Poles of the S matrix in the complex wave-number plane are examined for a Dirac particle scattering from an electrostatic square well in 1+1 dimensions. As the depth of the well increases, the poles describe trajectories in the k plane which illustrate how resonances move from the positive to the negative energy continuum, intermediately forming bound states.

We have measured the total destruction cross sections for ${\mathrm{H}}_3^{+}$ ions colliding with He, Ne, Ar, and Xe atoms in the velocity range from 2.5 to 7 atomic units (470 to 3700 keV). The collisional destruction cross section of ${\mathrm{D}}_3^{+}$ ions by Ar atoms was also measured, and was found to be comparable to the ${\mathrm{H}}_3^{+}$ values. The cross-section data were analyzed in two different ways. It was first established in a strictly empirical way that the cross sections for all noble gases may be scaled, in the energy range studied, by velocity-independent factors. In addition, the data were found to be suitably fitted by a semiempirical version of the free-collision model of Meron and Johnson [Phys. Rev. A 41, 1365 (1990)].

Photoionization cross sections of atoms often display various structures near thresholds, such as Cooper minima and shape resonances. In view of the dispersion relation connecting the real amplitude of Rayleigh scattering (elastic photon scattering from atomic electrons) and the photoeffect cross section, one may expect that the structures in photoionization cross sections imply corresponding features in the real anomalous scattering factor, which also can now be quite precisely measured experimentally. In this paper we study the detailed structures of the real anomalous scattering factor f ’, in an effort to understand the connections with structures in the photoeffect cross section.

A partially linearized Thomas-Fermi-Weizsäcker theory is proposed to study charged particles interacting with jellium. This simple theory can be derived by linearizing contributions involving the Thomas-Fermi kinetic-energy density. The calculations are based on a nonlinear inhomogeneous integrodifferential equation that includes the potential along the lines suggested by the original Thomas-Fermi-Weizsäcker theory. Exchange-correlation effects are neglected. The coefficient of the von Weizsäcker term is prescribed according to Kato’s cusp condition in order to investigate both heavy and light particles in jellium. This theoretical framework is applied to compute the stopping power of a jellium for slow protons and antiprotons, induced electron densities, positron annihilation rates, and the electron-correlation function for antiparallel spin. Illustrative comparisons with the results of other theories are also made.

Recombination spectra are measured in the wavelength range 300–850 nm resulting from collisions of 5-eV O${(}^3$P) atoms with NO adsorbed on ${\mathrm{MgF}}_2$, Ni, and Ti surfaces. The dependence of the chemiluminescence intensity on surface temperature (240–340 K) is measured, and activation energies for desorption of the physisorbed NO obtained. Activation energies as a function of wavelength for each material are also reported. It is found that, with minor variations, the recombination spectra are similar for the three surfaces, and that the emitter is very likely electronically excited ${\mathrm{NO}}_2$. All three materials exhibit a greater tendency to emit at the lower temperatures. ${\mathrm{MgF}}_2$ has the greatest tendency to chemiluminesce, followed by Ni then Ti. Also, the activation energies for NO desorption are similar for the surfaces, and are independent of emission wavelength. The results are interpreted as a single mechanism of removal, with increasing T, of physisorbed NO from saturated surfaces of different coverage.

A systematic evaluation of one-electron matrix elements appearing in the theory of charge-exchange processes in ion–metal-surface scattering is presented. The conduction-band electrons are described by jellium-type wave functions, while hydrogenic wave functions are employed for the electronic states of the ion. By applying Fourier-transform methods and complex integration techniques, exact closed-form expressions for overlap and Coulomb matrix elements are derived for arbitrary hydrogenic quantum numbers, momenta of the conduction-band electrons, and distances of the ion from the surface. The general case of arbitrary energy difference between initial and final state (including the strictly resonant case) is treated. For the near-resonant case, an expansion of the matrix elements about the resonant limit is derived. The effect of the motion of the ion is taken into account by including electronic translational factors. The actual computation of the matrix elements involves multiple summations, which can be accurately performed even for high-lying ionic Rydberg states. Structural properties of the matrix elements are revealed by studying, for typical cases, their dependence on the various parameters. Possible applications of our method are indicated.

The time-dependent Schrödinger equation for a Coulomb collision between a heavy point charge and a harmonically bound electron is solved exactly numerically. The energy transferred to the electron is studied as a function of impact parameter and projectile charge. Special attention is given to the Barkas effect and the transition from light-ion to heavy-ion stopping. The results are contrasted with classical and recent approximate results, whose precision and ranges of validity are discussed. Comparison with experimental data is made on the basis of an oscillator model of atomic stopping.

A unified theoretical description of various forms of time- and frequency-resolved stimulated-emission pump-probe (PP) spectroscopy of molecules is outlined. The expressions for the integrated and the dispersed PP signal are derived in the limit of an optically thin medium. In the limit of ultrashort pulses, the connection between the PP signals and the appropriate time-dependent observables of the molecular system are established. The PP signals obtained with probe pulses of finite duration are expressed in terms of the simpler quantities pertaining to the ultrashort limit. The apparent paradox that it seems possible to achieve simultaneously high time and frequency resolution is discussed. It is shown that the dispersed PP spectrum carries information on electronic population dynamics, coherent excited-state vibrational motion, as well as electronic dephasing processes. It may thus be difficult to interpret in general. The integrated PP signal, on the other hand, possesses a particularly simple interpretation in the limit of ultrashort pulses: It directly reflects the electronic population dynamics of dipole-allowed excited states. The general conclusions are illustrated by computational results for a model system representing multidimensional vibrational motion and ultrafast internal conversion in excited singlet states of pyrazine.

We study, within a time-independent framework, the photodetachment of an ion by a weak high-frequency field in the presence of a field of low frequency ${\mathrm{\omega }}_{\mathit{L}}$. We explore the role played by the ponderomotive energy ${\mathit{P}}_{\mathit{L}}$ due to the low-frequency (LF) field. If ${\mathit{P}}_{\mathit{L}}$≪ħ${\mathrm{\omega }}_{\mathit{L}}$, the threshold energy for photodetachment by the high-frequency field is increased by the amount ${\mathit{P}}_{\mathit{L}}$, while if ${\mathit{P}}_{\mathit{L}}$≳ħ${\mathrm{\omega }}_{\mathit{L}}$ the threshold energy is Idecreased,P due to tunneling through the barrier formed by the atomic potential and the LF field. If ${\mathit{P}}_{\mathit{L}}$>ħ${\mathrm{\omega }}_{\mathit{L}}$ the low-frequency field behaves like a dc field, but the strong repulsive barrier has a characteristic height of 2${\mathit{P}}_{\mathit{L}}$, in contrast to the case of a true dc field (where the height is infinite). If the kinetic energy of the outgoing photoelectron is smaller than or comparable to 2${\mathit{P}}_{\mathit{L}}$, the photodetachment probability is sensitive to the polarization of the low-frequency field, and exhibits ripples as the high frequency varies. These ripples are due to the interference of the direct photoelectron wave and the wave that reflects from the repulsive barrier. The differences between the low-frequency field and a true dc field are elucidated.

With the goal of increasing the accuracy of Penning-trap mass spectroscopy to a part in ${10}^{11}$, we model the motion of two simultaneously trapped, dissimilar ions. Simultaneous cyclotron resonance on two trapped ions will circumvent the problem of temporal instability in the trapping fields. Conservation of energy and canonical angular momentum require that, in the regime appropriate for mass spectroscopy, the average interion spacing be an approximate constant of the motion. Cyclotron-frequency perturbation from ion-ion repulsion is therefore limited. Orbits that minimize measurement errors from residual field imperfections are shown to be both stable and attainable. Experimental results demonstrating the simultaneous trapping of a single ${\mathrm{N}}_2^{+}$ ion and a single ${\mathrm{CO}}^{+}$ ion are presented.

In this paper we discuss the excitation of a localized molecular ground-state wave function by a short laser pulse. With a one-dimensional approach we show when it is possible to excite a considerable fraction of the ground state without too much distortion of the shape of the wave packet. This is of interest in time-resolved molecular experiments where an excited wave packet is often taken as the initial state. We solve the two coupled wave equations numerically and compare results to an analytical approximation based on the Rosen-Zener model. The validity of the approximation and its breakdown is considered in detail. Special attention is paid to the effect of lengthening the pulse duration and the consequences of the accompanying number of Rabi flops occurring in the area theorem. When the approximation breaks down, the wave packet becomes distorted and spread out, but there are still interesting coherence effects due to the interplay between the Rabi flopping and the molecular dynamics; these are displayed and discussed. Finally, the relationship to other works and possible generalizations are presented.

We adapt an earlier semiclassical theory of laser cooling of an arbitrary multistate atom [J. Javanainen, Phys. Rev. A 44, 5857 (1991)] to the limit of low light intensity. The formal theory is implemented analytically on a computer using mathematica. Expressions of light-pressure force and diffusion are provided for ${\mathit{j}}_1$=1/2→${\mathit{j}}_2$=3/2 and ${\mathit{j}}_1$=1→${\mathit{j}}_2$=2 atoms in a one-dimensional optical confinement area in which the pair of counterpropagating waves has orthogonal polarizations. In our models the cooling temperature decreases as the level degeneracy increases.

Computations are carried out for the ${}_{}{}^1{}_{}{}^{}$S(6${\mathit{s}}^2$)${\mathrm{-}}^1$P(6s,6p) coherent laser excitation of ${}_{}{}^{137}{}_{}{}^{}\mathrm{Ba}$ and ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}$ in a magnetic field. Results are presented for both the steady-state and time-dependent excited-state populations of the Zeeman-split magnetic sublevels. The quantum-statistical Liouville-equation approach (for the reduced density matrix) is compared to the rate-equations approach. Significant differences are found between these, due to the interference between strongly overlapping lines (especially for ${}_{}{}^{137}{}_{}{}^{}\mathrm{Ba}$). The time-evolution profiles indicate that the ${}_{}{}^{137}{}_{}{}^{}\mathrm{Ba}$ transient time is much longer than that of ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}$.

A comprehensive approach to semiclassical quantization of the quadratic Zeeman effect in the hydrogen atom (QZE) is presented which utilizes the connection between the Kepler system and the four-dimensional harmonic oscillator. Past attempts to quantize the QZE have encountered problems associated with singularities arising because of a classical separatrix. Here, a uniform semiclassical quantization scheme that passes smoothly through the separatrix is developed using classical perturbation theory. This method accounts for the topologically distinct kinds of dynamics that arise in the QZE, and provides good estimates of tunneling splittings. Extension to the quantization of arbitrarily-high-order classical perturbation expansions is straightforward.

We have numerically solved a simplified set of Maxwell-Bloch equations for a two-field, three-level model. Excitation from the ground state to the upper state is a two-photon process with a nonresonant intermediate state. Amplified spontaneous emission can occur from the upper excited state of the model system to the intermediate state. The equations can contain terms corresponding to the dynamic Stark effect resulting from the amplified spontaneous-emission field. Inclusion of these terms significantly reduces the excitation probability when the irradiance of the exciting field is above the threshold for occurrence of amplified spontaneous emission from the upper excited state. These theoretical results qualitatively explain a recent experimental observation of the decreased excitation probability for such a process in gas-phase xenon.

Two models for the measurement of position and momentum of systems with one degree of freedom are developed: (i) a two-detector model and (ii) a four-detector model. The two-detector model describes measurements with statistics given by s-order diagonal quasiprobabilities ρ’(α,s) with an upper bound ${\mathit{s}}_0$≤-1 for s which is system-state dependent. In order to have s-order statistics, both detectors must be prepared in single-mode squeezed vacuum states which are equally squeezed by a factor depending on the value of s. On the contrary, the four-detector model, with statistics given by s-order positive nondiagonal quasiprobabilities ${\mathrm{\rho }}_{\mathit{t}}$(α,β,s), replaces the restriction in s by a restriction ${\mathit{t}}_0$≤-1 for t (for each order s there is a family of nondiagonal quasiprobabilities parametrized by the parameter t). In order to have s-order statistics, the four detectors must be prepared in multimode squeezed vacuum states, with the squeeze parameters depending on s and t.

When Coulomb scattering takes place near mirrors, additional scattering amplitudes occur due to the reflection of virtual photons. Under certain conditions these amplitudes can interfere, in a purely quantum-mechanical fashion, giving rise to possibly observable fringes in the differential-scattering cross section. The effect is calculated here for a Coulomb potential near a single mirror and also between a pair of parallel mirrors. The experimental feasibility is then briefly discussed.

Classically, two coincident light pulses propagating through two dispersive media will become broadened and their degree of coincidence will be reduced. When entangled photon pairs from parametric down-conversion are considered instead, it is found that the dispersion experienced by one photon can exactly cancel the dispersion experienced by the other in such a way that their coincidence is maintained. The dispersion cancellation is independent of the separation between the two photons and provides a further example of the nonlocal nature of the quantum theory.

The interaction of an M-level atom with a single mode of a cavity field initially in a squeezed state is investigated in this paper. The time evolution of nonclassical characteristics of the field, such as the field squeezing, antibunching, and sub-Poisson distribution, is computed and discussed in detail. It is found that the initial coherent excitation strength has crucial influence on how such nonclassical behavior can be maintained in the propagation of squeezed light.

We present an exact nonlinear derivation of the spectrum of fluctuations in the difference of output intensities for the signal and idler beams generated by intracavity two-photon gain, when the cavity decay rates are the same for the two modes, and taking into account the atomic fluctuations. For the field inside the cavity, we show that the variance in the difference of intensities may be up to 50% below the shot-noise value. We also consider the case of different decay rates, and show that the noise in the output-intensity difference vanishes at zero frequency, for single-ported cavities, and as long as the only source of field decay is the transmission through the mirror. Within this general approach, we show that for the two-photon laser there is a strong correlation between signal and idler output beams when the relay-level detuning is larger than the power broadening. We calculate, in lowest order, the correction to the noise spectrum of the difference of intensities due to the population of the relay level.