A method to calculate electron-capture cross sections for collisions between an arbitrary $n_i$$l_i$$m_i$ shell of a hydrogenic target and an arbitrary $n_f$$l_f$$m_f$ shell of a fast bare projectile has been developed in the framework of the continuum distorted-wave approximation. Analytical expressions are derived for the Coulomb integrals in closed form in terms of Gauss hypergeometric functions in a terminating series. As an application, the cross sections in ${\mathrm{N}}^{7+}$+H(1s) collisions are calculated in the energy range between 10 and 40 MeV and compared with existing theoretical calculations. The total charge-transfer cross sections have been evaluated by applying an $n^{\mathrm{-}3}$ law for n≥7 levels.

We present a theoretical treatment of resonant two-photon ionization in the presence of a noisy laser. The atom is modeled by a two-level system, while the statistical fluctuations of the field are described within the framework of the pre-Gaussian model. We show that previous results obtained by using Ornstein-Uhlenbeck statistics are recovered in the appropriate limit in the case of frequency fluctuations. We also give new results in the case of phase and amplitude noise.

Selected K molecular-orbital (MO) transitions in collisions of 100-, 160-, and 200-MeV ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$ on ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$ and 200-MeV ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$ on ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$ have been isolated in a MO x-ray–K x-ray coincidence measurement. This experiment exploits the cascade relationship between the MO x rays emitted in transitions from the (2p${\pi }_x$, 2pσ) MO’s into the 1sσ MO and the characteristic K x ray which follows from the filling of the ensuing vacancy in the projectile or target atoms after their separation. In both symmetric and asymmetric systems, most of the high-energy MO x rays (C2 radiation) were found to be in coincidence with characteristic K x rays while the low-energy MO x rays (C1 radiation) were not correlated to the K x rays. Noncascade processes due to multiple vacancies in the 1sσ and 2pσ MO’s were also found to contribute a small amount to the true MO x-ray–K x-ray coincidences. Theoretical estimates of the relative contributions of the isolated transitions as well as contributions from multiple vacancies are discussed.

Absolute oscillator strengths in the region of carbon and fluorine K-shell excitation have been derived for ${\mathrm{CH}}_2$${\mathrm{CH}}_2$, ${\mathrm{CH}}_2$CHF, cis-CHFCHF, ${\mathrm{CH}}_2$${\mathrm{CF}}_2$, ${\mathrm{CHFCF}}_2$, ${\mathrm{CF}}_2$${\mathrm{CF}}_2$, 1,3-${\mathrm{C}}_4$${\mathrm{H}}_6$, and 1,3-${\mathrm{C}}_4$${\mathrm{F}}_6$ from electron-energy-loss spectra recorded under dipole-dominated conditions. The methods used to derive absolute oscillator strengths from relative energy-loss intensities are discussed in detail. The accuracy of the procedures is tested through comparisons with literature results for ${\mathrm{N}}_2$, CO, and ${\mathrm{CO}}_2$. The total C 1s→${\pi }^{\mathrm{*}}$ and C 1s→${\sigma }^{\mathrm{*}}$(C—F) intensities increase systematically as the degree of fluorination increases. The spectra are discussed in terms of bond-length correlation and potential barrier concepts.

The two-photon-resonant, three-photon (2+1) ionization spectrum of atomic nitrogen produced by photodissociation of nitrous oxide has been determined between 2692 and 2687 Å, and shows two peaks corresponding to the N ${}_{}{}^2{}_{}{}^{}\mathrm{}_{1/2}^{}{}_{}{}^{}$←${\mathrm{}}^2$D°${\mathrm{}}_{3/2}$,5/2 transitions. The photoelectron spectrum for (2+1) ionization via the ${}_{}{}^2{}_{}{}^{}\mathrm{}_{1/2}^{}{}_{}{}^{}$ state displays a single ${\mathrm{N}}^{+}$ photoelectron peak corresponding to the production of the ${}_{}{}^3{}_{}{}^{}\mathrm{P}$ ground state. The photoelectron angular distribution following ionization via the ${}_{}{}^2{}_{}{}^{}\mathrm{}_{1/2}^{}{}_{}{}^{}$←${\mathrm{}}^2$D°${\mathrm{}}_{5/2}$ transition shows a distinct minimum along the polarization axis of the laser light (β=-0.2±0.1). Implications of this anisotropy for the relative dipole amplitudes into the different ɛs and ɛd ionization channels are discussed.

A transition-matrix theory for two-photon ionization processes in rare-gas atoms or isoelectronic ions is presented. Uncoupled ordinary differential equations are obtained for the radial functions needed to calculate the two-photon transition amplitude. The implications of these equations are discussed in detail. In particular, the role of correlations involving virtually excited electron pairs, which are known to be essential to the description of single-photon processes, is examined for multiphoton ionization processes. Additionally, electron scattering interactions between two electron-hole pairs are introduced into our transition amplitude in the boson approximation since these have been found important in two-photon ionization of xenon by L’Huillier and Wendin [J. Phys. B 20, L37 (1987)]. Application of our theory is made to two-photon ionization of the 3p subshell of argon below the one-photon ionization threshold. Our results are compared to previous calculations of McGuire [Phys. Rev. A 24, 835 (1981)], of Moccia, Rahman, and Rizzo [J. Phys. B 16, 2737 (1983)], and of Pindzola and Kelly [Phys. Rev. A 11, 1543 (1975)]. Results are presented for both circularly and linearly polarized photons. Among our findings are, firstly, that the electron scattering interactions, which have not been included in previous calculations for argon, produce a substantial reduction in the two-photon single-ionization cross section below the one-photon ionization threshold, which is in agreement with findings of L’Huillier and Wendin for xenon. Secondly, we find that de-excitation of virtually excited electron pairs by absorption of a photon is important for describing the interaction of the atom with the photon field, as in the case of single-photon ionization processes, but that further excitation of virtually excited electron pairs by the photon field has completely negligible effects, indicating a major simplification of the theory for higher-order absorption processes.

A method is developed for studying transient stimulated Raman scattering in the quasi-steady-state regime when the input pump field consists of a repetitive periodic sequence of pulses. The method is most attractive for cases where the single-pulse duration is substantially shorter than the repetition time scale, making a straightforward numerical simulation very costly, time consuming, and potentially intractable. The method is applicable to any periodic electric field envelope including that generated by a finite number of longitudinal modes with arbitrary phase. A second numerically efficient method is developed for treating the buildup of the entire pulse train. In addition, an analytic solution is found in the undepleted-pump regime which illuminates the underlying physics of the process.

Self-oscillations are predicted for a simple nonlinear optical system consisting of two counterpropagating waves in a two-level medium. Oscillations at frequencies of $T_1^{\mathrm{-}1}$ and the Rabi frequency are expected for certain limits of system parameters. The physical origin of these instabilities is traced to parametric amplification in the medium. The possibility of experimental verification is discussed.

The gain, phase shift, wave-front curvature, and radius of the radiation envelope in a free-electron-laser amplifier are obtained in the small-signal regime. The electron beam is assumed to have a Gaussian density distribution in the transverse direction. Numerical calculations indicate that the radius and curvature of the radiation beam entering a wiggler asymptote to unique spatially constant values after a finite transition region. However, in the asymptotic region the wave fronts are divergent. Analytical expressions for the gain, phase shift, curvature, and spot size are derived. It is shown analytically that small perturbations of the optical waist and curvature about the matched value are spatially damped out, indicating the stability of the matched envelope. When the electron-beam envelope is modulated in space, the optical spot size oscillates with an almost identical wavelength but is delayed in phase. In the case of small-amplitude long-wavelength betatron modulation of the electron-beam envelope, generation of optical sidebands in wave-number space is examined and the effect on the dispersion characteristics of the primary wave is found to be negligible for typical experimental parameters.

We discuss analytically the resonance fluorescence of a three-level ladder system whose two transitions are simultaneously saturated by the fields from two lasers. The laser fields have fluctuating phases, which may be correlated to some extent. We generalize the dressed-atom approach of Cohen-Tannoudji and Reynaud [J. Phys. B 10, 345 (1977)] to deal with phase fluctuations under conditions of overall two-photon resonance, but not single-photon resonance on the individual transitions. In this respect we also generalize the master-equation approach of Lawande, Puri, and D’Souza [Phys. Rev. A 33, 2504 (1986)]. The effect of spontaneous emission and laser fluctuations on the resonance fluorescence quintet is discussed in detail, and shown to marked effects. We also investigate the effect of these quantities on the steady-state dressed-atom occupation probabilities, and point out that the double-resonance experiment can be used to prepare the atom in a given dressed state with high probability.

We have performed an experimental study of a high-Q Rhodamine 6G ring dye laser and have measured bichromatic emission with wavelength spacings as large as 110 Å when the laser operated bidirectionally. The bichromatic emission vanished at all excitations when the laser was forced into unidirectional operation using a Faraday isolator. However, when a weak reflected beam was allowed to make a single pass in the direction opposite to that allowed by the Faraday device, bichromatic emission is recovered at the higher pump powers. The experiments show that no discontinuities occur in the intracavity power as a function of excitation and that the intracavity fields which are completely consistent with the measured thresholds are not capable of producing Rabi splittings larger than a few angstroms. In addition, we have observed no structure in the spontaneous emission spectrum of the dye when the bichromatic emission (80-Å splitting) was present in the laser mode. We have been able to quantitatively fit the threshold and wavelengths of the bichromatic emission using a distributed feedback mode analysis with a cavity-mode-induced susceptibility grating.

We consider a ring laser whose counterpropagating modes are coupled by a spatial modulation in the gain medium. We derive a nonlinear Fokker-Planck equation for these modes. In this way we show that the diffusion coefficient of the relative phase angle may vanish in both linear and nonlinear theory.

In this paper we present molecular-dynamics and kinetic-theory calculations of the interdiffusion coefficients in dense binary ionic mixtures for conditions appropriate to both astrophysical and inertial-confinement fusion (ICF) plasmas. The diffusion coefficient is the product of a Green-Kubo integral and a thermodynamic prefactor. The molecular-dynamics and kinetic-theory estimates of the Green-Kubo portion agree very well, and it is found that this integral may also be well represented by the usual concentration-weighted sum of self-diffusion coefficients. In addition, the low-density limit of the thermodynamic prefactor is shown to represent an enhancement of the diffusion by the ‘‘ambipolar’’ electric field.

This paper deals within the relativistic framework with the wave propagation in magnetizable fluids, assumed to be perfect, magnetically soft, isotropic, and inhomogeneous with an arbitrary isotropic law χ=χ(T,r,‖b${\Vert }^2$) (χ,T,r,‖b‖ being the magnetic susceptibility, the proper temperature, the proper material density, and the strength of the magnetic field, respectively). The characteristic manifolds of the flow are determined in a very elegant and rigorous manner which avoids the extensive algebraic manipulations one usually encounters in the classical methods of characteristics. It is shown that in a magnetic medium there exists a hyperbolic region of nonsteady flows of magnetizable fluids. This implies the existence of magnetosonic waves of the same kind as in nonmagnetic fluids (χ or μ=const), that is, as in ordinary magnetohydrodynamics. However, in magnetic fluids there is the possibility of the development of instabilities similar to that which arise in nonmagnetic fluids with transverse and longitudinal pressure [M. Cissoko, Ann. Mat. Pura Appl. 111, 331 (1976)].

A formal expansion in spherical harmonics or Cartesian tensors of the pair correlation function of a liquid subjected to a shear rate is discussed. Expressions for the coefficients to tensor rank 4 are evaluated via a nonequilibrium molecular-dynamics simulation of an inverse twelve soft-sphere liquid undergoing Couette flow. It is shown that the expansion converges slowly if the product τγ>0.05, where τ is the Maxwell relaxation time and γ is the shear rate. Further, the fourth-rank coefficient that represents cubic symmetry is significant for our model system. The microstructure of a shear liquid is demonstrated by intensity plots of particles around a given central particle. We have derived expressions for the expansion coefficients using a relaxation-time model and the comparison between them and the simulations is generally very good.

Solutions of tetramethoxysilicon were reacted, using both acid and base as catalysts, until near the sol-gel transition. Portions of the reacting mixture were quenched by dilution, and the average cluster mass and correlation length were measured with use of static and dynamic light scattering. Critical exponents describing the divergences of the average mass and correlation length were found to be larger than the predictions of either the percolation or Flory-Stockmayer theory.

The propagation of an electromagnetic wave in weakly nonlinear but strongly magnetized electron-positron plasmas is investigated. A quasistatic slow plasma response to the wave is shown to result in solitons with the height directly proportional to the strength of the ambient magnetic field. A dispersion relation is derived in this case of magnetized plasma and the result is used to confirm the recent suggestion of self-modulational formation of pulsar microstructure.

The energy gain and the trapping threshold of the driven particles (protons or electrons) in the counterstreaming electron-beam wake-field accelerator (CWFA) are investigated. The CWFA relies on the same physical mechanism as the plasma wake-field accelerator (PWFA) but differs from the PWFA in that it uses a relativistic counterstreaming electron beam instead of a stationary plasma as the medium for supporting the plasma waves.

The phase-space distribution of semi-infinite nuclear matter is expanded in an ħ series analogous to the low-temperature expansion of the Fermi function. Besides the usual Wigner-Kirkwood expansion, oscillatory terms are derived. In the case of a Woods-Saxon potential, a smallness parameter is defined, which determines the convergence of the series and explains the very rapid convergence of the Wigner-Kirkwood expansion for average (nuclear) binding energies.

The orbital scaling function for period tripling in near conformal mappings is constructed with use of the fixed point of the period-tripling operator for conformal maps. It is an expansion of the nearest-neighbor vectors of the (n+1)-times-bifurcated orbit in terms of a local basis consisting of analogous vectors from the previous level. It is used to evaluate the singularity spectrum of the distribution of areas enclosed by the three points bifurcating out of the same point.