set of multimode equations derived from the Maxwell-Bloch equations for ring-cavity boundary conditions. We obtain analytic expressions for the instability conditions. In a plane-wave analysis, we find that a portion of the lower transmission branch can be unstable in addition to the upper-branch instability found in purely absorptive bistability. Also, a new disconnected region of instability can exist on the upper branch. Our analysis becomes particularly simple for equal and opposite cavity detunings and we explore this case in detail. We extend our treatment to include a Gaussian transverse intensity profile and show that the instabilities remain in the presence of Gaussian averaging. We also show that many of the results obtained in the rate-equation approximation hold when the atomic linewidth and atomic decay rate are of the same order.

The effect of counter-rotating terms in the interaction Hamiltonian on the photon statistics is investigated for a single-mode laser. The treatment is based on the Scully-Lamb model. A perturbation expansion is used to derive an equation of motion for the field-density matrix. The counter-rotating terms are found to lead to both transient and secular effects. With some reasonable approximations the steady-state photon-number distribution is derived and it is shown that the counter-rotating terms tend to raise the threshold of laser action and broaden the photon-number distribution. The relative size of these effects is found to be very small and depends on the square of the ratio of the atomic linewidth and the transition frequency.

The large-scale fluctuations of Stokes light generated by stimulated Raman scattering have been studied experimentally by measuring the probability density function of Stokes pulse energies. The size and shape of the scattering region and the rate of collisional dephasing of the scatterers determine the degree of coherence of the Stokes light, and this in turn determines the form of the probability distribution. The experiments were performed for several diameters of the scattering volume, and for various collisional dephasing rates. The results of the experiments are compared to a recently reported quantum theory, and qualitative agreement is found. The need for a more accurate theory is pointed out.

The nonlinear response of a two-level system interacting with two pump beams of different frequencies is studied with a view to examine several recent experiments on nonlinear mixing of high orders, instabilities in homogeneously broadened lasers, and holes in homogeneous lines. Such a nonlinear response is calculated with use of the continued fractions given in our earlier work [J. Opt. Soc. Am. B1, 164 (1984)]. Saturation effects lead to the appearance of many structures at submultiples of the Rabi frequency. The origin of these subharmonics in nonlinear-response functions is explained. It is shown that collisions not only lead to hole burning at the line center for weak fields but can also lead in moderate fields to the appearance of structures at subharmonics of the Rabi frequency. Existence of collision-induced coherences similar to those in four-wave mixing is shown in six-wave mixing. Exact results for the degenerate nonlinear mixing of arbitrary order are presented for arbitrary values of field strengths. Saturating fields create holes at the line center of such nonlinear mixing signals. Gain profiles of two modes symmetrically displaced from line center are also given. Numerical results, with complete account of saturation and collisions, for a variety of nonlinear-response functions are presented.

An analytic solution is presented for the time development of an n-level atom in resonant interaction with n-1 lasers in a branch configuration, which is an alternative generalization of the three-level atom to the commonly studied cascade configuration. The same analytic approach is also applied to a four-laser resonant interaction with a four-level atom in a cyclic configuration, where it is found that a change of phase of any one of the lasers has a critical effect on the population dynamics and, with certain Rabi frequency and laser phase relationships, double-quantum transitions can be eliminated completely.

The spatially inhomogeneous distribution of the light intensity and of the excitation density is investigated for systems showing cavityless optical bistability due to increasing absorption. The formation and motion of spatial kink structures is analyzed in detail within a rate-equation approach. Analytical estimates for the kink formation process are presented and compared to numerical results.

In this paper it is shown experimentally that with the use of a laser Doppler velocimeter, the fluid velocity can be determined from the measurement of $Q_C$(S) [the squared cosine transform of the time-interval probability, W(theta), between two consecutive photopulses] or from the measurement of $Q_R$(X) [the square-wave transform of W(theta)]. By using a computer simulation method, the accuracy of these techniques is compared with the one of the usual intensity correlation techniques. It is found that the measurement of $Q_C$(S) or $Q_R$(X) provides more accurate results than the intensity correlation technique. It is expected that the advantage of these techniques increases as the intensity of the detected light beam decreases.

Parametric instabilities in the interaction between a cold-electron beam, a static or electromagnetic pump, and a scattered (signal) electromagnetic wave are studied. The interaction schemes are classified according to the mutual sense of propagation of the waves and the beam. The unified analysis yields the known convective and absolute slow-plasma-wave instabilities [forward- and backward-wave free-electron lasers (FEL)]. In addition, we identify the possibility of convective and absolute fast-plasma-wave instabilities. Analysis and numerical computation of gain and oscillation in both known and new instability mechanisms are performed in the framework of a general model beyond the range of previously reported studies. A general approximate threshold condition expression for all the possible absolute instabilities is given. All of these instabilities may appear in practical schemes like FEL oscillators as parasitic effects. Their relative importance is considered by means of numerical examples.

The way in which surface tension acts as a singular perturbation to destroy the continuous family of needle-crystal solutions of the steady-state growth equations is analyzed in detail for two local models of solidification. All calculations are performed in the limit of small surface tension or, equivalently, small velocity. The basic mathematical ideas are introduced in connection with a quasilinear, isotropic version of the geometrical model of Brower et al., in which case the continuous family of solutions disappears completely. The formalism is then applied to a simplified boundary-layer model with an anisotropic kinetic attachment coefficient. In the latter case, the solvability condition for the existence of needle crystals can be satisfied whenever the coefficient of anisotropy is arbitrarily small but nonzero.

We show explicitly that, in a realistic model of diffusion-controlled dendritic solidification, Ivantsov’s continuous family of steady-state needle crystals is destroyed by the addition of surface tension. Our starting point is the exact integro-differential equation for the one-sided model, in two dimensions, in a moving frame of reference. In the limit of large undercooling, where the range of the diffusion field is much smaller than the radius of curvature of the tip of the needle, we are able to reduce this problem to a linear, inhomogeneous differential equation of infinite order. We derive a solvability condition for this equation and show that solutions cease to exist for arbitrarily small but finite, isotropic surface tension.

A solution is presented for the steady-state transport in a prism containing fixed scattering centers, and bounded by walls of temperatures $T_1$ and $T_2$ having emissivity e. S-wave scattering, specular reflection, and Boltzmann statistics are assumed. Numerical results are obtained for the thermodynamic quantities over the full range of the Knudson number.

Several methods for nonequilibrium computer simulation of plane Couette flow are analyzed by kinetic theory. The boundary-value problem for the nonlinear Boltzmann equation is related to the stochastic, Lees-Edwards, and ‘‘non-Newtonian’’ dynamics methods. It is found that the kinetic-theory and computer simulation methods can be put into close correspondence, except for one form of the non-Newtonian equations of motion. The effects of homogeneous, nonconservative forces used to maintain constant temperature are also studied. For a special interatomic force law exact scaling relations are obtained to relate isothermal and nonisothermal solutions to the Boltzmann equation. For other force laws this scaling relationship is only approximate.

The connection between stochastic differential equations and associated Fokker-Planck equations is elucidated by the full functional calculus. One-variable equations with either additive or multiplicative noise are considered. The central focus is on approximate Fokker-Planck equations which describe the consequences of using ‘‘colored’’ noise, which has an exponential correlation function and a correlation time τ. To leading order in τ, the functional-calculus approach generalizes the τ-expansion result and produces an approximate Fokker-Planck equation free from certain difficulties which have plagued the less general approximations. Mean first-passage-time behavior for bistable potentials, an additive case, is discussed in detail. The new result presented here leads to a mean first-passage-time formula in quantitative agreement with the results of numerical simulation and in contrast with earlier theoretical conclusions. The theory provides new results for the multiplicative case as well.

A series of five aluminum imploding-wire experiments were performed to investigate the dependence of plasma temperature, density, size, and x-ray emission above 1 keV on the initial wire-array diameter and mass per unit length. The plasmas were created by imploding cylindrical arrays of fine wires with the Blackjack 5 pulse generator. In these experiments the array diameter and mass per unit length were varied by factors of 2 and 4.5, respectively. The electron temperatures were determined from the slope of the free-to-bound continuum, the intensity ratios of selected x-ray-emission lines and strength of the continuum edges. The line ratios were interpreted by means of a collisional radiative equilibrium model. Plasma ion densities were obtained from the total x-ray emission above 1 keV. The size of the plasma that emits above 1 keV was inferred from x-ray pinhole photographs and from measurements of the line broadening caused by the finite source size. As the initial diameter of the wire array was increased, the array mass was decreased in order to maintain constant implosion time and optimum energy coupling from the pulse generator to the load. The larger-diameter, lower-mass arrays produced larger-diameter, higher-temperature, lower-density plasma pinches. With the simultaneous increase in array diameter and decrease in array mass, the electron temperature increased from 0.5 to 0.8 keV, the ion density decreased from 4×${10}^{19}$ to 0.13×${10}^{19}$ ${\mathrm{cm}}^{\mathrm{-}3}$, the diameter of the plasma column increased from 1.2 to 5.5 mm, and the x-ray emission above 1 keV decreased from 20 to 0.45 kJ.

This work investigates the dynamics of concentration fluctuations in a binary mixture, isobutyric acid in water, when the critical mixing point is approached from within the two-phase region. The scaled diffusion coefficient $D^{\mathrm{*}}$ for both sides of the coexistence curve is in good agreement with the recently proposed dynamic scaling function in the scheme of mode-coupling theory. We find that the dynamic amplitude ratio has the same value R=1.06±0.04 both above and below $T_c$, which is in good agreement with a universal value predicted from recent theories and experiments. It is also found that the coefficient ratios Γ/${\Gamma }^{\mathrm{-}}$=4.9±2.0 for the isothermal osmotic compressibility and ${\xi }_0$/${\xi }_0^{\mathrm{-}}$=2.0±0.4 for the correlation length are in good agreement with those suggested by the universality of Γ/${\Gamma }^{\mathrm{-}}$ and of ${\xi }_0$/${\xi }_0^{\mathrm{-}}$ from scaling theories.