We report a theoretical study of He(1${\mathit{s}}^2$)+hν→${\mathrm{He}}^{+}$(1s,2s,2p)+${\mathit{e}}^{\mathrm{-}}$ photoionization processes, for photon energies greater than 65.4 eV. We pay special attention to the energy region 69.0–73.0 eV, where recent synchrotron experiments exhibit clearly resonant structure associated to 3lnl’ doubly excited states of He. Our method is based on a Feshbach partitioning of the total wave function that includes explicitly resonant structure. Total and partial cross sections do not depend on parametrization, although an obvious one can be obtained in a straightforward manner in the vicinity of isolated resonances; this is very useful for the analysis of most of the resonance peaks observed experimentally. An appealing feature of our approach is the use of ${\mathit{L}}^2$-integrable basis sets to describe the scattering wave functions. Our discretization method provides coupled continuum states with the proper δ-function normalization and with the correct asymptotic behavior. With this method, we have calculated partial photoionization cross sections for leaving the ion in the 1s, 2s, and 2p levels, and the results are in good agreement with recently published experimental data. A complete set of parameters describing the first twelve resonances in partial cross sections is also provided.

Cross sections for positronium formation by capture from the negative hydrogen ion are given. Orthogonalization corrections to the Coulomb (first-order) Born approximation (CBA) differential and total cross sections are calculated using approximate ${\mathrm{H}}^{\mathrm{-}}$ wave functions of both Löwdin [Phys. Rev. 90, 123 (1953)] and Chandrasekhar [Astrophys. J. 100, 176 (1944)]. The present calculation of the CBA cross sections using the post interaction for Löwdin’s wave function (LCBAPS) disagrees with the calculation of Choudhury, Mukherjee, and Sural (CMS) [Phys. Rev. A 33, 2358 (1986)], whereas our results using the prior interaction agree. Thus, where CMS found an order of magnitude post-prior discrepancy in the differential cross sections except at forward angles, and a markedly different shape to the minima, the present post and prior results differ by 1–10 % at 100 eV, and the minima have the same shape and occur within one degree of each other. Chandrasekhar’s ‘‘open-shell’’ wave function, which is superior to Löwdin’s in bound-state problems since it gives a negative binding energy, gives post and prior cross sections that are almost indistinguishable at this energy and are 1/2 to 2/3 as large as the LCBA. Various methods of orthogonalizing the unbound projectile to the possible bound states are considered. It is found that treating the atomic nuclei as if they were isotopic spin projections [Straton and Girardeau, Phys. Rev. A 40, 2991 (1989)] of a single type of ‘‘nucleon’’ gives cross sections that are an improvement over the CBA.

Detailed calculations of energies and widths of Ca autoionizing states and the related resonance structure in electron-impact excitation of the 4s-4p transition in ${\mathrm{Ca}}^{+}$ are performed using the diagonalization method. This method is divided into two steps: a three-state (4s,3d,4p) close-coupling calculation of cross sections and extensive configuration-interaction calculations of wave functions of autoionizing states. Both steps take into account the correlations related to one- and two-body core-polarization potentials. The results of calculations of energies, oscillator strengths, and autoionizing widths of doubly excited states of Ca are in better agreement with the experimental data than any other calculation. Rich resonance structure is predicted by theory at incident electron energies below the 5s threshold. The present results support the general pattern of the measurements of Frontov [Opt. Spectrosc. 9, 460 (1985)], although there are some discrepancies in the details, particularly the existence of the high and broad resonance at that threshold. A detailed comparison with the previous resonance calculations by Mitroy et al. [Phys. Rev. A 38, 3339 (1988)] is carried out.

The processes of Coulomb excitation and ionization of atoms by a fast charged particle moving along a classical trajectory are studied. The target electrons are described by the Dirac equation, while the field of the incident particle is described by the Lienard-Wiechert potential. The theory is formulated in the form most convenient for investigation of various characteristics of semiclassical atomic collisions. The theory of sudden perturbations, which is valid at high enough velocities for a high projectile charge, is employed to obtain probabilities and cross sections of the Coulomb excitation and ionization of atomic hydrogen by fast multiply charged ions. Based on the semiclassical sudden Born approximation, the ionization cross section and the average electronic energy loss of a fast ion in a single collision with an atom are investigated over a wide specific energy range from 500 keV/amu to 50 MeV/amu.

High-energy (25–28-keV) electron-impact spectroscopy (HEEIS) has been used to measure a relatively complete Bethe surface for molecular nitrogen. This surface, placed on an absolute scale by Bethe-sum-rule normalization of the generalized oscillator strength (GOS), has been employed to obtain the x-ray incoherent scattering factor S(K) as a function of the momentum transfer K by use of a sum rule of the GOS. Ground-state correlation effects on S(K) were obtained by comparing the experimental results with theory based on a near-Hartree-Fock molecular wave function. The results are compared with recent theoretical calculations of valence-shell correlation effects. It is argued that x-ray and electron-scattering experiments offer the most sensitive tests currently available for valence-shell electron-correlation effects in the ground electronic states of molecules. The results obtained coupled with available theory suggest that correlation effects on the one-electron density play a dominant role in the determination of the total correlation energy of the nitrogen molecule.

A theory is developed to describe the spectral line shape due to interference between electric-dipole-allowed and collision-induced transitions in pure rotational molecular spectra. Motivation was provided by experimental data available for HD-inert gas systems. This theory is based on a master-equation approach to induced spectra employed by Alber and Cooper [Phys. Rev. A 33, 3084 (1986)]. The active molecule is considered to be immersed in a bath of perturbers. An expression for the absorption coefficient is obtained within the binary collision approximation that contains terms due to allowed, induced, and interference contributions. Effects due to m mixing, J mixing, and successive collisions are included. Low-order approximations of the theory eventually reduce to results of earlier efforts, namely, the pioneering description of collisional interference by Herman, Tipping, and Poll [Phys. Rev A 20, 2006 (1979)] and refinements to it through consideration of rotational level mixing. The principal attribute of this approach is the treatment of allowed and collision-induced transitions in a consistent manner.

Decay of single-K-shell-vacancy states of xenon atoms by the emission of photon pairs that continuously share the transition energy was studied. The vacancy states were generated by electron-capture decay in ${}_{}{}^{131}{}_{}{}^{}\mathrm{Cs}$. A pair of high-purity germanium detectors and a fast-slow coincidence system with a (128×512×512)-channel pulse-height analyzer were used in the measurements. Accurate energy calibration was made by a careful determination of positions of peaks due to crosstalk among the detectors via Ge K x rays. Identification of events due to the two-photon decay is based on the shifts of energy sums. From the numbers of events in the ridges, the relative differential probabilities of 2s→1s, 3s→1s, 3d→1s, and 4sd→1s two-photon decay were derived. They are compared to the values derived from the results of non-relativistic calculations for hydrogen and hydrogenic ions of Shapiro and Breit [Phys. Rev. 113, 179 (1959)], of Tung, Ye, Salamo, and Chan [Phys. Rev. A 30, 1175 (1984)], and of Florescu [Phys. Rev. A 30, 2441 (1984)], and to the results of the following studies of two-photon decay of single-K-shell-vacancy states of xenon atoms: a calculation based on the theory of Bannett and Freund [Phys. Rev. Lett. 49, 539 (1982); Phys. Rev. A 30, 299 (1984)], a nonrelativistic calculation of Wu and Li [J. Phys. B 21, 1509 (1988)], and relativistic calculations of Mu and Crasemann [Phys. Rev. Lett. 57, 3039 (1986); Phys. Rev. A 38, 4585 (1988)], and of Tong, Li, Kissel, and Pratt [Phys. Rev. A 42, 1442 (1990)]. As expected, no events due to the np→1s two-photon transitions were observed and upper limits are given.

We suggest the quantum Heisenberg group ${\mathit{H}}_{\mathit{q}\left(\mathit{J}\right)}$(4) as the dynamical symmetry group of a diatomic-molecule system. The deformation parameter q of the ${\mathit{H}}_{\mathit{q}\left(\mathit{J}\right)}$(4) symmetry group is a function of J (the quantum number of the angular momentum of the rigid rotation) and characterizes the interaction between vibration and rotation. The vibrational and rotational structures of diatomic molecules are compactly expressed using the quantum-group-theoretic approach. Taylor expansions of the analytic formulas from this approach reproduce the results of the anharmonic-oscillator and the nonrigid-rotator models. For some randomly selected molecules in particular states, the parameters are computed to fit the phenomenological formulas to high accuracy.

The problem of calculating the time-evolution operator within a given n shell for a hydrogenlike atom located in nonstationary electric and magnetic fields has been studied. Using the Fock SO(4) group reduces this to a set of problems with a time-dependent Hamiltonian that can be written as a linear combination of operators which span a finite-dimensional Lie algebra. Alternative methods of evolution-operator parametrization, through a product-of-exponents procedure (the Wei-Norman method) and by means of D functions based on Euler angles and Cayley-Klein parameters, are discussed. It is shown that the evolution-operator calculation can be reduced to the investigation of a pair of two-level systems. The approach developed here is applied to the problem of evolution of a hydrogen atom in constant and harmonic electric fields. Analytical solutions obtained within the frame of standard perturbation theory, in the resonance and adiabatic approximations, and for the case of quasidegeneracy are given.

The collisional interaction of heavy-water clusters with TiD has been studied theoretically via three independent methods with the aim of estimating cluster-fusion yields. Particular attention was paid to multiple wide-angle-scattering processes between deuterons and heavy beam or target atoms. In order to achieve adequate statistics in molecular-dynamics simulations, the elastic-scattering cross section was enhanced by, roughly, increasing the deuteron charge at constant mass. Deuteron spectra were then determined by extrapolation to Z=1. The validity of the procedure was confirmed by comparison with simulations using unscaled interaction potentials. Monte Carlo simulations were also performed, using a code that incorporates target motion and allows for larger cluster and target size. Cross sections for double wide-angle-scattering events (Fermi shuttles) were computed directly. By all three methods we find clear evidence that deuterons are accelerated far beyond the limits imposed by single-scattering kinematics. We find exponential tails with slopes approximately inversely proportional to the incident energy per cluster atom. Estimated fusion yields increase very strongly with the energy per beam atom and lie 8 to 18 orders of magnitude below those reported experimentally.

We demonstrate the possibility of Bose-Einstein condensation (BEC) of an ideal Bose gas confined by one- and two-dimensional power-law traps. One-dimensional systems display BEC in traps that are more confining than parabolic: U(x)∼${\mathit{x}}^{\mathrm{\eta }}$,η<2. Two-dimensional systems display BEC for any finite value of η. A possible experimental configuration for a two-dimensional trap is described.

We present a theoretical description of a scheme in which coordinated laser pulses transfer population efficiently from any initially populated state (e.g., the ground state) to a multiply excited state of an atom or molecule without producing appreciable population in intermediate states. Our analytic results for multilevel excitation transfer provide a simple yet instructive extension to the counterintuitive pulse sequence studied previously for a three-state system.

We describe atomic hydrogen diamagnetism within the framework of multichannel quantum-defect theory using an R-matrix approach. The calculated photoionization spectrum in the range of magnetic field B=${10}^3$–${10}^4$ T shows that the quasi-Landau resonances are broad interlopers that perturb high Rydberg states converging to the Landau thresholds, forming complex resonances. A partial-cross-section analysis indicates that electron population of different Landau channels depends on the azimuthal quantum number and parity of the final states. For odd-total-parity final states with m=1, the photoionized electron is predicted to escape predominantly in the higher Landau channels, while for final states with m=0, it escapes in the lower channels. This property is reflected in the shape of autoionizing resonances, which are more like peaks for m=1, but are more like dips (window resonances) for m=0.

We discuss the transition between two limiting cases of transverse spin relaxation due to magnetic-field inhomogeneities: very fast spatial diffusion, when the spins relax exponentially with time, and very slow spatial diffusion, when the spins relax exponentially with the cube of the time. Both limiting cases as well as intermediate cases can be described in terms of Airy functions, which are the eigenfunctions of the time-independent Torrey equation. Branch points in the eigenvalue spectrum and other interesting properties follow from the fact that the Torrey equation is not self-adjoint.

Current x-ray laser designs rely on amplifying spontaneous emission in a high-temperature plasma. A central problem in the study of x-ray lasers is determining and optimizing the degree of transverse spatial coherence for holographic applications. The inherent non-power-orthogonal character of the normal modes in a general amplifying medium necessarily results in excess noise and cross-correlation effects that can significantly affect the predicted coherence and intensity profiles of an x-ray laser. In particular, loosely bound discrete transverse eigenstates of the paraxial wave equation have previously been found to dominate the intensity and coherence in the low-amplification regime if the continuum eigenstates are omitted from the spectrum [London, Strauss, and Rosen, Phys. Rev. Lett. 65, 563 (1990)]. A detailed analysis of the role of excess noise on steady-state laser intensity and coherence is presented for the simple case of a transverse square gain and density profile in a finite geometry. The inclusion of the continuum portion of the spectrum is found to substantially reduce the level of excess noise and to alter the coherence predictions for low and intermediate gain-length products.

This paper provides a general treatment of the pulse-propagation problem in doped fiber amplifiers within the rate-equation approximation. The dopants are modeled as a two-level system whose dynamic response is governed by the population relaxation time ${\mathit{T}}_1$ and the dipole relaxation time ${\mathit{T}}_2$. For incident optical pulses with a width ${\mathit{T}}_0$ such that ${\mathit{T}}_1$≫${\mathit{T}}_0$≫${\mathit{T}}_2$, pulse amplification is governed by a Ginzburg-Landau-type equation that includes gain saturation, gain dispersion, fiber dispersion, fiber nonlinearity, and the detuning effects occurring when the carrier frequency of the input pulse does not coincide with the gain peak. In the absence of gain saturation, this equation has solitary-wave solutions in the form of chirped solitons. Our numerical results show that the chirped solitons are stable only in the normal-dispersion regime. In the case of anomalous dispersion, as is the case for erbium-doped fiber amplifiers, the amplified pulse develops many subpulses. The effect of gain saturation on pulse amplification is also discussed.

We consider a system of two masers that are pumped by the same beam of excited atoms. The atoms pass first through one maser and then through the other. As a result, the first maser modifies the pump going into the second and an effective coupling results. We examine this system in the amplifier configuration, i.e., we do not consider saturation effects. The fields in the two masers are mutually coherent and can, under the proper circumstances, be free of noise in their relative phase. Therefore this system exhibits behavior similar to that of a correlated-emission laser. We also find that the photon number in the second maser grows faster than that in the first. These effects should be observable even if the pump beam has a finite velocity spread.

Polarization modulationalal instability in a nonlinear dispersive birefringent medium refers to the exponential growth of polarized sidebands due to mixing with an orthogonally polarized pump. We show that this instability extends to the nonlinear regime of strong coupling between the waves. By reducing the coupled nonlinear Schrödinger equations that govern the interaction to a finite-dimensional integrable Hamiltonian system, we show that nonlinear modulational instability originates from bifurcations of spatial eigensolutions of the three-wave interaction. Spatial recurrence of the field evolutions and period doubling related to the existence of spatially unstable eigensolutions are relevant for applications which make use of polarization modulational instability (or birefringence-matched third-order three-wave mixing) in the strong-depletion regime. In contrast to previous results obtained by means of linearized equations, we find that efficient frequency conversion, when strong coupling is accounted for, occurs for initially wave-vector-mismatched waves.

The existence of dark spatial solitons of the TM type is examined. This type of two-dimensional solitary wave is found to exist in the self-defocusing nonlinear medium of a Kerr-law type in the range of the wave effective index ${\mathit{n}}_{\mathrm{eff}}$ from 0.82${\mathit{n}}_0$ to ${\mathit{n}}_0$ of the linear refractive index of the medium. This contrasts with dark spatial solitons of the TE type, which exist in the range of ${\mathit{n}}_{\mathrm{eff}}$ from 0 to ${\mathit{n}}_0$. The longitudinal component is shown to play a key role leading to this distinction. The comparison between TM and TE solitons is also made on other aspects. For example, the field profile of the TM soliton is shown to vary with the wave effective index, whereas that of the TE soliton is characterized by the hyperbolic tangent function, independent of ${\mathit{n}}_{\mathrm{eff}}$.

We report on the observation of several nonlinear optical processes in connection with two-photon excitation of ${\mathrm{H}}_2$ by 193-nm radiation generated by a narrow-bandwidth ArF laser system: stimulated electronic hyper-Raman scattering, parametric four-wave mixing (PFWM), and stimulated resonant Raman scattering (SRRS). These processes lead to the generation of several intense lines in the ir and vacuum ultraviolet (vuv). vuv generation occurs by two interconnected schemes: first, a vuv wave at λ∼109 nm is generated by PFWM (power up to 16 kW). This wave subsequently generates Stokes lines around λ∼150 nm by SRRS. The frequencies of these waves are tunable over spectral intervals of ∼20 ${\mathrm{cm}}^{\mathrm{-}1}$ by phase matching with admixture of various gases (e.g., noble gases, ${\mathrm{N}}_2$, ${\mathrm{D}}_2$). With additional irradiation of ir laser radiation, four-wave mixing (FWM) takes place. In this case, continuously tunable vuv radiation (tuning range ∼600 ${\mathrm{cm}}^{\mathrm{-}1}$) can be generated with power in the 10- and 100-kW range. The tuning ranges are localized around the rovibronic resonances X-B. FWM is not possible on resonance. As in the case of PFWM, Stokes lines are generated by SRRS, tunable over intervals up to ∼60 ${\mathrm{cm}}^{\mathrm{-}1}$. The susceptibilities governing the processes involved are calculated. The agreement between the theoretical expectations and the experimental results is very good with respect to the frequency dependence. The calculated absolute values of the vuv intensities, however, turn out to be by far too high. This is due to the neglect of several limiting processes which will be discussed together with the experimental results. In addition to the processes mentioned above, several B-X resonance transitions exhibit a limited tunability (∼10 ${\mathrm{cm}}^{\mathrm{-}1}$). It is proposed to explain this tunability in terms of stimulated two-photon emission.