Processes with three or more charged particles in the final state exhibit a particular threshold behavior, as inferred by the famous Wannier law for a ($2e+$ion) system. We formulate a general solution which determines the threshold behavior of the cross section for multiple fragmentation. Applications to several systems of particular importance with three, four, and five leptons (electrons and positrons) in the field of a charged core, and two pairs of identical particles with opposite charges, are presented. Threshold exponents for these systems are predicted, while some previously suggested threshold laws are revised.

Radial matrix elements of multipole type involving the product of two Coulomb functions appear in many problems of theoretical atomic physics. Here we investigate some of their properties, with a generalization which includes the possibility of having the two functions related to two different charges. These would typically appear in calculations of ionization cross sections, going beyond the well studied case where the two charges are equal (elastic scattering or discrete excitation). We provide analytical formulas for the evaluation of matrix elements and recursion relations connecting them, both in the exact quantal formulation and in the WKB approximation. These theoretical results are illustrated by considering, within the Coulomb projected Born model, the electron impact ionization of ${\mathrm{Mg}}^{+}$ and ${\mathrm{Ar}}^{7+}$ with a relatively moderate incident energy. The radial matrix elements are evaluated with our exact quantal formulas and in the WKB approximation. The agreement is impressive, and is reflected in the values of triple, double, and single differential cross sections. Finally, a further study shows how the semiclassical approximation yields a very good estimate of single cross sections.

One of the few exactly solvable time-dependent quantum-mechanics problems was first analyzed by Demkov and Osherov 30 years ago $($Zh. Éksp. Teor. Fiz. 53, 1589 (1967) [Sov. Phys. JETP 26, 916 (1968)]$)$. This model problem describes the interaction of a set of approximate stationary states with an additional state whose energy, in zeroth approximation, is a linear function of time. The Demkov-Osherov model is reexamined here using conventional Fourier transform methods. Emphasis on forward propagation in time eliminates the need for a Laplace transform of the wave function, as well as the resultant choice of contours for the evaluation of transition amplitudes. The evolution operator for the model Hamiltonian is expressed in terms of a single, frequency-dependent Sturmian. Such Sturmian functions are of considerable current interest in the analysis of nonadiabatic phenomena.

The dielectric description of the dynamical potential induced by swift protons in solids and the related stopping power is analyzed, using a combination of Mermin-type dielectric functions, which are fitted to available experimental data, to describe the optical properties of various materials. We apply this method to represent the energy loss functions of aluminum, silicon, amorphous carbon, and copper on a wide range of energy and momentum transfers. Using these functions we calculate the shape of the wake potential induced by swift protons; significant differences are obtained in the cases of carbon and copper, with respect to the results derived from simplified dielectric models. The energy loss functions are also applied to calculate the proton stopping power of each element, which are compared with experimental values.

We present a many-electron theoretical study of electron capture and excitation in collisions of ${\mathrm{H}}^{+}$ with ${\mathrm{Na}}_{20}$ clusters for impact energies 40–500 eV. The collision is treated semiclassically using the independent-electron model, and the cluster is described in the framework of the Kohn-Sham formalism with a local-density approximation which includes exchange, correlation, and a self-interaction correction. We have found that capture cross sections are $\sim \left(2\mathrm{}-5\right)\times {10}^{-14}\hspace{0.5em}{\mathrm{cm}}^2$ and dominate in the above energy range. In contrast with ion-atom collisions, excitation cross sections are comparable to the former, and multiple processes such as capture excitation cannot be neglected at low velocities. From the analysis of the vacancies originated in the collision, we have evaluated the energy deposited in the cluster, which is an essential parameter in the study of cluster fragmentation.

The effects of the rotational motion on the chaotic behavior of triatomic Lennard-Jones clusters are studied. A set of initial momentum distributions with tunable parameters is chosen to correspond to various rigid-body rotations around symmetry axes of the cluster. By smoothly varying the direction of the initial kicks given to the cluster, periodic transitions between regular and chaotic regimes are obtained. A study of initial conditions leading up to such transitions shows that the major factor that determines the extent of the chaotic behavior is the initial partitioning of the kinetic energy between the rotational and vibrational motion. From the analysis of the time evolution of various properties it is concluded that the basic role of this initial partitioning is to control the energy transfer between the kinetic and the potential energy.

The recent experimental characterization of the ${\mathrm{Al}}_{77}$ cluster by Ecker et al. [Nature 387, 379 (1997)] detailed a fascinating onionlike structure whose inner core we report on here. The clusters ${\mathrm{Al}}_{12}$ and ${\mathrm{Al}\mathrm{@}\mathrm{Al}}_{12}$ have been studied in detail. Potential-energy surfaces have been examined using density-functional methodology and basis sets with effective core potentials. The stationary points located with this methodology were then further analyzed using full-electron basis sets of triple-zeta plus double polarization size. Two stationary points have been located on the ${\mathrm{Al}}_{12}$ surface, a staggered minimum of $D_{5d}$ symmetry and a saddle point of Hessian order three in an eclipsed conformation with $D_{5h}$ symmetry. The cationic, neutral, and anionic surfaces of ${\mathrm{Al}\mathrm{@}\mathrm{Al}}_{12}$ were explored. Structures similar to the ${\mathrm{Al}}_{12}$ stationary points were found for the anionic ${\mathrm{Al}\mathrm{@}\mathrm{Al}}_{12}^{-}$ cluster though in this case the staggered minimum had icosahedral symmetry and the eclipsed stationary point was a true transition state. No atom-in-a-cage–type structure could be located for the cationic ${\mathrm{Al}}_{13}^{+}$ cluster, but one minimum was found for the neutral. That $C_1$ minimum is in astonishing agreement with the core of Ecker’s ${\mathrm{Al}}_{77}$ cluster having center-to-surface bond lengths that range from 2.635 to 2.850 Å and average 2.744 Å.

The temporal behavior of the 19th harmonic of a Ti:sapphire laser generated in argon was investigated by a cross-correlation technique at intensities close to saturation. Pulses about half as long as predicted on the basis of the scaling law of the atomic dipole strength on intensity were found. Analysis shows that this is a consequence of both the intensity-dependent dipole phase and the depletion of the medium by ionization.

Photoelectron imaging spectroscopy relies on the properties of the ballistic trajectories of photoelectrons moving in a homogeneous electric field. In this paper we show that the simple picture of parabolic trajectories is no longer valid when slow photoelectrons produced in the vicinity of the zero-field ionization threshold, and especially just above the saddle-point energy, are concerned. The discussion presented here is based on the exact classical simulation of the trajectories of photoelectrons in the combined Coulomb and Stark field. It is shown that under rather common experimental conditions the influence of the Coulomb interaction on the projection pattern of photoelectrons at large distance is dramatic. In standard photoelectron imaging spectroscopy a single feature corresponds to a given ionization channel, while we show here that the observed features are much more complex for slow photoelectrons. We then discuss the relevance of our classical simulations as compared with wave-packet calculations. Finally, the application of this effect to the precise characterization of near-zero-energy resonance in atoms in external fields and to the dynamics of zero-kinetic-energy electrons is presented.

We present a detailed theoretical formulation of the problem of an electron moving in a static electric field, a laser field, and an atomic potential. Our formulation treats the electron-atom interaction in the zero-range potential approximation and employs both the quasienergy approach and an analytic expression for the Green’s function describing electron propagation in a combination of static and laser electric fields. Our formulation is applied to one- and two-photon detachment of ${\mathrm{H}}^{-}$ in a strong static electric field and takes into account all final-state interactions of the detached electron with the static and laser fields and with the atomic core. Our results show that rescattering effects are small in the case of one-photon detachment, where our results are close to those obtained previously by Gao and Starace [Phys. Rev. A 42, 5580 (1990)], who ignored rescattering effects but who found a strong-field treatment of the laser field to be important, even in the limit of weak laser fields, owing to interference terms involving both the laser and static electric fields. Our results for two-photon detachment of ${\mathrm{H}}^{-}$, on the other hand, show that rescattering effects are very significant. In the presence of a strong static electric field, moreover, the two-photon detachment cross section is found to be very sensitive to the magnitude of the static field.

Coulomb explosion of molecules induced by an intense femtosecond probe laser pulse provides an approach to measure structure and dynamics of internuclear wave packets on a natural spatial (Å) and temporal (fs) scale for molecules. The technique is illustrated by applying it to study photodissociation of ${\mathrm{I}}_2$ initiated by a femtosecond pump pulse. We report a resolution of ∼2–4 Å in the internuclear range ∼7–14 Å using an 80-fs probe pulse. We discuss the ultimate spatial and temporal resolution of the technique, as well as the possibilities of observing dynamics of dissociating polyatomic molecules. Intense femtosecond laser pulses not only provide a way of probing molecular dynamics but they are also an efficient means to initiate dynamics in, e.g., molecular ionic states.

A comprehensive study of the hydrogen atom in the presence of parallel electric and magnetic fields is presented from the standpoint of classical mechanics for a nonzero magnetic quantum number $m.\mathrm{}$ The transition from pure Zeeman effect to Stark effect is explored intensively by means of Poincaré surfaces of section for a pair of $m$ values and for different values of the field strengths. It is found that the transition from pure Zeeman effect to Stark effect passes through a saddle-node bifurcation.

Quantum beats provide a useful tool in spectroscopy for the evaluation of fixed energy level differences. However, in wave-packet dynamics the motion of wave packets about molecular energy surfaces provides time-dependent energy differences. Thus a superposition of wave packets on two excited energy states can yield quantum beats with a time-dependent frequency that depends on the molecular dynamics. We explore this problem with examples and simple models of wave-packet quantum beats. The effects of separating wave packets, and wave packet dispersion, are of especial interest. Calculations are performed using a numerical integration of the time-dependent Schrödinger equation with three energy states and time-dependent couplings. The effects of spontaneous emission are determined by using a fully quantum mechanical Monte Carlo wave-function method.

We have investigated the radial Rydberg wave-packet dynamics in the two-valence-electron atom calcium by femtosecond pump-probe spectroscopy. The classical periodic motion of the Kepler electron as well as the quantum mechanical revival structure were observed when employing the phase sensitive detection technique. Preliminary results are reported on Rydberg wave-packet autoionization under the influence of an isolated excitation of the remaining outer core electron.

Multiphoton ionization rates from the dressed $1s{\sigma }_g^{+}$ and$2p{\sigma }_u^{+}$ states of${\mathrm{H}}_2^{+}$ are calculated within the Floquet approach. For linearly polarized light, and parallel transitions, we determine ionization rates for a range of internuclear separations. A rich structure of multiphoton resonances has been found. These features are not reproduced by quasistatic field models. The values of ionization rates as well as their bond-length dependence are studied and compared with wave-packet calculations. Differences between results and reasons for discrepancies are discussed. Finally, we present plots of dressed-state wave-function densities in order to illustrate laser-induced orbital hybridization.

Nondispersive electronic Rydberg wave packets may be created in atoms illuminated by a microwave field of circular polarization. We discuss the spontaneous emission from such states, and show that the elastic incoherent component (occurring at the frequency of the driving field) dominates the spectrum in the semiclassical limit, contrary to earlier predictions. We calculate the frequencies of single-photon emissions and the associated rates in the “harmonic approximation,” i.e., when the wave packet has approximately a Gaussian shape. The results agree well with exact quantum-mechanical calculations, which validates the analytical approach.

A detailed quantum-mechanical description of an electron in a Penning trap is developed in which nonlinear relativistic effects as well as stochastic effects arising from radiative damping and the continuous measurement of the electronic motion are taken into account. A master equation is derived that describes the influence of these environmental effects on the bistable dynamics of the electron. Manifestations of measurement-induced fluctuations on the bistable dynamics of individual continuous measurement processes are investigated with the help of the quantum state diffusion model.

The classical analysis of H-atom ionization by elliptically polarized microwave fields is performed for a realistic three-dimensional model of an atom. As a limiting situation the circular polarization case is discussed in detail too. The sensitivity of initial electronic orbits of different orientation to microwave perturbation is studied analytically using the Chirikov overlap criterion. Generally the orbits lying in the polarization plane are most vulnerable to microwave perturbation, although important exceptions from this rule of thumb are found. In particular a class of orbits is found that is unusually stable against the perturbation. This behavior is linked to vanishing widths of the corresponding resonance islands within the first-order perturbation theory. The results of a recent experiment [Bellerman et al., Phys. Rev. Lett. 76, 892 (1996)] are qualitatively reproduced by the theory.

We interpret measurements of photoassociative spectroscopy in a gas of lithium atoms at ultralow temperatures in which photons are absorbed into high vibrational levels of excited electronic singlet and triplet states of ${\mathrm{Li}}_2.$ The excited vibrational levels decay by spontaneous emission into the vibrational continuum and the discrete vibrational levels of the ground singlet and lowest triplet electronic states. Spontaneous emission into discrete levels produces molecules that are no longer trapped, and decay into the vibrational continuum can produce atoms with sufficient kinetic energy to escape the trap. We present values of the efficiencies of trap loss by radiative excitation as a function of the trap depth for individual excited vibrational levels of the singlet and triplet states of the ${}^6{\mathrm{Li}}_2$ and ${}^7{\mathrm{Li}}_2$ molecules.

We propose and analyze theoretically a scheme for atomic guiding and cooling in a dark hollow laser beam generated from the collimated output beam of a ${\mathrm{LP}}_{01}$ mode in a micrometer-sized hollow optical fiber. In the scheme, cold atoms from a magneto-optical trap are loaded into the blue-detuned dark hollow beam, move down in the dark hollow beam, and experience transverse Sisyphus cooling induced by the dark hollow beam and a weak repumping beam. In the longitudinal direction, the guided atoms experience heating from the gravity field and cooling from the upward-propagating dark hollow beam and repumping beam. We estimate the transverse two-dimensional equilibrium temperature, the final longitudinal mean velocity, and the total loss of the guided atoms. Our calculations show that a transverse equilibrium temperature of $\sim 1.2\mu \mathrm{K},$ a final longitudinal mean velocity of 0–4.41 m/s, and a guiding efficiency of 65–95 % may be obtained.