Showing papers in "Physical Review A in 1974"

Exchange corrections of K x-ray emission rates

Abstract: Separate relativistic Hartree-Fock solutions for atoms in their initial and final states are used for calculating the radiative decay of a $K$-vacancy state. The matrix-element calculations include the exchange effects of the nonzero overlap of wave functions from different subshells. Results are presented for the filling of the vacancy by the $p$ electrons for a set of elements from $Z=10\mathrm{to}98$. The Hartree-Fock theory is also used for calculating the rates of production of multiple-vacancy states in the decay process. In contrast to earlier single-potential calculations, the calculated values of ratios of the rates of the $K$ x-ray components are in good agreement with the experimental values.

Ordered phases of a liquid of biaxial particles

Abstract: A simple model for an interacting liquid of particles lacking an axis of rotational symmetry is proposed. The four order parameters necessary to describe an ordered phase are identified. An ensemble of such particles is described by a mean field theory. A phase diagram showing both uniaxial and biaxial phases results. The model predicts a phase diagram similar to that of the phenomenological model of Alben.

Retardation in the resonant interaction of two identical atoms

Abstract: The problem considered is that of two identical two-level atoms a fixed distance $r$ apart, one of which is excited at $t=0$. A simple improvement on the usual on-shell approximation (which in the single-atom case is part of the Weisskopf-Wigner approximation) yields new solutions for the various probability amplitudes in the form of infinite series involving all the retardation times $\frac{\mathrm{nr}}{c}$. The truncated solutions involving only the single retardation time $\frac{r}{c}$ are compared with previously published results both when all photon modes are allowed and when only photons propagating along the interatomic axis are allowed. When the retardation times are neglected, the series are summed to give the well-known results of Stephen and others.

Measurements of electric dipole polarizabilities of the alkali-metal atoms and the metastable noble-gas atoms

Abstract: The $E\ensuremath{-}H$-gradient balance technique has been used to measure the static electric dipole polarizabilities of the alkali-metal atoms and the tensor polarizabilities of the $^{3}P_{2}$ metastable noble-gas atoms. All of the measurements are normalized to the scalar polarizability of $^{3}S_{1}$ metastable helium, a value which has been accurately calculated. The scalar polarizabilities of the alkali atoms, in units of ${10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{3}$, are for lithium, 24.3 \ifmmode\pm\else\textpm\fi{} 0.5; sodium, 23.6 \ifmmode\pm\else\textpm\fi{} 0.5; potassium, 43.4 \ifmmode\pm\else\textpm\fi{} 0.9; rubidium, 47.3 \ifmmode\pm\else\textpm\fi{} 0.9; cesium, 59.6 \ifmmode\pm\else\textpm\fi{} 1.2. For the $^{3}P_{2}$ metastable noble-gas atoms we measure the $\mathrm{zz}$ components of the polarizability tensors for ${m}_{J}=1 \mathrm{and} 2$, which completely determines the polarizability tensors for all ${m}_{J}$. For ${\ensuremath{\alpha}}_{\mathrm{zz}}({m}_{J})$ we find, in units of ${10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{3}$, for neon, 28.4 \ifmmode\pm\else\textpm\fi{} 0.6 (${m}_{J}=1$) and 26.7 \ifmmode\pm\else\textpm\fi{} 0.5 (${m}_{J}=2$); argon, 49.5 \ifmmode\pm\else\textpm\fi{} 1.0 (${m}_{J}=1$) and 44.7 \ifmmode\pm\else\textpm\fi{} 0.9 (${m}_{J}=2$); krypton, 52.7 \ifmmode\pm\else\textpm\fi{} 1.0 (${m}_{J}=1$) and 46.8 \ifmmode\pm\else\textpm\fi{} 0.9 (${m}_{J}=2$); xenon, 66.6 \ifmmode\pm\else\textpm\fi{} 1.3 (${m}_{J}=1$) and 57.4 \ifmmode\pm\else\textpm\fi{} 1.1 (${m}_{J}=2$). The rare-gas results, while more precise, are in good agreement with earlier work. The alkali-metal results are in excellent agreement with recent theory and the experiment of Hall and Zorn.

Van der Waals forces and zero-point energy for dielectric and permeable materials

Abstract: It is pointed out that symmetries of Maxwell's equations under interchange of electric and magnetic fields can be exploited to convert calculations of van der Waals forces between electrically polarizable particles and dielectric materials into results for magnetically polarizable particles and permeable materials. In particular, the forces between perfectly conducting materials calculated from ideas of zero-point radiation are the same as the forces between infinitely permeable materials. Combinations of dielectric materials and permeable materials can lead to repulsive van der Waals forces. For example, two infinitely permeable parallel plates are attracted together with exactly the same force as obtained by Casimir for the van der Waals attraction between two perfectly conducting plates. On the other hand, two parallel plates of area $A$ and separation $d$, one of which is a perfect conductor and one of which is infinitely permeable, are repelled by a force $F=\frac{7}{8}\frac{{\ensuremath{\pi}}^{2}\ensuremath{\hbar}cA}{240{d}^{4}}$, differing in magnitude by a factor of $\frac{7}{8}$ from Casimir's attractive force. A calculation of the repulsive force is given based on ideas of classical electromagnetic zero-point radiation.

Instabilities in continuous-wave light propagation in absorbing media

Abstract: The stability of a monochromatic constant-intensity laser beam propagating through a resonant medium is considered. It is found that many absorbers should exhibit a region of negative conductivity and, consequently, amplify perturbations. The associated gain is dependent on a number of variable parameters, such as laser-beam intensity, perturbation frequency, relaxation times, degeneracy, transverse mode, inhomogeneous broadening, etc. Putting absorbers inside Fabry-Perot interferometers allows the construction of plane-wave devices with a bistable output.

Landau--Ginsburg equations for an anisotropic superfluid

Abstract: A discussion of an anisotropic ($p$ state) Fermi superfluid with a spatially varying order parameter is presented. We restrict ourself to the Landau-Ginzburg region and consider spatial variations governed by the linear gap equation. The kernel of the linearized gap equation is shown to be related to a current-current correlation function of quasiparticles in the normal state. This relation permits the calculation of the two coherence lengths ${\ensuremath{\xi}}_{L}$ and ${\ensuremath{\xi}}_{T}$ defined earlier in the framework of a phenomenological Landau-Ginzburg theory, and a discussion of boundary conditions for the order parameter at interfaces. A significant anisotropy in the coherence lengths is found (${\ensuremath{\xi}}_{L}=\sqrt{3}{\ensuremath{\xi}}_{T}$), which reflects itself in the nature of the supercurrents. The boundary conditions at specularly and diffusely reflecting surfaces lead us to expect that the vector $\stackrel{^}{l}$, which describes the orbital angular momentum of a Cooper pair in an "axial" state, is anchored normal to the walls. Some consequences of these results on various experimental problems (fourth sound, monodomain production, Josephson couplings, behavior in thin capillaries) are briefly discussed.

Average energy expended per ion pair in liquid argon

Abstract: The measurement of the $W$ value, the average energy expended per ion pair, in liquid argon for internal conversion electrons emitted from $^{207}\mathrm{Bi}$, is carried out by the electron-pulse method. Comparing with the $W$ value (26.09 eV) for $\ensuremath{\alpha}$ particles in a gas mixture of argon (95%) and methane (5%), the $W$ value in liquid argon is determined to be ${23.6}_{\ensuremath{-}0.3}^{+0.5}$ eV. This value is clearly smaller than that in gaseous argon (26.4 eV). Such a reduction of $W$ value in liquid argon can be explained by assuming the existence of the conduction band in liquid argon as in solid argon. Under this assumption, the $W$ value in liquid argon is estimated by applying the energy-balance method, which was used for the rare gases by Platzman. The calculated value thus obtained is in good agreement with the experimental result. Following the same method, the $W$ values for liquid krypton and liquid xenon are also estimated.

Lagrangian theory for a self-avoiding random chain

Abstract: The Lagrangian theory of random chains with excluded volume is used to study ${Z}_{N}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$, the number of chains with $N$ links, starting from the origin and arriving at a point $\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}$. Its asymptotic expression ($N\ensuremath{\rightarrow}\ensuremath{\infty}$) is ${Z}_{N}(r)\ensuremath{\simeq}{N}^{\ensuremath{\gamma}\ensuremath{-}1\ensuremath{-}\ensuremath{ u}d} F(r{N}^{\ensuremath{-}\ensuremath{ u}})$, where $\ensuremath{\gamma}$ and $\ensuremath{ u}$ are critical indices. The short- and long-range behaviors of $F(x)$ are calculated in terms of $\ensuremath{\gamma}$ and $\ensuremath{ u}$. In particular, it is shown that for $x\ensuremath{\ll}1$, we have $F(x)\ensuremath{\simeq}F{x}^{\ensuremath{\theta}}$ with $F=\mathrm{const}$ and $\ensuremath{\theta}=\frac{(\ensuremath{\gamma}\ensuremath{-}1)}{\ensuremath{ u}}$.

Influence of negative-ion processes on steady-state properties and striations in molecular gas discharges

Abstract: Theoretical and experimental studies of negative-ion processes in weakly ionized glow discharges have been conducted. Emphasis in these investigations has been directed towards analysis of gas mixtures in which negative ions are produced by dissociative electron attachment of C${\mathrm{O}}_{2}$, CO, or ${\mathrm{O}}_{2}$. It is shown that attachment, detachment, and clustering reactions normally occurring in discharges containing these species can significantly affect both the steady-state and transient characteristics of the plasma, even when an external source of ionization is provided. The magnitude and electron temperature dependence of the electron-molecule attachment coefficient is found to be particularly important. Specifically, analysis shows that when the electron attachment coefficient has a strong positive dependence on electron temperature, and a magnitude exceeding that of the ionization coefficient, an ionization instability can occur. This instability will occur under these circumstances when the negative-ion concentration is comparable to the electron density. Numerical evaluation of the conditions required for this electron-attachment---induced mode of ionization instability results in good agreement with experimentally determined conditions for the onset of striations in gas mixtures for which the charged-particle kinetics can be calculated in detail. In other cases, observed differences between theory and experiment have been related to uncertainties associated with the loss mechanisms of clustered negative ions in the discharge.

Photoionization of neon between 100 and 2000 eV: Single and multiple processes, angular distributions, and subshell cross sections

Abstract: All aspects of photoionization in the soft-x-ray region are taken into account, and a complete partitioning of the photoionization cross section of neon is given in terms of single-electron processes in $2p$, $2s$, and $1s$ subshells and multiple-electron processes involving these subshells. The various processes, including their angular dependences, are identified and studied by the technique of photoelectron spectrometry. The partition relies solely on experimental evidence. Absolute subshell cross sections for the emission of a single electron are compared with current theoretical predictions: The single-particle, frozen-structure model (Cooper, 1962) that uses the Herman-Skillman potential overestimated ${\ensuremath{\sigma}}_{2p}$ by up to 15%, ${\ensuremath{\sigma}}_{2s}$ by (25-35)%, and ${\ensuremath{\sigma}}_{1s}$ by about 20%; the random-phase-approximation-with-exchange model (Amusia, 1972) that includes multielectron correlation and uses Hartree-Fock wave functions predictions correctly ${\ensuremath{\sigma}}_{2s}$ at $110lh\ensuremath{ u}l220$ eV, where comparative data exist. The absolute cross section for double ionization in the $L$ shell is 5 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}20}$ ${\mathrm{cm}}^{2}$ at $h\ensuremath{ u}=278$ eV as compared with the theoretical value of 4 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}20}$ ${\mathrm{cm}}^{2}$. The energy dependence of simultaneous excitation and ionization processes in the $L$ shell is reported. A finite threshold value is observed and a plateau at higher energy is indicated. For $h\ensuremath{ u}g130$ eV, $\ensuremath{\epsilon}l,{n}^{\ensuremath{'}}{l}^{\ensuremath{'}}$ transitions are found to be most probable in which the continuum electron changes its angular momentum, $\ensuremath{\Delta}l=\ifmmode\pm\else\textpm\fi{}1$, and the excited electron retains its momentum, $\ensuremath{\Delta}l=0$, namely $2{p}^{6}\ensuremath{\rightarrow}2{p}^{4}\ensuremath{\epsilon}d,np$. Anisotropy parameters $\ensuremath{\beta}$ for $2p$ electrons agree well with theoretical results; however an unexplained maximum near $\ensuremath{\theta}={0}^{\ensuremath{\circ}}$ at $h\ensuremath{ u}g1$ keV is found for the angular distributions of $2p$ photoelectrons.

Ising model for tricritical points in ternary mixtures

Abstract: An Ising model with spin $S=1$ at each lattice point which exhibits multiple tricritical points is presented. This is a generalization of the Blume-Emery-Griffiths model which was used for describing the tricritical point in ${\mathrm{He}}^{3}$-${\mathrm{He}}^{4}$ mixtures. The model is solved in the molecular-field approximation. It is found that its thermodynamic behavior near the tricritical point is in qualitative agreement with the thermodynamic behavior of ternary fluids near their tricritical points.

Density fluctuations in liquid rubidium. II. Molecular-dynamics calculations

Abstract: Molecular-dynamics (MD) calculations on liquid rubidium at 46 \ifmmode^\circ\else\textdegree\fi{}C and 1502 g ${\mathrm{cm}}^{\ensuremath{-}3}$ have been made using a suitable pair potential Whereas for wave number $\ensuremath{\kappa}l12$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ propagating density fluctuations were obtained, only overdamped nonpropagating fluctuations are found for larger $\ensuremath{\kappa}$ For all $\ensuremath{\kappa}$ there is good agreement with recent neutron inelastic-scattering experiments The mean-square acceleration given by MD is found to be much larger than the value derived from another neutron experiment extending over $\ensuremath{\kappa}=4 \mathrm{to} 8$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$; the reason for the discrepancy is analyzed to show that the neutron-scattering data cannot be interpreted in terms of the mean-square acceleration alone

Ab initio effective potentials for use in molecular quantum mechanics

Abstract: We have investigated the method of effective potentials for replacing the core electrons in molecular calculations. The effective potential has been formulated in a way which simplifies computations while producing wave functions of ab initio quality. The effective potential is expressed in an analytic form which (i) represents the actual ab initio nonlocal potential (as defined by the matrix elements for a given basis set) and (ii) permits efficient computations of the effective-potential integrals (by incorporating the properties of Gaussian basis functions). To minimize the number of basis functions required in the molecular calculations, we define a new ab initio effective potential derived from modified Hartree-Fock valence orbitals whose core character has been removed. The effective-potential method as formulated becomes a very strong and reliable tool in attempting calculations on very large molecules. Applications to Li, Na, and K are presented.

Binding and Coulomb-deflection effects in L -shell Coulomb ionization by heavy charged particles. Low particle velocities

Abstract: Experimental cross sections for $L$ -shell ionization by heavy charged particles, of atomic number small compared to the target atomic number and with velocities low compared to the $L$ -shell orbital velocities, can be smaller by more than an order of magnitude than the quantum-mechanical predictions in the plane-wave Born approximation (PWBA). The contribution of two effects, not contained in the PWBA, is derived. These effects are the binding of the $L$ -shell electrons to the moving particle during collision and the Coulomb deflection of the particle in the field of the target nucleus. As developed here for $L$ shells and previously for $K$ shells, the theory treats the excitation of inner shells from perturbed stationary states (PSS) and incorporates the effect of the Coulomb-distorted wave of the heavy charged projectile semiclassically. It agrees well with experimental $L$ -shell cross sections of 16 different target atoms for protons, and accounts for the isotope effect observed on various targets with protons and deuterosn of equal velocities.

Configuration-interaction study of atoms. I. Correlation energies of B, C, N, O, F, and Ne

Abstract: The configuration-interaction method has been used to calculate the wave functions and energies for the ground state and some selected excited states of the atoms B to Ne. A systematic way of selecting atomic orbital basis and configurations has been developed and is reported in some detail. The calculated total correlation energies range from 95 to 97% of the empirical correlation energy. Calculated term energies of the carbon atom are within 2% of the spectroscopic values. The correlation energies were analyzed in terms of contributions from various classes of configurations, and these contributions were compared with results of previous work. The energy contributions from the class of configurations of triple and higher electron excitations are estimated to be of the order of (3-4)% of the total correlation energy, which is larger than previous estimates of (1-3)% for these atoms.

Study of pretransitional behavior of laser-field-induced molecular alignment in isotropic nematic substances

Abstract: We have measured the optical Kerr effect and the intensity-dependent ellipse rotation in order to study the pretransitional behavior of field-induced molecular alignment in the isotropic nematic substances $p$-methoxy-benzylidene $p\ensuremath{-}n$-butylaniline (MBBA) and $p$-ethoxy-benzylidene-$p$-butylaniline (EBBA). The results agree well with predictions of the Landau---de Gennes model. Both the order-parameter relaxation time and the steady-state field-induced birefringence show critical divergence towards the isotropic \ensuremath{\rightarrow} nematic transition with a ${(T\ensuremath{-}{T}^{*})}^{\ensuremath{-}1}$ temperature dependence. In the case of MBBA, our results are also consistent with the results from light scattering, but the method we use is perhaps more straightforward and accurate. The nonlinear refractive indices and other relevant parameters of the materials are derived from the experiment.

Density fluctuations in liquid rubidium. I. Neutron-scattering measurements

Abstract: We report neutron-scattering measurements of the coherent scattering function $S(Q,\ensuremath{\omega})$ of liquid rubidium at 315 K, in the range of wave vectors $1.25\ensuremath{\le}Q\ensuremath{\le}5.5$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$. In this range there is no evidence of peaks at finite $\ensuremath{\omega}$ in $S(Q,\ensuremath{\omega})$ plotted at constant $Q$. On the other hand the Fourier transform $F(Q,t)$ exhibits structure, notably for $Q=2.0$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$, which indicates at least two characteristic (wavelength-dependent) relaxation times in the liquid. For wave vectors g3.0 ${\mathrm{\AA{}}}^{\ensuremath{-}1}$, $F(Q,t)$ may be characterized by a single relaxation time. These results, in conjunction with our results for $Ql1.0$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$, offer the possibility of detailed comparisons with models of the liquid state and with molecular-dynamics calculations.

Time-dependent projection-operator approach to master equations for coupled systems

Abstract: In this paper we derive master equations for two or more systems coupled to each other, perhaps strongly, by using a generalization of the usual projection-operator technique to include time-dependent projection operators. The coupled systems may be either similar or dissimilar and classical or quantum mechanical. Whereas the customary approaches to coupled systems are best able to treat situations in which some of the systems are "baths" with a specified density operator or phase-space probability density, our approach allows us to treat situations where it is necessary or convenient to treat the coupled systems on an equal footing. In our scheme the "relevant" part of the full density operator is considered to be the uncorrelated part of the full density operator and is a symmetric functional of the reduced density operators of each of the coupled subsystems. The "irrelevant" part of the density operator is then the part describing correlations between the coupled systems. Our formalism is particularly useful where systems are coupled to one another predominantly in a self-consistent fashion. First, we develop exact master equations for two coupled systems, taking as our prototype the dynamical problem of quantum optics, where a spatially extended collection of two-level atoms interact with a multimode optical field. We then generalize our results to $N$ coupled systems, taking as our prototype the kinetics of a classical nonideal gas interacting through two-body forces, and derive exact master equations for the system. We then consider as examples several approximate theories resulting from our exact equations. In the case of the imperfect gas we investigate the low-density limit and show how Bogoliubov's form of the Boltzmann equation emerges from our formalism, as well as corrections due to Klimontovich. We consider as special cases of our exact quantum-optical equations the equations in the first Born approximation, with and without memory, and show how several existing quantum-optical master equations are contained in our general results. As a second example in quantum optics, we consider the case where the predominant behavior of the system is described by the self-consistent-field or coupled Bloch and Maxwell equations and derive a first-order perturbation description for deviations from self-consistent-field behavior.

Hydrodynamic fluctuations near the convection instability

Abstract: Hydrodynamic fluctuations of a horizontal liquid layer heated from below are considered in the vicinity of the point where convection sets in because of buoyancy. It is assumed that convection occurs in the form of nearly two-dimensional rolls. Close to the instability, the hydrodynamics (described in the Boussinesq approximation) is simplified considerably by the appearance of a slow mode which dominates the motion of all hydrodynamic variables. It is described by a slowly varying complex amplitude whose absolute value and phase describe the strength and the position of the convection rolls, respectively. Generalizing previous work by several authors, an approximate equation of motion is derived, which is satisfied by the slow variable. New in this analysis is the inclusion of fluctuating terms, which leads to a Langevin equation. The fluctuations are shown to satisfy a detailed-balance principle. Consequently, a generalized thermodynamic potential can be defined, which was discussed briefly in an earlier paper. It depends as a functional on the slow variable, which thereby assumes the role of an order parameter of the transition. I give a further evaluation of the hydrodynamic fluctuations for a horizontally unbounded liquid layer on both sides of and at the B\'enard point by using my potential and applying various approximations. For strictly two-dimensional flows (i.e., independent of one horizontal coordinate) I calculate the time-independent steady-state properties (coherence lengths) without any further approximation by relying on published numerical data obtained for one-dimensional Ginzburg-Landau fields. Dynamic steady-state properties (coherence times) for that case and fluctuations in the three-dimensional case are calculated in a quasilinear approximation which reproduces the time-independent results for two-dimensional flows reasonably well. In the purely heat-conducting region my results contain some earlier results of Zaitsev and Shliomis in lowest order. Large and long-lived fluctuations of velocity and temperature are shown to appear at the critical wave number as the liquid is brought near the convection instability. They are due to the random appearance and disappearance of convection cells. Their size and lifetime at the B\'enard point are only limited by nonlinear coupling of the critical modes to other passive modes. In the heat-convection region, the coupling to passive modes stabilizes the amplitude of the convection cells; only slow fluctuations of the positions of the rolls remain (for unbounded layers) and destroy the long-range order of the one-dimensional roll lattice, in agreement with well-known general theorems. If the B\'enard point is approached from this side, the stabilizing influence of the passive modes decreases and is efficient only for the large fluctuations at the B\'enard point. Approached from either side, the B\'enard point resembles the critical point of a Landau phase transition. The width of the region around the B\'enard point where the Landau description breaks down is calculated and found to be unobservably small in realistic liquids. An experimental check of these results, though very tedious, seems possible and very worthwhile.

Propagation of sound in water. A molecular-dynamics study

Abstract: Fluctuation phenomena occurring in a system of 216 water molecules, studied by molecular dynamics at 1 g ${\mathrm{cm}}^{\ensuremath{-}3}$ and 10 \ifmmode^\circ\else\textdegree\fi{}C, indicate that (i) transverse currents persist in the form of propagating collective coordinates even for a wavelength of about 20 \AA{}, with indications that the same will happen for much longer wavelengths. The velocity of propagation is 1.05 \ifmmode\times\else\texttimes\fi{} ${10}^{5}$ cm ${\mathrm{sec}}^{\ensuremath{-}1}$. In the region of 20 \AA{} the lifetime of the fluctuation appears to increase linearly with increasing wavelength. (ii) Density fluctuations at 20 \AA{} are found to be propagating but only marginally; the corresponding velocity of sound is 1.8 \ifmmode\times\else\texttimes\fi{} ${10}^{5}$ cm ${\mathrm{sec}}^{\ensuremath{-}1}$. (iii) The spectrum of density fluctuations exhibits a secondary maximum at a much higher frequency than the normal frequency of sound propagation and it is suggested that experiments should be directed to the region of this "high-frequency sound."

Spectroscopy and collision theory. III. Atomic eigenchannel calculation by a Hartree-Fock-Roothaan method

Abstract: Previous papers have expressed various experimental spectral data in terms of a single set of parameters (eigen-quantum-defects, transformation matrix, and excitation dipole moments). The parameters pertain to eigenstates of an electron-ion scattering matrix which represents only the effect of short-range interactions. This paper presents a method for calculating the same parameters by solving the many-electron Schr\"odinger equation for an atom within a limited spherical volume. Quantitative results, for Ar states with $J=1$ and odd parity, are compared with data extracted earlier from an analysis of spectral data, and are also used to reproduce the first 65 discrete line positions and their intensities, the positions and profiles of autoionization lines, and the branching ratio of the photoionization.

Self-phase modulation and short-pulse generation from laser-breakdown plasmas

Abstract: This paper is a complete report on both the experimental and theoretical aspects of the recently discovered self-phase modulation in laser-breakdown plasmas. Mainly responsible for these effects is the sudden index change which accompanies the ionization of the gaseous medium. Two theoretical models are introduced for the phase and amplitude modulation induced by the plasma. These effects are applied to the problem of short-optical-pulse generation, with emphasis on the prospects for producing a pulse consisting of only a few optical cycles. The techniques described here have the unique advantage that the generation mechanism is linear, resulting in particularly clean, reproducible and predictable optical transients. Methods are suggested for raising the plasma nucleation intensity by further cleaning up the gas. It is shown that index dispersion of the optical components may place a lower limit on pulse duration.

Weyl's theory applied to the Stark effect in the hydrogen atom

Abstract: A short review of Hermann Weyl's theory for singular second-order differential equations is given and its numerical aspects are discussed. It is pointed out that this method is suitable for the treatment of perturbations which make the spectrum continuous. The Stark effect on the ground state of the hydrogen atom is taken as an example. The spectral density, the imaginary part of Weyl's "$m$ function," is calculated numerically using Runge-Kutta integration and Airy integrals for the asymptotic region. Showing $\ensuremath{\delta}$-function-like behavior with poles of $m$ on the real axis for the discrete levels, the spectral density involves approximate Lorentzians for the metastable states of the continuous spectrum, corresponding to poles of $m$ in the complex plane. Trajectories of these poles for electric fields up to 0.25 a.u. are shown for the one-dimensional as well as for the full three-dimensional problem.

Instability of certain shear flows in nematic liquids

Abstract: We have studied the simple shear flow, in the laminar regime, of a nematic (uniaxial) liquid film between two glass plates with carefully imposed boundary conditions. In the case considered here, the optical axis at rest is normal both to the flow velocity and to the velocity gradient. Using various methods of optical observation, we find the following facts: (a) When the shear rate s is below a certain threshold ${s}_{c}$, the optical axis is unperturbed everywhere. When $sg{s}_{c}$, it becomes distorted. ${s}_{c}$ is inversely proportional to the sample thickness. (b) When a stabilizing field $H$ is applied, ${s}_{c}$ increases. Furthermore, above a certain limiting field ${H}_{L}$, the nature of the instability changes: a pattern of rolls appears, the rolls being parallel to the (average) flow lines. These effects are then explained in terms of the Ericksen-Leslie-Parodi equations describing the couplings between orientation and flow in a nematic fluid. This analysis has led in turn to the prediction and observation of other remarkable effects occurring when the shear rate is modulated (at low frequencies) and when two fields $H$ (magnetic) and $E$ (electric) are applied at right angles.

Macroscopic electromagnetic theory of resonant dielectrics

Abstract: The application of the macroscopic Maxwell equations to the resonant interaction of electromagnetic radiation and dielectric crystals consisting of molecules coupled via retarded dipole fields is investigated. The macroscopic fields are defined by space averaging over volume elements of linear dimensions $\ensuremath{\Delta}$ satisfying $a\ensuremath{\ll}\ensuremath{\Delta}\ensuremath{\ll}\ensuremath{\lambda}$, where $a$ is the intermolecular separation and $\ensuremath{\lambda}$ the wavelength in vacuo. The essential point of our method is the direct derivation from the microscopic equations of a constitutive relation for a finite dielectric, taking proper account of the radiation reaction terms and avoiding the use of an expansion in powers of the molecular polarizability. The results lead to a simple interpretation of the expressions for the internal fields derived by Vlieger along similar lines, and verify the validity of the standard equations of dispersion theory to all points inside the medium a distance $\ensuremath{\Delta}$ away from the surface. The transmission and scattering of radiation at or near a molecular resonance by media of over-all extent small and large compared to the wavelength are discussed for sphere and slab geometries, and the effective natural linewidths are calculated. The limits of validity of the constitutive relation are discussed, and the existence of frequency regions where the macroscopic description breaks down due to the appearance of large spatial variations in the dipole moments is pointed out. As an example of such "antiresonant" behavior and of the role played by the higher-order radiation-damping terms, the scattering of light from two interacting molecules is treated in detail. In the absence of sufficiently strong dissipative damping, the occurrence of antiresonance is predicted to be a general phenomenon giving rise to large oscillations in the scattering cross section even in the presence of spatial dispersion in a narrow region around the frequency where the expression for the macroscopic index of refraction diverges.