Recent experiments (‘‘inversion effect’’) on the free ${\mathrm{NO}}_2$ molecule reveal unexpected results which are in contradiction to our knowledge on the properties of a small molecule. Making an unconventional assumption on the time evolution of the free ${\mathrm{NO}}_2$ molecule, we are able to describe these experimental results consistently.

A new method for calculating atomic multiphoton processes is presented here with application to two-photon processes in atomic hydrogen. The $L^2$-basis-set approach exploits explicit expansion of the Coulomb radial function and resolvent in terms of Pollaczek polynomials and functions to achieve compact expressions for two-photon radial transition amplitudes. This allows efficient calculation of the Bethe logarithm even for highly excited hydrogenic states and two-photon ionization amplitudes near and above the one-photon ionization threshold. Above the one-photon threshold, the complete-basis limit of the highly oscillatory amplitude is computed by applying the epsilon algorithm carefully to a sequence generated from only 10–15 basis functions. The approach is extended below the one-photon threshold by splitting the transition amplitude into a sum of two formally divergent but geometriclike series, whose analytic continuation is realized by the epsilon algorithm to yield a clearly defined and efficient interpolation between the resonances at highly excited Rydberg states. This suggests a new $L^2$-basis formulation of the quantum-defect method. The extension to complex basis functions and many-electron atoms in strong fields is discussed.

A multichannel quantum-defect theory focused on the time-delay matrix is applied to the analysis of Rydberg levels and autoionization resonances of the chlorine atom. The analysis shows that recently observed photoionization cross sections above the 3$p^4$${(\mathrm{}}^3$P) threshold of the chlorine ion may be interpreted in terms of unresolved groups of resonances with three different total angular momenta J and approximately the same energy. Experimental data of Rydberg levels were used to determine the phase shift of the collisional eigenstate (quantum defect) and the time-delay matrix for the electron-ion scattering process. The LS coupling scheme is assumed for the electron + ion compound state. The channel interaction strengths and dipole matrix elements of even-parity states relevant to electron-ion collisional and recombination processes are obtained. The branching ratio of photoelectrons is calculated.

Rydberg spectra of the chlorine atom 3$s^2$3$p^4$${(\mathrm{}}^3$P)ns, J=(1/2), (3/2), and (5/2), are calculated by use of an eigenchannel quantum-defect method. The results indicate that the channel interactions due to electrostatic and spin-orbit potentials are weak. The effect due to channel interaction of the 3s3$p^6$ configuration is completely negligible. Agreement with emission data is excellent (≲0.2% accuracy except for the lowest n=4 levels). Autoionization resonances are predicted.

The performance of our new gas-phase photoelectron spectrometer and the Canadian Synchrotron Radiation Facility beamline at the Synchrotron Radiation Center (Stoughton, Wisconsin) is demonstrated with use of Xe 4d photoelectron spectra. The beamline employs a Grasshopper monochromator with a 1° grazing angle on the M1 mirror, and the Leybold-Heraeus combined lens-analyzer system is mounted at the magic angle to eliminate polarization and β effects. Both the photon and electron resolutions are very close to theoretical, and we have obtained Xe 4$d_{5/2}$ spectra with total widths as small as 0.262 eV at 94 eV photon energies. We have measured accurately and computer fitted the Xe 4$d_{5/2}$:4$d_{3/2}$ branching ratio from 74 to 150 eV photon energies. There is good qualitative agreement between our measured values and the latest theoretical relativistic random-phase-approximation values. Possible reasons for quantitative differences between theory and experiment are discussed.

We calculate cross sections and transition rates for the photoexcitation and photoejection of an electron initially bound by its image charge to a plane infinite wall, impenetrable to the electron; the electromagnetic wave is incident at an arbitrary angle. The problem reduces to that of a one-dimensional system consisting of an electron bound to a potential -${\mathrm{Ze}}^2$/z for z>0 and ∞ for z≤0 (i.e., a one-dimensional hydrogen atom), with an oscillating electric field parallel to the z axis. Particularly interesting cases include ‘‘murium,’’ a perfectly conducting wall, for which Z=(1/4), and a liquid-helium wall, a case of experimental interest, for which the static dielectric constant is ε=1.057 and Z=(ε-1)/4(ε+1)=0.0069. The dependence of the photoejection cross section on the outgoing energy is the same near threshold as that for photoejection from a real hydrogen atom. This result may seem surprising since neither parity nor angular momentum is conserved.

The $L_2$,3${\mathrm{M}}_4$,5${\mathrm{M}}_4$,5 Auger-electron spectra of Ga and Ge have been measured for the first time from their atomic vapors with use of electron-impact excitation. The spectra have also been calculated theoretically by taking explicitly into account the partially filled outermost shell. The satellite structure arising from doubly ionized initial states has been investigated by calculating relativistically the energies of satellite lines and comparing them with the experimental spectra. The comparison with the solid-state Auger spectra gives for the free-atom–solid energy shifts 19.1 eV for Ga and 18.7 eV for Ge, by using vacuum and Fermi levels as the reference levels for free atoms and solid samples, respectively. These shift values agree well with the estimates calculated by the semiempirical thermochemical model.

A pair of germanium detectors and a three-parameter analyzer were applied in an experimental study of the creation and of the decay of atomic states with a double K-shell vacancy, created in the decay of ${}_{}{}^{109}{}_{}{}^{}\mathrm{Cd}$. Assuming a variable intensity ratio of the K${\alpha }_1$ and K${\alpha }_2$ hypersatellite lines, their shift with respect to the diagram lines, ${\Delta }_{K\alpha }^h$=546±20 eV, and the shift of the Kα satellite lines with an initial L-shell vacancy, ${\Delta }_{K\alpha }^s$($L^{\mathrm{-}1}$)=54±6 eV, were obtained. The former result is in agreement with the previous experimental result of van Eijk et al. and with the theoretical result of Chen et al., but the latter result is significantly lower than the theoretical value of 73 eV. For the I(K${\alpha }_1$${}^h$)/I(K${\alpha }^h$) intensity ratio, a value of 0.54±0.11 was obtained. From the numbers of counts in the hypersatellite-satellite peaks the intensity ratios of the hypersatellite lines I(K${\beta }_{1\mathcal{’}}$${}^h$)/I(K${\alpha }^h$)=0.195 ±0.016, and I(K${\beta }_{2\mathcal{’}}$${}^h$)/I(K${\alpha }^h$)=0.055 ±0.008 were obtained. The former value seems to be larger than the theoretical value 0.168, while the latter value is significantly larger than the theoretical value 0.029. Also the I(K${\beta }_{1\mathcal{’}}$${}^s$)/I(K${\alpha }^s$) and I(K${\beta }_{2\mathcal{’}}$${}^s$)/I(K${\alpha }^s$) intensity ratios of the satellite lines for the L-, M-, and N-shell initial spectator vacancies were derived. Within the errors the results are in agreement with the corresponding values for the diagram lines. The probability of creation of double K-shell vacancies per ${}_{}{}^{109}{}_{}{}^{}\mathrm{Cd}$ decay was determined to be (6.07±1.12)×${10}^{\mathrm{-}5}$, in accord with the result (6.25±0.54)×${10}^{\mathrm{-}5}$ of van Eijk et al.

The output of semiconductor laser resonators containing saturable absorbers is calculated with use of a semiclassical model that takes into account radial variation of the laser mode and the gain. The results show that more absorption is required for bistability to exist compared to the plane-wave case, and that transverse effects must be included to predict the switching intensities accurately.

We discuss the time-dependent power spectrum of fluorescence light produced by a two-level system driven by a smooth, short, resonant laser pulse. We show how the multipeak structure of the spectrum develops in time. The possibility of a smooth transition to the conventional Mollow spectrum is discussed.

We have studied the fluorescent spectra arising from the interaction of a four-level atom with a strong bichromatic field and a weak signal field simultaneously. The atomic system consists of two upper excited states ‖3〉 and ‖4〉 and two lower states ‖1〉 and ‖2〉 and the two laser fields, whose frequency modes ${\omega }_a$ and ${\omega }_b$ are initially populated, operate between the states ‖2〉⇆‖4〉 and ‖2〉⇆‖3〉, respectively. Using the Green-function formalism and a model Hamiltonian, where all the free and interacting fields are quantized, we have studied the transitions ‖4〉⇆‖1〉 and ‖3〉⇆‖1〉 of the signal field in the limit of high photon densities of both laser fields. The expression of the spectral function for the ‖1〉→‖4〉 transition describes stimulated one-photon and three-photon processes, respectively. The one-photon spectra near the frequency ω≊${\omega }_{41}$ of the signal field consist of a central peak and two pairs of sidebands whose intensities take always positive and negative values indicating that attenuation and amplification (stimulated emission) of the signal field takes place at the frequencies in question, respectively. The spectral function for the three-photon process near the frequency ω≊${\omega }_{41}$-2${\omega }_a$ describes two pairs of sidebands whose intensities are always negative implying that strong amplification of the signal field occurs. The computed one-photon and three-photon spectra are presented graphically for different values of Rabi frequencies and detunings of both laser fields, respectively. Then using a classical description of both laser fields, the spectral functions describing one-photon and three-photon processes are calculated and the derived results are compared with the corresponding ones when the fields are quantized. It is found that the results obtained when the fields are quantized and in the limit of high photon densities describe the classical as well as the quantum nature of the photons which is lost in the classical treatment.

The propagation of a weak optical pulse through a resonant two-level atomic medium is discussed in the paraxial approximation. Transverse propagation effects within that approximation are treated exactly by development of the method of Fresnel transforms. In particular, for a temporally short pulse with an amplitude of arbitrary transverse spatial dependence it is shown that longitudinal propagation is not affected by diffractive spreading. Thus diffraction does not attenuate the characteristic ringing of one-dimensional pulse propagation in resonant media.

We investigate the early stages of superfluorescent emission from a large spherical volume containing atoms all initially in the same excited state. The electric polarization fluctuations that characterize a fully inverted atomic system, and which trigger superfluorescence, are found to cause field amplification only in vector spherical-harmonic multipole modes of limited order. The field and polarization fluctuations obey Gaussian statistics, a result that has been used to calculate the angular correlation of intensities radiated in any two directions. Components of the electric field radiated in two arbitrary directions and circularly polarized in opposite senses are found to be uncorrelated. They thus have no intensity-intensity or higher-order correlations. Field components which are circularly polarized in the same sense, however, are shown to be correlated over an angular range that is proportional to the ratio of the wavelength to the radius of the sphere.

An exact solution of the master equation for the three-photon hyper-Raman process is obtained by a matrix method. Several cases of the photon statistics are considered and the appearance of photon-antibunching effect and the violation of the classical Cauchy inequality are discussed.

Starting from the general QED Hamiltonian for the free-electron laser (FEL), a quantum-mechanical, many-particle theory of the FEL in the laboratory frame is presented. When suitable variables are introduced, the Hamiltonian is seen to a good approximation to be formally identical to the nonrelativistic Hamiltonian in the resonant (Bambini-Renieri) frame used in other treatments. The derivation is given for a general multimode laser field, although only the simpler case of single-mode operation is discussed in detail. It is shown how the large-gain evolution equations for the field, in the small-signal regime, may be obtained from the quantum theory. Then, from fourth-order perturbation theory, the change in the first two moments of the photon-number distribution in a single pass through the FEL is computed. Large-gain and saturation terms are obtained, for arbitrary values of the quantum recoil (i.e., both the classical and quantum-mechanical regimes are included). The evolution of the photon statistics over many cavity round trips is discussed. In the small-signal regime, the variance of the photon-number distribution is shown to correspond, to a good approximation, to that of thermal, or ‘‘chaotic,’’ radiation. At saturation, a significant reduction of the fluctuations is expected, but no conclusions can be drawn from the perturbation-theory approach. A numerical calculation of the buildup of the field from vacuum (through spontaneous emission) is presented. For simplicity, a uniform, circularly polarized, static wiggler is assumed in the text; however, the theory may be generalized (along lines shown) to deal with nonuniform, linearly polarized and/or traveling electromagnetic-wave wigglers.

A microscopic model of degenerate four-wave mixing including the quantization of the medium is given. Thus the full effects of loss and spontaneous emission on the squeezing attainable are analyzed. We examine separately the squeezing in the output fields for counterpropagating four-wave mixing, copropagating four-wave mixing, and four-wave mixing in a single-ended optical ring cavity. Good squeezing is possible only in certain limits of atomic parameters.

Light-induced drift arises when optically excited atoms with a Doppler-selected velocity suffer a diffusive friction that is different from that of ground-state atoms. When the atoms form an optically dense system, this drift can cause a piston effect, which sweeps the atoms in the propagation direction of the field. We derive coupled differential equations for the density of atoms and the light intensity, with an explicit expression for the drift velocity in terms of easily accessible parameters. Solutions of these equations are obtained for the stationary state in a closed cell. The density at the dark end of the cell, considered as the response to the incident-light intensity as its driving force, exhibits a discontinuity resembling a second-order phase transition for an optically dense system. We also obtain solutions with a soliton character, describing a localized density packet moving at uniform speed.

The transition parameters for the freezing of two one-component liquids into crystalline solids are evaluated by two theoretical approaches. The first system considered is liquid sodium which crystallizes into a body-centered-cubic (bcc) lattice; the second system is the freezing of adhesive hard spheres into a face-centered-cubic (fcc) lattice. Two related theoretical techniques are used in this evaluation: One is based upon a recently developed bifurcation analysis; the other is based upon the theory of freezing developed by Ramakrishnan and Yussouff. For liquid sodium, where experimental information is available, the predictions of the two theories agree well with experiment and each other. The adhesive-hard-sphere system, which displays a triple point and can be used to fit some liquids accurately, shows a temperature dependence of the freezing parameters which is similar to Lennard-Jones systems. At very low temperature, the fractional density change on freezing shows a dramatic increase as a function of temperature indicating the importance of all the contributions due to the triplet direction correlation function. Also, we consider the freezing of a one-component liquid into a simple-cubic (sc) lattice by bifurcation analysis and show that this transition is highly unfavorable, independent of interatomic potential choice. The bifurcation diagrams for the three lattices considered are compared and found to be strikingly different. Finally, a new stability analysis of the bifurcation diagrams is presented.

Large classical systems are studied by two different stochastic simulation techniques which bear close resemblance to those used in studying relativistic quantum field theory. The first technique inverts a large sparse matrix by the Von Neumann–Ulam procedure. The second procedure reduces the problem to the Monte Carlo evaluation of a functional integral. Large resistive networks, both homogeneous and inhomogeneous, and wave propagation in media described by lumped parameters are treated in detail. The systematic and random errors incurred in the procedure and the emergence of the continuum limit are investigated.

We study the expansions for the off-diagonal thermal kernel of quantum systems with a nonuniform, time-independent magnetic field in physically relevant parameters. In particular, the high-temperature expansion and a new heavy-mass expansion is discussed. We provide recursion relations and a diagrammatic method to calculate the coefficients in these expansions. We compare these expansions in detail with the semiclassical expansion derived previously [Phys. Rev. A 30, 2024 (1984)]. As an illustration we present the first few coefficients explicitly.