Bohr’s classical (nonrelativistic) model of charged-particle stopping is evaluated explicitly for arbitrary values of projectile charge and speed. This removes the logarithmic cutoff from the original expression and generates a stopping formula which can be utilized also to extend the range of practical applicability of Bloch’s theory. As expected such a formulation appears to be a better starting point than the Born approximation for estimating stopping powers of heavy ions at velocities v<${\mathit{Z}}_1$${\mathit{e}}^2$/ħ. © 1996 The American Physical Society.

A generalized Thomas-Fermi-Weizsäcker theory is proposed to investigate the screening and slowing down of charged particles moving through a homogeneous jellium with arbitrary nonrelativistic velocity. This theory involves a velocity-dependent modification of the Thomas-Fermi kinetic-energy density near the projectile. Nonlinear inhomogeneous integrodifferential equations are derived for the dynamically screened potentials of protons and antiprotons. The stopping power of a noninteracting electron gas for the rotational-symmetric limit of the screened potential is approximated in a simple form. At typical metallic densities, this approximation of the antiproton stopping power finds about half of the equivalent proton stopping power near the electronic stopping power maximum. At lower velocities the results are in fair agreement with previous density functional calculations. In the large-velocity region the two stopping powers merge. Higher approximations including the breakdown of the rotational symmetry are discussed in detail. © 1996 The American Physical Society.

The energy loss of ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{+}$ ions in polycrystalline Al, Zn, and Au films has been determined by the transmission method in the energy range between 1 and 200 keV. The velocity dependence of the different projectile-target pairs has been analyzed, as well as the ratio of the energy losses of helium ions and protons in the different materials. An increase of this ratio toward very low velocities has been observed and possible explanations are explored. The results are compared with the existing theoretical models and semiempirical approximations, and observed differences are discussed. © 1996 The American Physical Society.

Energy losses and charge-state distributions for 2-MeV ${\mathrm{C}}^{3+}$ and ${\mathrm{C}}^{4+}$ ions incident under glancing angles on flat and step-rich SnTe(001) single crystal surfaces are measured by using a magnetic spectrometer with high-energy resolution. The charge-state distributions and the mean charge number 〈Q〉=3.74±0.07, measured for specular reflection from flat surfaces, are almost independent of incident charge state and angle. By means of a freezing distance model, the freezing distance ${\mathit{D}}_{\mathit{f}}$ and the effective charge number ${\mathit{Q}}_{\mathit{f}}$ within the distance ${\mathit{D}}_{\mathit{f}}$ from the surface are derived as ${\mathit{D}}_{\mathit{f}}$=1.5±0.1 Å and ${\mathit{Q}}_{\mathit{f}}$=3.22±0.06 from the observed energy losses for specular reflection. Reflection from stepped surfaces allows a direct measurement of the charge-state distribution in the surface vicinity as a function of the distance from the surface. The obtained charge-state distribution does not depend on the distance, which is in harmony with the freezing distance model. However, the mean charge number in the surface vicinity 〈${\mathit{Q}}_{\mathit{H}}$〉=3.53±0.05, calculated from the charge-state distributions, is slightly larger than the effective charge number ${\mathit{Q}}_{\mathit{f}}$ derived from the energy loss data. This difference between ${\mathit{Q}}_{\mathit{f}}$ and 〈${\mathit{Q}}_{\mathit{H}}$〉 may be attributed to autoionization processes. The general trend that the mean charge in the surface vicinity is smaller than that for specularly reflected ions can be explained in terms of velocity matching of the 2-MeV ${\mathrm{C}}^{\mathit{i}+}$ ions and the N-shell electrons of SnTe. © 1996 The American Physical Society.

The photoejection of Na and ${\mathrm{Na}}_2$ from surfaces prepared by adsorption of sodium vapor on solid films of polydimethylsiloxane (PDMS) of various molecular weights and structures is found to be dependent on light intensity and frequency. At low power levels the desorption yields of Na and ${\mathrm{Na}}_2$ are linear functions of desorbing light power and exhibit frequency thresholds for photoejection analogous to the photoelectric effect. The frequency thresholds are 9500 ${\mathrm{cm}}^{\mathrm{-}1}$ for Na and 11 500 ${\mathrm{cm}}^{\mathrm{-}1}$ for ${\mathrm{Na}}_2$, and the 2000-${\mathrm{cm}}^{\mathrm{-}1}$ difference can be accounted for with a model in which the alkali-metal species form charge-transfer complexes ${\mathrm{Na}}^{+}$${\mathrm{PDMS}}^{\mathrm{-}}$ and ${\mathrm{Na}}_2^{+}$${\mathrm{PDMS}}^{\mathrm{-}}$, with the cations stabilized by interaction with the oxygen atoms of the PDMS polymer backbone. The ejection mechanism takes place by a reverse charge transfer to form a less polar complex with enough energy to eject Na or ${\mathrm{Na}}_2$ from the surface. © 1996 The American Physical Society.

Recent experiments with trapped cooled atoms have produced evidence for Bose-Einstein condensation (BEC). Among the atoms used are ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, with attractive low-energy interaction. A potential barrier separating the condensed part from the collapse is studied and stability limits are established. The lifetime due to tunneling is estimated and is found to be very small. We further argue that BEC should have significant angular momentum L/N∼1ħ and thus both states with angular momentum ${\mathit{l}}_{\mathit{z}}$=0,1 should be ‘‘macroscopically’’ populated. Eventually, as rotation is slowed down, collapse and strong reheating should occur, in amusing resemblance to a supernova explosion. © 1996 The American Physical Society.

For the study of energy quantization in low-frequency potentials and the accompanying quantum effects we analyze a silicon double-crystal arrangement exploiting dynamical diffraction of neutrons to achieve the required extremely high energy resolution. The first crystal prepares a minimum-uncertainty beam that passes a potential region whose influence on the neutron energy is analyzed by the second crystal. With realistic parameters, changes of neutron energy below 0.5 neV can be resolved. This permits a test of quantized energy transfer in periodically time-dependent potentials of a frequency below 100 kHz. We also discuss three specific examples how to observe the quantum phenomena arising from the macroscopic wave packets thereby generated. © 1996 The American Physical Society.

A different approach to high-precision measurement of rotation, acceleration, and gravitation is presented. Our Moiré deflectometer is based on geometric propagation of an atomic (or molecular) beam through a set of three identical gratings. Accelerated movements of the gratings with respect to the atomic beam result in a change of the total transmitted intensity. The device is nondispersive, i.e., atoms with a broad energy distribution and without collimation can be used. Furthermore, rotational and linear (gravitational) acceleration can easily be distinguished and measured simultaneously. In a certain sense the Moiré deflectometer represents the classical analog to a quantum-mechanical matter-wave interferometer. Experimental results on a test system demonstrate that its sensitivity to rotation and gravitation is already in the range of commercially used inertial sensors. It can be increased straightforwardly by orders of magnitude. © 1996 The American Physical Society.

This paper examines the feasibility of constructing an experiment that detects the atomic stimulation of a photon-emission process. A beam of atoms (bosons) in an excited state is passed through an atomic trap that traps the atoms when they are in their internal ground state. When the trap contains a Bose-Einstein condensate, the cross section for absorption of the atomic beam is increased. We examine a particular model in which this atom stimulation is observable and is also characterized by the emission of photons in a narrow cone in the direction of the atomic beam. © 1996 The American Physical Society.

${\mathrm{C}}_{60}$ vapor was bombarded by ${}_{}{}^{136}{}_{}{}^{}\mathrm{Xe}_{}^{35+}{}_{}{}^{}$ and ${}_{}{}^{136}{}_{}{}^{}\mathrm{Xe}_{}^{18+}{}_{}{}^{}$ ions in the energy range 420–625 MeV to study the various ionization and fragmentation processes that occur. Since the center-of-mass energies used in this work exceeded those of previous studies by several orders of magnitude, new excitation and dissociation modes were expected and indeed found. Positive ions were extracted from the interaction region and their times of flight were measured both singly and in coincidence with other ionic fragments. A wide range of stable charge states and cluster sizes from monatomic carbon up to ${\mathrm{C}}_{60}$ was observed. Even-numbered carbon fragments dominated the heavier mass range but both even and odd carbon numbers occurred at lower masses. Evidence was found for three qualitatively different ionization and fragmentation channels suggesting different ranges of collision impact parameters: ionization of the parent ${\mathrm{C}}_{60}$ molecule, loss of even numbers of carbon atoms, and ‘‘multifragmentation’’ into many small fragments. This latter mode included the production of singly charged ${\mathrm{C}}_{\mathit{n}}^{+}$ fragments with all values of n being observed from n=1 up to at least n=19. We interpret our results in terms of a theoretical model that indicates that the total interaction cross section contains comparable contributions from (a) excitation of the giant dipole plasmon resonance, and (b) large-energy-transfer processes that lead to multiple fragmentation of the molecule. The distribution of fragment cluster masses for n≲20 is reproduced by a ‘‘percolation theory’’ description analogous to that used to describe multifragmentation of nuclei by high-energy protons. © 1996 The American Physical Society.

In the optical Stern-Gerlach effect the interaction of a two-level atom with an optical-field gradient causes a state-selective deflection that leads to a splitting of the atomic trajectory. The semiclassical approach to this problem actually predicts a splitting of the atomic beam into two paths, similar to the well-known magnetic Stern-Gerlach effect for spin 1/2. Here we study a model in which the quantum nature of the field is taken into account and we show, in particular, that for an initial coherent state of the cavity light the optical Stern-Gerlach effect manifests itself as a splitting of the atomic beam into two groups containing, however, many spots. © 1996 The American Physical Society.

We present an extensive set of measurements on one-dimensional sub-Doppler cooling and channeling in counterpropagating light beams. The experimental method consists of the measurement of the profile of an initially subrecoil collimated atomic beam, which is deflected by the interaction with the light field. The initial velocity of the atoms in the direction of the laser beams is varied in the range -1≤${\mathit{v}}_{\mathrm{\perp }}$(${\mathrm{ms}}^{\mathrm{-}1}$)≤1 by changing the angle between atomic and laser beams. For the orthogonal circular polarization (${\mathrm{\sigma }}^{+}$${\mathrm{\sigma }}^{\mathrm{-}}$) sub-Doppler cooling configuration, the force and the diffusion coefficient characterizing the cooling process have been determined as a function of the initial velocity ${\mathit{v}}_{\mathrm{\perp }}$ from the average deflection and broadening of the atomic beam profile. We observe transient effects due to the slow evolution of the distribution over the magnetic sublevels to an equilibrium. The experimental results agree very well with quantum Monte Carlo simulations and semiclassical calculations. For the orthogonal linear polarization (${\mathrm{\pi }}^{\mathit{x}}$${\mathrm{\pi }}^{\mathit{y}}$) configuration, we demonstrate the validity of the well-known Sisyphus picture for the cooling mechanism by comparing the experimental data to the results of a simple semiclassical Monte Carlo model incorporating only the dipole force and optical pumping. In weak standing waves of either circular or linear polarization, we demonstrate the characteristic features of channeling. © 1996 The American Physical Society.

The radiative renormalization technique is used to analyze two-level systems with permanent dipole moments under the influence of a single-frequency applied field. The advantage of radiative renormalization over the usual perturbative or harmonic balance techniques lies in the computational ease with which the density matrix operators can be determined to any order in applied field. We characterize the absorption and dispersion of a typical two-level system within this framework and find that although the absorption saturates as expected with increasing incident field strength, additional oscillatory behavior is evident at extremely high field strengths. The structure and period of these oscillations is dependent upon the magnitude of the permanent dipole moment. Our general formalism can easily be extended to the study of other nonlinear optical phenomena. © 1996 The American Physical Society.

The energy spectrum of a neutral atom bound in the magnetic field created by a straight line direct current is given by the Rydberg formula for particles with spin less than 3/2. An adiabatic representation leads to a natural understanding of this spectrum and provides a good approximation to the bound state energy levels. A more accurate finite element method is applied to directly solve the time-independent Schrödinger equation for neutral particles with arbitrary spin. A combination of the finite element method with multichannel quantum defect theory provides a more efficient method to calculate the bound state energies. In addition, new spectral features arise for particles with spin greater than 1. © 1996 The American Physical Society.

The time-dependent Schrödinger equation for ${\mathrm{H}}_2$${\mathrm{}}^{+}$ in a 600-nm, intense (I⩾${10}^{14}$ W/${\mathrm{cm}}^2$) laser field is solved numerically for a model which uses the exact three-body Hamiltonian with one-dimensional nuclear motion restricted to the direction of the laser electric field and three-dimensional electronic motion. High ionization rates of ${\mathrm{H}}_2$${\mathrm{}}^{+}$ are found, exceeding those of neutral atomic hydrogen. This confirms, by the rigorous, full dynamical calculation, the recently discovered charge-resonance-enhanced ionization (CREI)—all previous demonstrations of CREI were based on the ‘‘frozen nuclei’’ model. The numerical kinetic-energy spectra of dissociating fragments are compared with recent experimental results. They can be interpreted by a simple bond softening mechanism (or laser-induced avoided crossing in a dressed-state representation), in which the binding forces are completely suppressed by the strong electric field and thus the dissociating fragments move as free particles with a kinetic energy close to their initial vibrational energy until they reach a critical distance R=${\mathit{R}}_{\mathit{c}}$≅8 bohr, where they are rapidly ionized, due to CREI. The harmonic generation spectra calculated from our non-Born-Oppenheimer simulations show that the high harmonics are also generated when the nuclei cross this critical distance R=${\mathit{R}}_{\mathit{c}}$. © 1996 The American Physical Society.

We present a simple model calculation to interpret the recent data of Kohlweyer et al. [Opt. Commun. 117, 431 (1995)] and von der Linde et al. [Phys. Rev. A 52, R25 (1995)] on the generation of higher harmonics at metal surfaces by powerful femtosecond laser pulses. The model presents an adaptation of our earlier work [Phys. Rev. A 49, 3106 (1994)] to the present situation. © 1996 The American Physical Society.

A polarization of sodium atoms in a simple trap based on the light-induced drift effect is reported. A sapphire capillary with one side closed and heated up to high temperature was used as the trap. The capacity of the trap is about 5×${10}^{11}$ atoms. The achieved polarization of trapped atoms in the gas phase is about 90%. The full polarization of atoms in the trap is estimated at 25% at the temperature of 1400 °C. The adsorption energy of sodium atoms on a sapphire surface is determined to be 2.5 eV. © 1996 The American Physical Society.

Charge resonance-enhanced ionization is examined for combinations of intense, linearly polarized laser fields, and their second harmonic (1ω-2ω) for both a diatomic molecular ion (${\mathrm{H}}_2$${\mathrm{}}^{+}$) and an asymmetric linear triatomic molecular ion (${\mathrm{H}}_3$${\mathrm{}}^{2+}$). Ionization is found to be strongly dependent on the relative phase between the two colors in both cases. In particular for ${\mathrm{H}}_2$${\mathrm{}}^{+}$ one can achieve nearly complete ionization of electrons at one of the nuclei only. For the asymmetric linear triatomic molecular ion (${\mathrm{H}}_3$${\mathrm{}}^{2+}$) enhanced ionization is shown also to occur at large critical distances. In the presence of two color fields, the ionization rate of the asymmetric ${\mathrm{H}}_3$${\mathrm{}}^{2+}$ can be controlled again by tuning the relative phase between the driving fields. The phase control of the enhanced ionization can be rationalized in terms of field-induced over-the-barrier ionization and laser-induced electron localization or equivalently electron tunneling suppression. © 1996 The American Physical Society.

We present mixed gauge R-matrix Floquet calculations of multiphoton ionization of Li within a single active electron local model potential. The laser frequency ranges from 15 000 to 15 800 ${\mathrm{cm}}^{\mathrm{-}1}$, and at least three photons are needed to ionize the electron in the 2s ground state. We found that the measured ionization rate as a function of photon frequency results from ionization processes in different intensity regions of the laser. The experimental angular distribution of the ejected electrons can be explained using the high intensity portion of the laser for both the lowest ionization channel and the first above-threshold ionization channel. The calculated and experimental angular distributions agree well with each other and demonstrate the success of the R-matrix approach to the multiphoton ionization processes. © 1996 The American Physical Society.

We consider a mixture of resonant two-level molecules under velocity-selective excitation and a buffer gas. The corresponding kinetic equations are augmented by a strong-collision model with free parameters. We obtain the equilibrium velocity distribution functions of the resonant and buffer components. We then use the Boltzmann kinetic equations to derive the H-theorem analog for this mixture (valid for arbitrary values of the collision rates ν and the spontaneous decay rate γ) and discuss the implications for the stability of the stationary solutions. © 1996 The American Physical Society.