Multibeam Borrmann modes of single crystals exist in which in addition to the electric field being zero, the magnetic field and/or higher derivatives of the field (the electric field gradient, the magnetic field gradient, ...) are also zero at the equilibrium position of each atom in the crystal. These properties of multibeam modes are of particular interest in the case of γ-ray optics, since Mössbauer transitions occur with well-defined multipolarity, E1, M1, E2 (and in a few cases, M1-E2), in contrast to the electronic response of atoms which occurs as a hierarchy of multipole contributions, E1≫E2≫M1, etc. As we show, this well-defined multipolarity of nuclear transitions leads to three particularly interesting effects which occur at multibeam points of good single crystals containing resonant Mössbauer nuclei. (1) Certain multibeam Borrmann modes exhibit suppressed coupling both to the electrons and to the nuclei and will be anomalously transmitted at resonance, even when the nuclear transition is of multipolarity M1 or higher and there is no Zeeman splitting. Such simultaneous suppression is not possible in the usual two-beam case. (2) Other multibeam Borrmann modes exhibit particularly strong coupling to the nuclei, so that nuclear absorption is greatly enhanced. (3) Excited Mössbauer nuclei located at lattice sites within a crystal will have enhanced emission into certain of these weakly attenuated multibeam Borrmann modes (‘‘anomalous emission’’). While these last two effects can occur in the two-beam case, greater enhancements are possible in multibeam modes, since the coupling is proportional to the number of beams in the mode.

We have previously shown that two-beam Borrmann modes of good single Mössbauer crystals offer the possibility of achieving nuclear lasing at population-inversion densities substantially lower than would be required in an amorphous sample of the same material [J. T. Hutton, J. P. Hannon, and G. T. Trammell, Phys. Rev. A 37, 4269 (1988)]. In this paper we discuss the further improvements which are obtained in multibeam Borrmann modes (which consist of the coherent superposition of three or more plane waves within the crystal). These modes can have smaller absorption coefficients, and more importantly, stronger coupling to the nuclei, as well as sharper collimation than do corresponding two-beam modes, leading to even lower requirements for the population-inversion density needed to induce lasing.

The exact equivalence between a bad-cavity laser with modulated inversion and a nonlinear oscillator in a Toda potential driven by an external modulation is presented. The dynamical properties of the laser system are investigated in detail by analyzing a Toda oscillator system. The temporal characteristics of the bad-cavity laser under strong modulation are analyzed extensively by numerically investigating the simpler Toda system as a function of two control parameters: the dc component of the population inversion and the modulation amplitude. The system exhibits two kinds of optical chaos: One is the quasiperiodic chaos in the region of the intermediate modulation amplitude and the other is the intermittent kicked chaos in the region of strong modulation and large dc component of the pumping. The former is well described by a one-dimensional discrete map with a singular invariant probability measure. There are two types of onset of the chaos: quasiperiodic instability (continuous path to chaos) and catastrophic crisis (discontinuous path). The period-doubling cascade of bifurcation is also observed. The simple discrete model of the Toda system is presented to obtain analytically the one-dimensional map function and to understand the effect of the asymmetric potential curvature on yielding chaos.

The phenomenon of antibunching provides important support for the physical principle of the collapse of the wave function following a detection of a photon. In this paper we show that interrupted fluorescence in a three-level, V-configuration atom, with one transition strongly driven and one weakly driven, can be regarded as evidence supporting the complementary principle of ‘‘collapse by nondetection.’’ Use of this principle leads to the immediate deduction of remarkably simple general expressions for the average bright and dark periods, which allows these quantities to be calculated for both coherent and incoherent excitation without the need to solve the density-matrix equations, or even to find their long-term steady-state solutions. Thus the concept of collapse by nondetection appears to be not only valid but is also useful for predicting physically observable phenomena.

A new operator derivation of the relation giving the photon-number generating function, G(γ), in terms of the quantum characteristic function, C(ξ,${\xi }^{\mathrm{*}}$), is presented. The inverse problem is then solved, calculating C(ξ,${\xi }^{\mathrm{*}}$) directly from G(γ). Because G(γ) contains less phase information than C(ξ,${\xi }^{\mathrm{*}}$), we can either assume that the field has a completely random phase (e.g., a stationary field) or be content with calculating the phase average of C(ξ,${\xi }^{\mathrm{*}}$). We then derive an expression giving G(γ) for the superposition of two arbitrary, independent fields in terms of the individual G(γ)’s for each (stationary) field. A number of examples illustrate the methods, including a determination of the quantum characteristic function for a field with K-distributed amplitude fluctuations.

The well-known photon correlations of thermal light are now understood to result from the random superposition of independently emitted photons from spontaneous emission. Through random interference the number of photons evolves as a Bose-Einstein distribution rather than the Poisson distribution as one might expect for independent emissions of classical particles. By identifying terms in the density-matrix (ρ) equation for a linear amplifier, those terms giving rise to spontaneous emission were earlier distinguished from those causing amplification and absorption. We investigate the role of interference in the evolution of the photon statistics by further identifying terms in the equation for ρ${̇}_n$ solely responsible for quantum interference phenomena. The effects of this random interference on the photon factorial moments are quantified, even for those cases where the final field statistics are not Bose-Einstein. From our analysis we conclude that stimulated emission should be viewed as analogous to time-reversed absorption, rather than either a cascade process or pure constructive interference.

We propose an analytical solution to the propagation equation of the optical pulse both in free-electron lasers and in optical klystrons. Our results include in a natural way the lethargy and wave-packet spreading.

In this paper we use a recently suggested analytical solution of the pulse propagation equation in free-electron lasers (FEL) to get further information on the lethargy and on the velocity of propagation of the optical packet. We also introduce a refractive index for the FEL interaction. Finally, the supermodes relevant to the regime of long electron bunch are found analytically and a comparison with earlier numerical results is carried out.

A theory of four-wave mixing including effects of velocity-changing collisions is presented. Three fields with frequencies ω, ω, and ω+δ are incident on a vapor of ‘‘two-level’’ atoms having upper state b and lower state a. Two of the fields are counterpropagating and the third (of frequency ω+δ) makes a small angle with one of the others. The frequency ω is a nearly resonant (inside the Doppler width) with the a-b transition frequency. The phase-conjugate signal emitted at frequency ω-δ is calculated as a function of δ. Using a simple collision model in which collisions are phase interrupting in their effect on atomic coherence and velocity-changing in their effect on level populations, we discuss the conditions under which resonances characterized by the upper or lower radiative and collision rates can be observed. Assuming that the total (a+b) state population is conserved in the absence of collisions, it is shown that velocity-changing collisions can ‘‘open’’ the system and lead to a resonance characterized by the lower-state width (convoluted with the residual Doppler width). With increasing pressure, the width of this induced resonance structure decreases monotonically. For sufficiently high pressure, the collisional redistribution of velocity classes is complete—the system ‘‘recloses’’ and the narrow resonance disappears. The interplay of the collision-induced opening, line narrowing, and reclosing of the system is discussed, as is the relationship of these narrow resonances to the so-called pressure-induced extra resonances of Bloembergen and co-workers [Indian J. Pure Appl. Phys. 16, 151 (1978); Phys. Rev. Lett. 46, 111 (1981)].

We show that the kinetic equation governing the one-particle distribution function of the hard-sphere fluid, as obtained from the binary-collision expansion, reduces to the modified Enskog equation in the limit of infinite number of space dimensions. The contribution of loop diagrams is exponentially small. The transport coefficients of the fluid are obtained.

It is proven, using the Poisson-Boltzmann equation, that a point charge held fixed in an ideal ‘‘jellium’’ plasma attracts a finite amount of opposite charge arbitrarily close to itself. In two dimensions this condensate is insufficient to neutralize the charge completely; in three or more dimensions neutralization is complete. The proof, which extends and simplifies older results, is based on the idea that the concentration exp(-qφ/kT)/F dr exp(-qφ/kT) is a δ function when φ(r) is such that exp(-qφ/kT) has a nonintegrable singularity. It is also proven that the species in the plasma of opposite polarity to the immersed charge condense onto it in strict order of charge, largest first.

Fluid-theory calculations are presented of ion collection by electric probes in strongly magnetized plasmas with parallel flow. In the first calculations the problem is treated in a one-dimensional approximation but the cross-field transport of momentum is included in such a way as to model different ratios of viscosity to diffusivity. The results show that the flow deduced from probe measurements is not particularly sensitive to the assumed viscosity, provided it is finite. However, results with zero viscosity are qualitatively different from those with nonzero viscous momentum transport. The second set of calculations is two dimensional but only for fixed (unity) ratio of viscosity to diffusivity. The results are in remarkably good agreement with the corresponding one-dimensional model.

We apply a lattice model of oil-water-surfactant mixtures, proposed by Chen, Ebner, Jayaprakash, and Pandit, to a study of adsorption and wetting phenomena on an inert substrate, especially under conditions of three-phase coexistence. Mean-field and exact zero-temperature analyses are employed, and the qualitative behavior of the adsorption phase diagrams is studied systematically as a function of the adsorbate-substrate interactions. The phase diagrams are very rich, reflecting in part the competition between different wetting configurations made possible by having three coexisting phases. We also study the wetting of an interface between oil-rich and water-rich fluids by microemulsion phase.

The resistivity of liquid Li-Sn and Na-Pb alloys is calculated using the theory of ‘‘2$k_F$’’ scattering theory recently developed by Morgan et al. The partial structure factors are described by the mean-spherical approximation for a system of hard spheres with Yukawa tails. The calculated resistivity values are in very good agreement with experiment. The improvement over the widely used Faber-Ziman formalism is impressive.

Stark widths of six Cl ii, eight Cl iii, three Cl iv, and two F iii spectra lines and Stark shifts of six Cl ii and eight Cl iii spectral lines have been measured in a linear-pinch discharge plasma and compared with available experimental and theoretical data. The electron density determined by single-wavelength laser interferometry using the visible 632.8-nm transition of a He-Ne laser was 1.97×${10}^{23}$ ${\mathrm{m}}^{\mathrm{-}3}$. The electron temperature of 27 000 K was determined from the Boltzmann slope of several Cl ii spectral lines and from the intensity ratios of several Cl ii to Cl iii spectral lines. Since the majority of Cl ii, Cl iii, and Cl iv spectral lines investigated originate from 4s-4p transition arrays, the Stark-width (w) dependence on the upper-level ionization potential (I) of corresponding lines has been established and discussed both within one stage of ionization of chlorine and within several stages of ionization of chlorine and fluorine (including neutral chlorine and fluorine).

Simultaneously, the Stark-width dependence was found on the net charge (z) of the emitter core acting upon the optical electron undergoing transition. Similarly, Stark-width data obtained for F iii spectral lines originating from the 3s-3p transition array, together with other authors’ experimental and theoretical data of F i, F ii, and F iii spectral lines originating from the same transition arrays, were used to discuss the features of these dependences. The dependences are of the forms w=${\mathrm{AI}}^{\mathrm{-}a}$ (within one ionization stage of chlorine or fluorine) and w=${\mathrm{Bz}}^2$$I^{\mathrm{-}b}$ (among several ionization stages of chlorine or fluorine), where A, a, B, and b are constants independent of the ionization potential. The trends obtained were used to predict the Stark width of uninvestigated spectral lines originating from the given 4s-4p (chlorine) and 3s-3p (fluorine) transitions with an accuracy better than 30%.

The modification of the density profile caused by the ponderomotive force in a laser plasma is further studied. A completely self-consistent three-parameter family of solutions for the ponderomotive-force potential and density scale length in a steady-state laser plasma is first derived. The boundary and junction conditions are given by the self-similar solution. The obtained results are more accurate and rigorous than the previous results.

In this paper we present results from a self-consistent two-dimensional numerical simulation of the formation and propagation of streamers in nonattaching (${\mathrm{N}}_2$) and attaching (${\mathrm{N}}_2$-${\mathrm{SF}}_6$ mixture) gases using a one-moment fluid model. A numerical technique has been used which allows the solution of the space-charge equations in the presence of large gradients and dynamic range. Photoionization in the gas and photoelectric effect at the cathode have been taken into account. Streamers in the ${\mathrm{N}}_2$-${\mathrm{SF}}_6$ mixture have been found to be considerably different from those in ${\mathrm{N}}_2$. Spatial oscillations in the electron density have been observed for the ${\mathrm{N}}_2$-${\mathrm{SF}}_6$ mixture, which lead to a more complex field distribution and particle-flow dynamics. The results obtained for ${\mathrm{N}}_2$ have been compared to those obtained with use of a kinetic description of the electron dynamics. Comparisons with experimental observations and interpretation of experimental observations have been made for both ${\mathrm{N}}_2$ and ${\mathrm{N}}_2$-${\mathrm{SF}}_6$ mixtures.

We present measurements on the rotational temperature and the density of ${\mathrm{H}}_2$ in the metastable c ${}_{}{}^3{}_{}{}^{}\Pi _u^{\mathrm{-}}{}_{}{}^{}$ state in a multicusp ion source. The temperatures, determined by using resonance-enhanced multiphoton ionization, are in the range of 400–600 K. The density is obtained by the application of a one-photon ionization process, yielding a value of 3×${10}^9$ ${\mathrm{cm}}^{\mathrm{-}3}$ at a discharge current of 30 A. The variation of the metastable molecule density with discharge parameters can be qualitatively understood with a simple model which includes energy degradation of the primary electrons and quenching due to gas collisions.

Based on the psychological experimental fact that images in mental space are transformed into other images for pattern identification, a field theory of pattern identification of geometrical patterns is developed with the use of gauge field theory in Euclidean space. Here, the ‘‘image’’ or state function ψ[χ] of the brain reacting to a geometrical pattern χ is made to correspond to the electron’s wave function in Minkowski space. The pattern identification of the pattern χ with the modified pattern χ+Δχ is assumed to be such that their images ψ[χ] and ψ[χ+Δχ] in the brain are transformable with each other through suitable transformation groups such as parallel transformation, dilatation, or rotation. The transformation group is called the ‘‘image potential’’ which corresponds to the vector potential of the gauge field. An ‘‘image field’’ derived from the image potential is found to be induced in the brain when the two images ψ[χ] and ψ[χ+Δχ] are not transformable through suitable transformation groups or gauge transformations. It is also shown that, when the image field exists, the final state of the image ψ[χ] is expected to be different, depending on the paths of modifications of the pattern χ leading to a final pattern. The above fact is interpreted as a version of the Aharonov and Bohm effect of the electron’s wave function [A. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959)]. An excitation equation of the image field is also derived by postulating that patterns are identified maximally for the purpose of minimizing the number of memorized standard patterns.

The macroscopic description of a quantum particle with passive dissipation and moving in an arbitrary external potential is formulated in terms of the generalized Langevin equation. The coupling with the heat bath corresponds to two terms: a mean force characterized by a memory function μ(t) and an operator-valued random force. Explicit expressions are given for the correlation and commutator of the random force. The random force is never Markovian. It is shown that μ̃(z), the Fourier transform of the memory function, must be a positive real function, analytic in the upper half-plane and with Re[μ̃(ω+i$0^{+}$)] a positive distribution on the real axis. This form is then derived for the independent-oscillator model of a heat bath. It is shown that the most general quantum Langevin equation can be realized by this simple model. A critical comparison is made with a number of other models that have appeared in the literature.