Absolute total cross sections for electron-impact single ionization of ${\mathrm{Kr}}^{4+}$, ${\mathrm{Kr}}^{5+}$, and ${\mathrm{Kr}}^{7+}$ ions have been measured using a crossed-beams technique from below threshold to 500, 400, and 500 eV, respectively, with absolute uncertainties of 12% or less. The measured cross sections are in good agreement with distorted-wave calculations and show significant contributions from excitation autoionization. Nonzero cross sections below threshold for the ${\mathrm{Kr}}^{4+}$ and ${\mathrm{Kr}}^{5+}$ ions suggest the presence of metastable ions in those two species that were extracted from an electron-cyclotron-resonance ion source. Such evidence of metastable ions was not found in the case of the ${\mathrm{Kr}}^{7+}$ ion measurment.

We report on calculations for the electron-impact ionization of the krypton ions ${\mathrm{Kr}}^{4+}$–${\mathrm{Kr}}^{7+}$. Results are first obtained from a configuration-average distorted-wave calculation. Multiplet-resolution and channel-coupling effects are investigated using an LS-coupled nonrelativistic R-matrix method for the excitation autoionization of ${\mathrm{Kr}}^{6+}$ and ${\mathrm{Kr}}^{7+}$, and the inclusion of resonance effects is discussed. Term dependence and relaxation effects, which are found to be significant, are incorporated through the use of pseudo-orbitals. These R-matrix results are found to be in good agreement with LS-coupled distorted-wave calculations. Final results for the excitation-autoionization contributions for ${\mathrm{Kr}}^{6+}$ and ${\mathrm{Kr}}^{7+}$ are obtained in a semirelativistic intermediate-coupled distorted-wave approximation, including both term dependence and relaxation effects. Comparison to experiment is made where available.

We present total yields for emission of slow (${\mathit{E}}_{\mathit{e}}$≤50 eV) electrons due to the impact of slow (${\mathit{v}}_{\mathit{p}}$≤5×${10}^5$ m/s) highly charged ions [${\mathrm{Ar}}^{\mathit{q}+}$ (q≤18), ${\mathrm{Xe}}^{\mathit{q}+}$ (q≤51), and ${\mathrm{Th}}^{\mathit{q}+}$ (q≤80)] on clean polycrystalline gold. The highly charged ions were produced in the Lawrence Livermore National Laboratory electron-beam ion trap; electron yields have been derived from the respective measured electron emission statistics. The experimental data support a currently accepted scenario for multicharged ion-induced electron emission, which is largely based on a classical over-barrier model. In particular, we are able to distinguish different processes contributing to the total above-surface electron emission. In addition, an ultimate low-impact-energy limit due to projectile self-acceleration toward the metal surface, as a result of the projectile image charge, has been demonstrated and evaluated.

Measurements of ejected electron energy distributions are used in conjunction with electron spin labeling techniques to probe the mechanisms by which He(2 ${}_{}{}^3{}_{}{}^{}$S), He(2 ${}_{}{}^1{}_{}{}^{}$S), and He(2 ${}_{}{}^3{}_{}{}^{}$P) atoms are deexcited at Ar and Xe films adsorbed on a cooled Cu(100) substrate. The data for both surfaces contain features similar to those observed in gas-phase Penning ionization, indicating that ejection results, in part, from Auger deexcitation, i.e., surface Penning ionization. For Xe, however, additional features are observed that can be attributed to resonance ionization of an incident excited atom followed by neutralization of the resulting ${\mathrm{He}}^{+}$ ion through an interaction that involves neighboring Xe atoms in the film. Indeed, the Xe data provide an exceptional example of a surface at which Auger deexcitation and resonance ionization occur in parallel with one another, with a branching ratio that changes significantly as the internal energy of the incident atoms increases. The ejected electron yield from both Ar and Xe films is substantially higher than for clean Cu(100), indicating that such films might form the basis of an efficient thermal-energy helium metastable-atom detector.

Recent work on mean energy loss and straggling of ions in the presence of charge exchange has been extended to higher moments. The transient behavior of charge-exchange straggling has been determined as well as the skewness of the energy-loss profile. Formulas have been found for the two- and three-state cases where terms that have been well known in principle could also be written in a way that illustrates their respective origin. In addition to the frequently analyzed case of negligible energy loss in charge-changing events, we also mention explicitly the opposite situation where all energy loss is associated with charge exchange. The role of transients and skewness is very different in the two extremes. As in a previous paper by one of us, the notation has been kept general such as to allow for both collisional and spontaneous events, and no distinction needs to be made between charge exchange and change of excitation state. Finally we compare our calculations to recently obtained experimental results.

We present a theory of Auger neutralization for slow and compact ions scattered off metal surfaces. When an ion is near the surface, we propose a local model in which free-electron-gas quantities are scaled through the local electronic density at the ion position n(z). It is shown that the results of this local model can be joined to the results of a totally surface calculation, valid when the ion is far from the surface. We have calculated Auger neutralization rates and electron emission spectra for ${\mathrm{He}}^{+}$ ions interacting with a jellium surface of ${\mathit{r}}_{\mathit{s}}$=2.67${\mathit{a}}_0$. The effect of the ion potential on the metal-electron wave functions can be incorporated into the model by means of the effective density setup by the tunneling electrons. Its effect is found to be crucial when comparing our results with available experimental data for ${\mathrm{He}}^{+}$ scattered off Cu surfaces. This simple parameter-free theory yields Auger rates and electron emission spectra comparable with calibrated experiments.

We present numerical calculations of the evolution of an atomic wave packet in the optical potential created by a laser standing wave. These calculations do not rely on the Raman-Nath approximation, and fully account for transverse atomic motion within the standing wave. Our results show that atomic dynamics is important even for very brief interactions, and that the wave packet can become well localized during and shortly after the interaction. We propose several atomic beam splitters and deflectors which make use of this effect. This effect may also have repercussions for recent proposals to measure the position of an atom in a standing wave by monitoring the phase shift of the optical field; these schemes require that the field does not act back on the atom to alter its position wave function. A standing wave can also localize the wave packet in momentum space, which we show can be used to cool an atomic beam in one transverse dimension.

We analyze the condition of observation of Doppler-tuned multiphotonic (‘‘doppleron’’) resonances in an atom reflection by a standing evanescent wave. A theoretical model based on Ehrenfest’s theorem for external atomic motion is proposed. The light forces exerted by the stationary evanescent wave are calculated either with a perturbation approach, or with a continuous-fraction method. The appearance of the multiphotonic lines in the specularly reflected atomic beam is clearly shown. These predictions are in good agreement with previous and present experimental results, which are discussed.

The analytic solutions of equations, which describe the time behavior of density-matrix elements of a two-level medium driven by weak-probe tunable and strong fields, namely, scrE(t)=E(t)cos[ωt+φ(t)]+ɛ cos[(ω+δ)t], the amplitude E(t) and phase φ(t) of which are any arbitrary functions of time, are obtained. We obtain explicit expressions of the medium polarizability in two cases of the strong-field parameters modulation: first, E(t)=${\mathit{E}}_0$cos(ξ cosΩt), where ${\mathit{E}}_0$, Ω, and ξ are constants, and φ=0; and second, both the amplitude E(t) and the phase φ(t) are periodic functions of time, and E(t)=Cφ̇, where C is an arbitrary constant. These cases of modulation are generalizations of cases that were considered earlier. The first case of modulation causes a shift of the well-known Rabi resonances in the weak-probe absorption and dispersion spectra by the factor ${\mathit{J}}_0$(ξ) (${\mathit{J}}_0$ is the zero-order Bessel function of the first kind) in comparison with a nonmodulated exciting field. In the second case of the modulation, the Rabi resonances are present but the effect of such a modulation results in an attenuation of the amplitude-modulation effect. The values of the parameters ${\mathit{E}}_0$, Ω, C, and ξ and the frequency ranges in which the weak-probe gain, caused by resonant Rayleigh scattering and by three-photon scattering, takes place are determined for these two cases of the modulation.

The paper reports on experimental investigations of absorption and dispersion profiles of a strongly driven hyperfine transition at various pump field intensities and detunings when probed by a weak field. The transition lies at 5.4 MHz and corresponds to the ${\mathit{I}}_{\mathit{z}}$=0⇆-1 nuclear magnetic transition within the electron spin singlet of the ${}_{}{}^3{}_{}{}^{}$A ground state of the nitrogen-vacancy (NV) center in diamond. The inhomogeneous linewidth of the transition is 8 kHz whereas the homogeneous linewidth is 2.7 kHz, which is a factor of 3 larger than that limited by the population relaxations. The absorption and dispersion are obtained using Raman heterodyne detection, a coherent optically detected magnetic-resonance technique. Measurements are performed in a situation where there is an anticrossing of the ground-state electron-spin levels, as this leads to an enhancement of the hyperfine transition strengths and the optical sensitivity. Weak probe fields with Rabi frequency <0.6 kHz could then be used. The absorption and dispersion profiles were recorded for on-resonance pump fields of various strengths with Rabi frequencies of 0, 2.1, 3.7, 6.6, 11.8, and 21 kHz. In addition, the responses were recorded for an off-resonance field with a Rabi frequency of 55 kHz and detunings between -40 and +40 kHz. The corresponding response of an idealized driven two-level system has been calculated using an established density-matrix equation of motion formalism.

When normalized to the profiles with no driving field, the calculated and experimental profiles are in excellent agreement. The nitrogen-vacancy system provides a very clear experimental illustration of a driven two-level system and some aspects are highlighted. For on-resonance pumping, the dispersion profile consists of a positive and a negative absorptionlike peak separated by twice the pump Rabi frequency. The peaks correspond to a significant signal strength (index of refraction) whereas at the frequency of the peaks in dispersion, the absorption is zero. The corresponding absorption profile consists of two dispersionlike features separated by twice the pump Rabi frequency, and between the two features there is negative absorption or gain. For off-resonance pumping, there are again two features. For example, in absorption response, there is an absorption peak and an amplification peak symmetrically displaced from the pump frequency by the generalized Rabi frequency. In this off-resonance pumping situation, it is pointed out that gain occurs where there is inversion in the dressed state whereas gain for the on-resonance pumping situation is achieved without population inversion in either the bare or dressed state.

We have studied the (1+1’)-photon resonance-enhanced multiphoton ionization (REMPI) of ${\mathrm{H}}_2$ via ${\mathit{B}}^1$${\mathrm{\Sigma }}_{\mathit{u}}$ (ν=4, j=1,2) levels considering (i) the effect of interference of different ionizing channels via nearby vibrational levels of ${\mathit{B}}^1$${\mathrm{\Sigma }}_{\mathit{u}}$ (ν=0 to 3 and 5 to 14) and ${\mathit{C}}^1$${\mathrm{\Pi }}_{\mathit{u}}$ (ν=0 to 2) states, and (ii) the effect of coupling between these vibrational levels via the continuum. We have shown that for this REMPI process, these two effects can lead to a non-Franck-Condon vibrational distribution of ${\mathrm{H}}_2^{+}$ ions in the ${\nu }^{+}$=0 and ${\nu }^{+}$=1 levels of the ground X ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{}{}_{}{}^{}$ state. The nature of the deviation from the Franck-Condon vibrational distribution has been found to depend on the relative strength of different ionizing transitions and hence on the relative magnitude of dipole transition moments as well as the intensity of the laser connecting the intermediate levels to the continuum. As a result, the vibrational branching for transition via different rotational levels (j=1 and j=2) of the B ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{}{}_{}{}^{}$ (ν=4) state considering R(0) [i.e., X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{}{}_{}{}^{}$(ν=0, j=0) to B ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{}{}_{}{}^{}$ (ν=4, j=1)] and R(1) [i.e., X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{}{}_{}{}^{}$ (ν=0, j=1) to B ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{}{}_{}{}^{}$ (ν=4, j=2)] transitions, respectively, for the lower step excitation, has been found to exhibit a different nature of non-Franck-Condon distribution in the range of laser intensity 5×${10}^9$ to 9×${10}^{10}$ W/${\mathrm{cm}}^2$.

However, for the (1+1’)-photon REMPI via the ν=8, j=2 level of the ${\mathit{B}}^1$${\mathrm{\Sigma }}_{\mathit{u}}$ state considering R(1) [i.e., X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{}{}_{}{}^{}$ (ν=0, j=1) to ${\mathit{B}}^1$${\mathrm{\Sigma }}_{\mathit{u}}$ (ν=8, j=2)] for lower step excitation, this effect of interference has been found to be insignificant on the vibrational branching in ${\nu }^{+}$=1 and ${\nu }^{+}$=2 levels of the ${\mathrm{H}}_2^{+}$ ion in the ground state.

Bloch and Nordsieck [Phys. Rev. 52, 54 (1937)] outlined a successive-approximation procedure for the calculation of finite infrared radiative corrections to the cross section for potential scattering of a Dirac electron, based on the use of coherent states for the description of the asymptotic motion of the electron in the presence of the radiation field and on the introduction of positive- and negative-energy projection operators. An elaboration of that procedure is described here in which the projection operators are used to develop an effective-Hamiltonian formulation of the scattering problem. This allows for a clear separation of the nearly singular contributions to the cross section from the remainder to which ordinary perturbation theory is applicable. With the aid of the optical theorem and the low-frequency approximation for single-photon spontaneous bremsstrahlung, a first-order correction to the Bloch-Nordsieck cross-section sum rule is obtained. The result is expressed in terms of measurable field-free scattering parameters. With the initial photon state chosen to be highly occupied, the formalism is directly applicable to the problem of scattering in an intense, slowly varying external field. Nearly singular terms arising from virtual Compton scattering in initial and final states, which appear when the field is not of the plane-wave type, are shown to cancel in the final form of the cross-section sum rule. This low-frequency approximation is then easily applied to problems involving realistically modeled fields in the form of wave packets, for example.

We present an analytical and numerical analysis of collisionless motion of neutral particles in magnetostatic traps. We treat the example of an idealized Ioffe quadrupole trap, emphasizing that the essential features of coupling between the degrees of freedom are of general relevance for static traps. In common situations the coupling between axial and radial motion predominantly occurs in a regular way. The coupling is weak, in particular, when the frequency of axial oscillations ${\mathrm{\Omega }}_{\mathit{z}}$ is much smaller than the radial frequency ${\mathrm{\Omega }}_{\mathrm{\rho }}$ and the particle energy is much lower than the Zeeman energy in the center of the trap. Then, under an adiabatic change of the potential parameters, the quantity ${\mathit{scrE}}_{\mathit{z}}$/${\mathrm{\Omega }}_{\mathit{z}}$, where ${\mathit{scrE}}_{\mathit{z}}$ is a characteristic axial energy, is an approximate adiabatic invariant. If ${\mathrm{\Omega }}_{\mathit{z}}$ is decreasing and ${\mathrm{\Omega }}_{\mathit{p}}$ is constant, then the characteristic radial energy ${\mathit{scrE}}_{\mathrm{\rho }}$ will remain constant while ${\mathit{scrE}}_{\mathit{z}}$ decreases proportionally to ${\mathrm{\Omega }}_{\mathit{z}}$. This implies one-dimensional adiabatic cooling, which is an interesting option for gravitational studies of light atoms such as hydrogen and antihydrogen.

A rational ratio of the microwave frequency ω and the Kepler frequency Ω of microwave perturbed hydrogen Rydberg atoms results in a ω/Ω=K/M type resonance (K,M integer). This paper presents accurate analytical expressions for the widths of all K/M-type resonances within the framework of the one-dimensional model for microwave ionization of hydrogen Rydberg atoms. The analytical resonance widths are used together with Chirikov’s overlap criterion in a model to compute critical ionization fields in the adiabatic regime (ω<Ω). The model explains the experimentally observed phenomenon of stabilization at ω/Ω=1/M.

We have investigated both theoretically and experimentally saturated absorption of a long-lifetime transition in a calcium atomic beam excited either by a standing wave or by two counterpropagating traveling waves. For standing-wave excitation the usual saturation dip is turned into a peak and then evolves into a triplet as the laser intensity is increased. A theoretical framework has been developed to account for the interaction of atoms with multiple-wave excitation based on a combination of free propagators and S matrices, also applicable to atomic interferometry. The shapes of the wave packets prepared by optical beam splitters are derived. The experimental size and shape of the absorption signal are reproduced by theory only when the actual laser profile is accurately represented and if the recoil physics is introduced because of multiple momentum exchanges between atoms and light in strong laser fields.

We present a fully quantum-mechanical analysis of laser cooling of an angular momentum ${\mathit{J}}_{\mathit{g}}$=1 to ${\mathit{J}}_{\mathit{e}}$=1 transition in a laser configuration consisting of two counterpropagating linearly polarized laser beams. The essential feature of this configuration is the coexistence of velocity-selective coherent population trapping (VSCPT) and polarization-gradient cooling. The role of polarization-gradient cooling is to provide (i) for short interaction times ‘‘precooling’’ of the initial momentum distribution and (ii) in the long-time limit ‘‘confinement of velocities.’’ This eventually leads to a larger number of atoms being captured in the dark state when compared with the schme of Aspect et al. [Phys. Rev. Lett. 61, 826 (1988)]. We find that the optimum parameter values for polarization-gradient cooling and VSCPT are in a completely different parameter regime: polarization-gradient cooling works best off resonance and for low intensities, while VSCPT works best on resonance. We can combine the advantages of polarization-gradient cooling and VSCPT in a scheme where we cycle in time between the optimum cooling parameters for both cooling mechanisms.

Experimental energy spectra and energy-resolved angular distributions of photoelectrons produced by multiphoton ionization of atomic hydrogen are presented for several wavelengths bewteen 596 and 630 nm, peak intensities of about ${10}^{14}$ W/${\mathrm{cm}}^2$, and laser pulse durations of about 0.5 ps. Resonant ionization processes via ac Stark-shift-induced resonances with excited states dominate the spectra. The results of Sturmian-Floquet calculations of these spectra and angular distributions are presented; they are in fair agreement with the experimental data.

We present a non-Hermitian Born-Floquet theory of scattering of fast electrons by atoms in the presence of a strong monochromatic laser field. The interaction of the laser field with both the incident electron and the target atom is treated nonperturbatively, while the interaction of the incident electron with the target atom is treated in first Born approximation. Fluorescence is neglected. Detailed calculations are performed for the ‘‘elastic’’ scattering of 500 eV electrons by atomic hydrogen accompanied by the transfer of photons. The contribution of the entire spectrum of unperturbed atomic states to the dressing of the target is exactly taken into account by performing the calculations on a complex Sturmian basis set. In the nonresonant case, and for electric field strengths that are small with respect to the atomic unit, our Born-Floquet results are in agreement with those obtained using the semi-perturbative approach of Byron and Joachain (in which target dressing is treated in first-order perturbation theory) even at intensities where multiphoton ionization is nonperturbative. The Born-Floquet approach is particularly useful to study resonant cases, where the laser frequency matches a transition frequency in the atom. Two such situations are analyzed.

We derive a Fokker-Planck equation for the center-of-mass Wigner function of an atom moving in a Zeeman neutral-atom trap. The Zeeman structure of atomic sublevels is taken into account. Our analysis is limited to optical transitions between two sets of sublevels corresponding to angular momenta ${\mathit{j}}_{\mathit{b}}$=0 and ${\mathit{j}}_{\mathit{a}}$=1. Expressions for the light pressure, friction, and diffusion forces in the case of low intensity of the laser light are presented. An analytical solution for the stationary center-of-mass Wigner function as well as the size and geometry of the trap are found and discussed.

We discuss theoretically the cooling and localization of atoms in deep potentials induced by a far-off-resonant standing-wave laser. For a two-level atom cooling occurs via a Sisyphus mechanism. For a Λ system we discuss a Raman cooling scheme similar to the one proposed for laser cooling in ion traps.