Multiphoton ionization of hydrogen atoms by a strong multimode field when several final continuum states are populated is treated theoretically within a model based on the S-matrix formalism. The field is taken in dipole approximation, with zero bandwidth. Field-dressed Coulomb wave functions are used for the electron final states. Ionization rates are calculated for different numbers of photons absorbed in excess of the minimum number required to go into the continuum. In general, the calculated quantities are in good qualitative agreement with the corresponding experimental observations.

The recent discovery of ‘‘chevron’’ structured smectic-C (SC) layers in surface-stabilized ferroelectric liquid-crystal (SSFLC) cells [T. P. Rieker, N. A. Clark, G. S. Smith, D. S. Parmar, E. B. Sirota, and C. R. Safinya, Phys. Rev. Lett. 59, 2568 (1987)] enables the understanding of many commonly observed features of SSFLC director and layer structure. We present the full three-dimensional layer structure of zigzag walls, the predominant SSFLC defect, which we find to mediate change in chevron direction. We show that stabilization of the director field in SC chevron cells occurs at the chevron interface, so that SC chevron cells behave as two nearly independent cells optically and electrically in series.

Energies, wave vectors, and amplitudes of waves that are generated when a neutron is incident onto a moving parallel-sided plate are calculated by solving Schrödinger’s equation. It is shown that the wave entering the plate and those reflected at the plate surfaces suffer energy (frequency) changes due to ‘‘inelastic’’ interaction with the moving plate. The motion-induced phase shift caused by such a plate in a neutron interferometer is evaluated, including the contribution which arises in the presence of dispersion of the coherent scattering length, e.g., near a resonance or as a result of local-field effects. With thermal neutrons the amplitudes of reflected waves are about ${10}^{\mathrm{-}4}$ of the incident wave amplitude. Energy changes amount to 4×${10}^{\mathrm{-}3}$ (reflected waves) and to less than ${10}^{\mathrm{-}6}$ (entering wave) for neutrons with a 4-Å wavelength. Nonlinear contributions to the interferometric phase shift have to be taken into account when the plate and/or the medium velocity exceed 1% of the neutron velocity.

The extended coupled-cluster method (ECCM) of quantum many-body theory, which has been studied and developed in earlier papers in this series, is now applied to condensed Bose systems. The formalism is seen to provide a concise and convenient description of quite general nonstatic states of such systems with arbitrary spatial inhomogeneity. The entire ECCM description is based on the equations of motion for the set of linked-cluster amplitudes which, we have shown, completely characterize an arbitrary quantum system with a Schrödinger dynamics. Since all such amplitudes obey the cluster property, and hence may be regarded as a set of quasilocal, many-body, classical order parameters, the formalism is in principle perfectly capable of describing phase transitions and states of topological excitation or deformation and broken symmetry. At the lowest (mean-field) level of truncation, the formalism degenerates to the well-known Gross-Pitaevskii description of the condensate wave function or one-body order parameter. The treatment is developed in a fully gauge-invariant fashion, and is thereby shown to provide a complete hydrodynamical description, valid in the zero-temperature limit. In particular, by studying the off-diagonal one- and two-body density matrices in terms of the basic ECCM amplitudes, we derive balance (or local conservation) equations for such local observables as the number density, momentum density, and energy density. These are shown to be obeyed not only by the exact untruncated formalism but also by most practical truncation schemes in the ECCM configuration space.

The effect of the fully relativistic Breit term upon atomic energy levels is investigated. The gauge dependence of the retarded electron-electron interaction in a self-consistent-field scheme is studied both theoretically and numerically. The complete Breit operator mean values are computed in Lorentz gauge and compared with those of the semirelativistic retarded interaction in covariant and radiation gauges for high-Z heliumlike ion singly excited states. The off-shell energy case is considered in detail even for a perturbative approach.

Dynamic dipole, quadrupole, and octupole polarizabilities of the beryllium isoelectronic sequence up to Z=10 are calculated using time-dependent linear-response theory. Excitation energies and analytic representations of the singly excited Rydberg states of s, p, d, and f symmetries in their singlet configurations are also obtained for excitations up to principal quantum number n=8. The &(ω${)}_{\mathrm{\omega }\to 0}$ obtained compare well with existing static results. Excitation energies compare favorably with the available spectroscopic values. The oscillator strengths for the dipolar and quadrupolar transitions are calculated and the effective quantum numbers are estimated using the complete screening model. Agreement is reasonably good with existing data wherever available.

The capture and loss of electrons for incident bare, one-, two-, and three-electron 10–42-MeV carbon ions are studied. The one-electron-loss cross sections are compared with Glauber-approximation 1s ionization calculations, and a way of incorporating target-atom screening into the Glauber theory is proposed. The electron-capture cross sections agree reasonably well with eikonal-approximation results. The equilibrium charge states of the highest-energy C ions emerging from solid targets can be calculated accurately from gas-target equilibrium charge states using a theory incorporating excited-state effects.

We reexamine the pseudostate expansion used previously to evaluate van der Waals (vdW) coefficients and finite-mass corrections. In particular, we wish to understand the very rapid convergence of the expansion, which for the case of two hydrogenic atoms requires only ten terms to achieve an accuracy of 1×${10}^{\mathrm{-}10}$. The analysis proceeds from the representation of the vdW coefficients as integrals of single-atom frequency-dependent polarizabilities. These in turn can be expanded in power series with coefficients of the form ${\mathcal{J}}_n$$M^2$(nl)/($E_{\mathrm{nl}}$-$E_{1s}$${)}^k$, where M(nl) is a multipole matrix element between the ground (1s) and excited (nl) states. Although defined as sums over an infinite set of hydrogenic states, the coefficients of each order k are reproduced exactly by a finite sum over suitable pseudostates. By analytic continuation, the frequency-dependent polarizabilities computed using pseudostates are expected to be very close to the exact values, and hence the rapid convergence of the vdW coefficients is understood.

We have determined scaling laws for the densities of atomic and molecular hydrogen in a discharge. For diagnosis we use a multiphoton-ionization technique. Both atoms and molecules are detected in their electronic ground state. The lowest three vibrational levels of the molecules, with vibrational quantum numbers v’’=0, 1, and 2, are investigated separately. From the scaling laws for the v’’=1 and 2 populations, we obtain experimental evidence that they are produced by low-energy-electron collisions with unexcited molecules, and are destroyed predominantly by collisions with other discharge-produced particles, presumably atoms and/or thermal electrons. Scaling laws concerning the atomic density are found to be compatible with production mainly via primary electron excitations of electronic ground-state molecules and destruction dominated by wall collisions.

The differential cross section for the scattering of an electron by an impenetrable, infinitely long magnetic flux line with return magnetic flux uniformly distributed on the surface of a cylinder of radius a is calculated. The scattering is due to the Lorentz force from the magnetic field of the return flux. In the limit as the radius of the return flux goes to infinity (a→∞), the differential scattering cross section is the same as that obtained by Aharonov and Bohm (AB) for the scattering of an electron by an impenetrable, infinitely long magnetic flux line without return flux. The AB scattering cross section is, however, attributed to the effect of the vector potential in a field-free region so no force acts on the electron.

Polarization measurements have been performed and emission spectra in the visible and near ultraviolet have been acquired for transitions between Rydberg states of slow, highly charged neon ions (${\mathrm{Ne}}^{\mathrm{q}+}$, with q=10–5, and v≊0.09 a.u.), following electron capture from Na. Resolvable line splittings appear in those spectra for which the incoming projectile ions carry L-shell core electrons. The optical emission cross sections are much smaller for these ions and the radiation is significantly depolarized relative to those ions whose transitions are seen as structureless. These effects are attributed to the inhibition of Stark mixing by core interactions.

A quantal two-channel calculation is applied to study charge-transfer differential cross sections in ${\mathrm{Ne}}^{4+}$ on He collisions at laboratory impact energies from 220 to 500 eV. The experimental data of Tunnell et al. were used to fit empirical potential curves and coupling terms from which the observed oscillatory structures in the differential cross sections were analyzed. In contrast with the double-charge-transfer process in ${\mathrm{C}}^{4+}$ on He, where the oscillations in the differential cross sections are attributed to pure Stueckelberg oscillations, we demonstrated that the differential cross sections for charge transfer in ${\mathrm{Ne}}^{4+}$ on He exhibit many fine fast oscillations and the observed structures are due to the envelopes of these unresolved fast oscillations. Classical deflection functions are used to help in interpreting the calculated oscillations.

We have developed a general perturbative theory which describes how coherent wall interactions affect the NMR spectrum of nuclear-spin–polarized gases in containers of any shape. The important practical case of cylindrical containers with quadrupolar wall interactions has been worked out completely. The basic results are quite simple. The frequency shift and damping of the NMR spectrum depend on seven fundamental parameters: v, the mean thermal velocity of spin polarized atoms; λ, the mean-free path of spin-polarized atoms in the gas; l, a characteristic linear dimension of the container; A, an asymmetry parameter of the container; 〈θ〉, the mean twist angle experienced by the nuclear polarization of an atom as a result of a collision with the wall; 〈${\theta }^2$〉, the mean-squared twist angle experienced by the nuclear polarization of an atom as a result of a collision with the wall; and β, the angle between the symmetry axis of the container and the direction of the quantizing magnetic field.

Differential cross sections for electron-impact ionization of molecular hydrogen are presented in the factorized first Born, fixed-nuclei, frozen-core Hartree-Fock approximation. The wave function of the ejected electron is described by a Coulomb wave distorted by the static-exchange potential of the frozen ionic core. Transition matrix elements are evaluated in both the length and velocity forms using Padé-approximant corrections to initial estimates based on the Schwinger variational principle. For high-energy incident electrons, the length form is in excellent agreement with experimental Compton defects but the magnitude of the doubly differential cross section is too large. The magnitude of the doubly differential cross section in the velocity form is generally in good agreement with experiment; however, the maxima occur at energy losses which are too large, particularly for small linear-momentum transfers. Results of calculations of the triply differential cross section are also presented. The agreement with experiment is only fair for 250-eV incident electrons because of the breakdown of the first Born approximation.

Eigenvectors for an electron in an atom in parallel electric and magnetic fields are calculated, and a semiclassical interpretation of their behavior is obtained. Eigenvectors can in this case be regarded as ‘‘wave functions in angular momentum space.’’ The matrix equation defining the eigenvectors is written as a difference equation, and then converted to a pseudodifferential equation; a systematic procedure is then used to construct a semiclassical approximation. It is found that the same classical Hamiltonian that has been previously used to calculate semiclassical eigenvalues provides a WKB-type representation of the eigenvectors. The development sheds new light on action-angle formulations of quantum mechanics and on semiclassical approximations in action-angle variables.

It is demonstrated that perturbation theory combined with the variational principle in the form of the perturbational-variational Rayleigh-Ritz (PV-RR) matrix formalism is a powerful method for applying large-order perturbation theory (LOPT) to the Stark effect for hydrogenic ions. Unlike other more specialized LOPT methods, which do not invoke the variational principle, application of the PV-RR formalism is not restricted to one-electron systems. A paradigm is derived and implemented which permits the precise construction of a Rayleigh-Ritz variational ansatz from which the real Stark ground-state Rayleigh-Schrödinger perturbation series for the eigenfunction, eigenvalue, and arbitrary expectation values can be generated via the PV-RR procedure to any prespecified order in the most economical way possible. A novel method of analysis, based on a combination of the Stark virial, Hellmann-Feynman, and remainder theorems, is developed for studying the physical origins of high-order atomic and molecular polarizabilities; the procedure is illustrated by application to the hydrogenic Stark effect. It is concluded on the basis of this work and of similar high-order PV-RR polarizability calculations for ${\mathrm{H}}_2$${\mathrm{}}^{+}$ that the prospects for extending the PV-RR formalism to accurate polarizability studies of more complex systems are promising.

The purpose of this paper is to define the lowest pressure at which an atomic gaseous medium gives a cooperative or continuum response to an electromagnetic stimulus. This is done by examining the conditions for sufficient third-harmonic generation by the resonant atomic assembly. It is found that at such low pressures one would have 25 particles per λ/10-thick slice of the characteristic volume of the focused fundamental beam. The question of getting a cooperative response from an assembly of H atoms at such low pressures that strong interactions between two H atoms may be minimized is discussed. The criterion is also applied to get a cooperative response from the various nuclei in interaction with γ rays.

We study the photon statistics at the output of phase-sensitive amplifiers and absorbers. It is argued that the photon statistics is independent of a detailed description of the rigged energy reservoir; therefore, we use a simple phenomenological model including only three parameters. The mean number of photons and the Mandel parameter Q at the output are studied as a function of the reservoir state and the input state. General conditions for sub-Poissonian output light are stated with use of three characteristic moments of the input state. We find an interesting intermediate regime where the device can have a sub-Poissonian output for a certain class of super-Poissonian input states.

We analyze a model of a laser pumped by an incoherent source in a squeezed vacuum state. The squeezed pump introduces an anisotropy of phase in the laser output. Above threshold two stable solutions are found, with phases corresponding to the directions along which the noise of the bath is quenched. These solutions are illustrated by the potential function of the laser field. An analysis of fluctuations shows that the laser field has reduced phase fluctuations but not below the quantum limit.

A unified approach is presented for the treatment of stochastic fluctuations in four-wave-mixing processes, including uncorrelated and fully or partially cross-correlated input laser fields. The theory allows for phase as well as amplitude fluctuations and covers Markovian and non-Markovian (non-Lorentzian) input line shapes. The analogy between laser field fluctuations and molecular dephasing processes is discussed, and several types of fluctuation-induced resonances are considered. Uncorrelated input fields give rise to resonances similar to those described previously by Agarwal, while correlated input fields cause extra resonances of the type presented by us in earlier publications. Partial cross-correlations are treated here for the first time, with predictions for new effects: Oscillations in the intensity of the generated four-wave-mixing signal as a function of the degree of cross-correlation. The conditions for the experimental observation of these effects are discussed.