A model for cooling a system of bosons in a harmonic trap via their interactions with a thermal bath of other particles is studied. The master equation describing the evolution of the system is derived for an arbitrary number of spatial dimensions. This equation is characterized by transition rates between trap levels. We present an analytic approximation for these rates and compare it with exact formulas, derived for the case of an even number of spatial dimensions. Analytic expressions show very good agreement with the exact ones for a wide range of parameters. We also discuss the cooling dynamics in terms of the approximated rates.

Whole-atom differential cross sections for coherent scattering of 59.5-keV γ rays at 126° by Ti, Ni, Zn, Se, Mo, Ru, Cd, Sn, Te, Gd, Dy, Yb, W, and Pb were measured using a high-resolution lithium-drifted germanium detector. Form factors were extracted from the measured cross sections and the results were compared with predictions of form-factor theories.

Measurements have been made of the ionization cross sections of air, hydrogen, and argon by use of the KEK 500-MeV booster, the KEK 12-GeV main ring, and the Fermilab main ring. Within the beam duct of each of those accelerators, we placed a gas ionization monitor and recorded the current in the monitor as a function of the time elapsed since the beam injection for each pulse. This time is uniquely related to the instantaneous kinetic energy of protons. Because gas pressure in the monitor was kept sufficiently low (about ${10}^{\mathrm{-}5}$ Torr), the current is attributable to single ionizing collisions of protons with molecules and is therefore proportional to the specific primary ionization, or the ionization cross section (rather than the total ionization). The dependence of the cross section on proton kinetic energy, measured for air, hydrogen, and argon, agrees closely with the prediction of the Bethe theory, and is represented by a straight line on the Fano plot. The data were tested for consistency with other measurements for electrons and protons at lower kinetic energies. Implications of the work for the design of accelerator vacuum components and of particle detectors are included. For instance, the technique used in the present measurements can be readily applied to the determination of the pressure distribution in a beam duct at liquid-helium temperature of an accelerator using superconducting magnets.

Single photoionization of neutral atoms is examined theoretically for a situation in which the photoionizing laser is tuned close to the resonant frequency for transitions between the ground and first-excited states of the positive ion. The resonant coupling in the positive ion is shown to have a dramatic peak-splitting effect on the kinetic-energy spectrum of the ionized electron. An essential-states analysis of the photoionization process is presented, and a comparison is made with numerical results for one-dimensional helium. The agreement between the results establishes the validity of the essential-states approach. The possibility of superposing this core-coherence effect with laser-induced autoionization effects is considered.

High-resolution autoionization spectra of multiply charged Na-like states in silicon are presented. These states have been populated in collisions of ${\mathrm{Si}}^{5+}$ ions with 50 keV impact energy on two gas targets: He and Ar. The electron emission following the decay of core-excited 2${\mathit{p}}^5$3lnl’ (n=3–6) levels in Si iv has been measured. The comparison of electron spectra obtained after collisions with He and Ar is given. Theoretical Auger energies due to core-excited (2${\mathit{p}}^5$3${\mathit{s}}^2$), (2${\mathit{p}}^5$3s3p), (2${\mathit{p}}^5$3p3d), (2${\mathit{p}}^5$3s4s), and (2${\mathit{p}}^5$3s4f) states have been calculated relative to the (2${\mathit{p}}^6$${)}^1$S limit by using the multiconfiguration Hartree-Fock method. Additional theoretical estimates of Auger transition energies originating from (2${\mathit{p}}^5$3${\mathit{p}}^2$), (2${\mathit{p}}^5$3${\mathit{d}}^2$), (2${\mathit{p}}^5$3s4d), (2${\mathit{p}}^5$3s5p), (2${\mathit{p}}^5$3s6s), (2${\mathit{p}}^5$3s6p), and (2${\mathit{p}}^5$3s6g) are also presented.

The theory of double internal bremsstrahlung during an allowed electron-capture transition is developed in an approximation in which the atomic electron is treated nonrelativistically but the effects of the nuclear Coulomb field are fully included. For capture from the K shell detailed results are obtained for the intensity distribution of the two photons as a function of the photons’ energies and relative angle of emission. Numerical results are presented for the distribution of the sum of the photon energies for ${}_{}{}^{37}{}_{}{}^{}\mathrm{Ar}$ and ${}_{}{}^{55}{}_{}{}^{}\mathrm{Fe}$ and compared with available experimental data. It is found that the inclusion of Coulomb effects results in a substantial reduction in the intensity of the energy spectrum of the photons and improves quantitative agreement with the experimental data for ${}_{}{}^{37}{}_{}{}^{}\mathrm{Ar}$. However, for ${}_{}{}^{55}{}_{}{}^{}\mathrm{Fe}$ serious discrepancies remain.

We study the Rydberg-atom–ground-state-atom collisions within the framework of the quasi-free-electron model. We show that the general formulation of the problem based on the three-body Faddeev equations requires the off-shell extension of the two-body amplitude for electron-atom scattering. The two-body off-shell amplitudes for electron scattering by Rb and Cs atoms are calculated using the pseudopotential approach. The cross section for collisional quenching and broadening of Rydberg states due to perturbations by Rb and Cs atoms are calculated, and the results are compared with experimental data. The off-shell extension of the scattering amplitude usually improves agreement with the experiment. However, both on-shell and off-shell results fail in the region of low principal quantum numbers, where the multiscattering effects become important. Our calculations and their comparison with the experiments confirm that the ${\mathrm{Cs}}^{\mathrm{-}}$( ${}_{}{}^3{}_{}{}^{}$P) state is a resonance rather than a bound state.

A relationship between ionization by photons and by energetic charged particles interacting with matter is proposed and tested. The method is based on the recognition that both dipole and nondipole transitions are allowed for charged particles. The dipole component is shown to be related to photoabsorption, and the nondipole component to Compton scattering. As an example, we calculate the ratio of double to single ionization of helium by protons in terms of the corresponding ratios for photoabsorption and Compton scattering. At a proton energy of 400 MeV, this ratio is found to be 0.272%, with the dipole component contribution 0.211% and the nondipole component contributing the remaining 0.061%. The basic idea of our method may be readily extended to other many-electron processes, such as double excitation and excitation-ionization.

The cross sections for the photodetachment from the second bound state of the negative hydrogen ion, ${\mathrm{H}}^{\mathrm{-}}$(2${\mathit{p}}^2$ ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^{\mathit{e}}$), for photon energies above the H(n=2) threshold are calculated using a hyperspherical close-coupling method. This state is parity forbidden to autoionize into H(n=1)+e and has an extremely small binding energy of 0.01 eV. The results for low photon energies agree with earlier calculations. For energies near the H(n=3) threshold, two shape resonances are found in addition to many Feshbach resonances. These resonances are identified by examining adiabatic hyperspherical potential-energy curves.

Total cross sections have been examined theoretically by using the continuum distorted wave–eikonal initial state (CDW-EIS) and the plane-wave Born approximations for the ionization of hydrogenlike ions in the excited states with the principal quantum number n≤5 in collisions with bare ions in the keV/amu to MeV/amu range. For the ionization of hydrogenlike ions up to ${\mathrm{C}}^{5+}$(1s) by ${\mathrm{H}}^{+}$ at low energies, the present CDW-EIS prediction is in good accord with close-coupling calculation, while the Born prediction leads to a considerable overestimate. A comparison is made between the present results and other theoretical predictions as well as experimental measurements.

We present numerical results from solving the time-dependent nonlinear Schrödinger equation (NLSE) that describes an inhomogeneous, weakly interacting Bose-Einstein condensate in a small harmonic trap potential at zero temperature. With this method we are able to find solutions for the NLSE for ground state condensate wave functions in one dimension or in three dimensions with spherical symmetry. These solutions corroborate previous ground state results obtained from the solution of the time-independent NLSE. Furthrmore, we can examine the time evolution of the macroscopic wave function even when the trap potential is changed on a time scale comparable to that of the condensate dynamics, a situation that can be easily achieved in magneto-optical traps. We show that there are stable solutions for atomic species with both positive and negative s-wave scattering lengths in one-dimensional (1D) and 3D systems for a fixed number of atoms. In both the 1D and 3D cases, these negative scattering length solutions have solitonlike properties. In 3D, however, these solutions are only stable for a modest range of nonlinearities. We analyze the prospects for diagnosing Bose-Einstein condensation in a trap using several experiments that exploit the time-dependent behavior of the condensate.

We discuss a method for probing a system of cold bosonic atoms in a trap using intense short laser pulses. Above the critical temperature for Bose-Einstein condensation, such a system scatters very weakly. Coherent scattering occurs primarily in the forward direction within a solid angle determined by phase matching conditions for the thermal atomic distribution. Below the critical temperature, the number of scattered photons increases dramatically and the scattered light is emitted into a solid angle determined by the size of the condensate. Quantum statistics of the atoms explicitly effect the spectrum as well as the squeezing properties of the scattered light. The theory accounts for the atom-atom interactions.

We calculate the recombination probability for an atom interferometric experiment in which the beams interfere after one of them has been exposed to an intense laser. We choose a model one-dimensional atomic potential and find that if the intensity of the laser is large, there are recurrences in the recombination probability as a function of time, irrespective of the frequency of excitation. This implies that the particles exposed to the laser have a large amplitude to be in the localized initial state in spite of having sufficient energy to escape from the binding potential.

The analytical statistical tensor approach, by use of the concatenation of perturbation factors, is demonstrated to be a powerful technique in the study of coherent transients, i.e., conventional pulsed NMR signals. Under a wide variety of inhomogeneous broadening mechanisms the method provides times of occurrence, amplitude, and phase dependences of spin-echo signals. Complicated spin dynamics for any spin value may be readily calculated. The method is illustrated with a number of examples from the literature, including spin-echo formation under combined magnetic-dipole and electric-quadrupole interactions, magnetoacoustic excitation of the nuclear spin echo, and the cumulative two-pulse spin echo. The developed formalism provides deeper insight into problems of pulsed NMR, giving a more general overview on some of them, thereby demonstrating the versatility and power of the analytical approach.

High-order harmonic generation accompanying photoionization presents a clear plateau structure in situations where tunneling is the fundamental process for the ejection of the electron from the core. We describe here what is expected to happen when the laser intensity is so high that barrier suppression begins to be the dominant mechanism. We show that this is an ionization regime where harmonic generation decreases with intensity, obtaining therefore an upper practical limit for high harmonic generation. Thus we are able to predict situations where the harmonic cutoff appears at a lower energy than that expected by the standard ${\mathit{I}}_{\mathit{P}}$+3.17${\mathit{U}}_{\mathit{P}}$ law where ${\mathit{I}}_{\mathit{P}}$ and ${\mathit{U}}_{\mathit{P}}$ correspondingly are the ionization threshold for an electron in the ground state and ponderomotive energy.

The laser-assisted electron-impact excitation of 2s and 2p dressed states of hydrogen is studied. The interaction of a linearly polarized laser field with the colliding system is treated by the nonperturbative Floquet theory, while the interaction of the fast incident electron with the target atom is treated in the first Born approximation. The nonresonant collision in a low-intensity, low-frequency laser field is dominated by the process with no exchanged photon with the field, while at larger intensities the collision accompanied by the exchange of real or virtual photons is much more important. For the stimulated bremsstrahlung, the 1s→2s transition is strongly influenced by the resonant coupling between the final 2s and the intermediate 3p states. In the resonant cases, where laser frequency matches a transition frequency between the initial or final and an intermediate state, the collisions with the largest cross section are those in which the projectile induces a dipole transition in the atom.

Intermediate resonances are predicted to enhance or suppress the different electronic kinetic-energy peaks in above-threshold ionization (ATI) processes. We reach these conclusions on the basis of numerically exact three-dimensional computations of hydrogenic ATI proceedings via several field-broadened [3(s,p,d) or 4(s,p,d,f)] intermediate bound states. Two effects, one attributable to interferences between different resonances, operating in the circular polarization case, and one due to interferences between different ‘‘precursor’’ partial waves of the same resonance, operating in the linear polarization case, have been discovered. The latter effect is shown to give rise to the appearance of a doubling in each one of the partial-wave components of the ATI peaks, with each component experiencing an avoided-crossing-type process as the intensity is raised. We find that for near-resonance ATI, the breakdown of N-order perturbation theory occurs at much lower intensities than for off-resonance ATI.

This paper begins with an examination of the revival structure and long-term evolution of Rydberg wave packets for hydrogen. We show that after the initial cycle of collapse and fractional or full revival, which occurs on the time scale ${\mathit{t}}_{\mathrm{rev}}$, a new sequence of revivals begins. We find that the structure of the new revivals is different from that of the fractional revivals. The new revivals are characterized by periodicities in the motion of the wave packet with periods that are fractions of the revival time scale ${\mathit{t}}_{\mathrm{rev}}$. These long-term periodicities result in the autocorrelation function at times greater than ${\mathit{t}}_{\mathrm{rev}}$ having a self-similar resemblance to its structure for times less than ${\mathit{t}}_{\mathrm{rev}}$. The new sequence of revivals culminates with the formation of a single wave packet that more closely resembles the initial wave packet than does the full revival at time ${\mathit{t}}_{\mathrm{rev}}$, i.e., a superrevival forms. Explicit examples of the superrevival structure for both circular and radial wave packets are given. We then study wave packets in alkali-metal atoms, which are typically used in experiments. The behavior of these packets is affected by the presence of quantum defects that modify the hydrogenic revival time scales and periodicities. Their behavior can be treated analytically using supersymmetry-based quantum-defect theory. We illustrate our results for alkali-metal atoms with explicit examples of the revival structure for radial wave packets in rubidium.

Following the experiment of Jones et al. [Phys. Rev. Lett. 71, 2575 (1993)], we present a theory of coherent redistribution of population in a model Rydberg atom exposed to a sequence of two identical laser pulses separated in time and shorter in duration than the Rydberg-electron Kepler period. For different initial-population conditions, we solve the problem of redistribution in a fully analytical and rigorously nonperturbative way, thus obtaining discrete-state population amplitudes, dependent on laser intensity, and a time delay between the pulses. Using this solution, we study the population in a given state versus pulse delay (Ramsey fringes), as well as the corresponding Fourier spectrum, for both low and high laser intensities. From the number of frequency components and their positions in the Fourier spectrum, we deduce the redistribution of the initial-state population over a number of states by the first pulse. Within our model calculations we achieve qualitative agreement with the experimental observation of Jones et al. that an increase in laser intensity results in a general increase in the number of frequency components in the Fourier spectrum. Our theoretical results are also consistent with the experimental finding of Noordam et al. [Phys. Rev. Lett. 68, 1496 (1992)] that Raman transitions via the continuum between different Rydberg states are essential for population redistribution. We suggest new experiments to measure the effect of the initial-state depletion on the Fourier spectrum. As follows from our model calculations, some frequency components (both low and optical) present in the low-intensity Fourier spectrum should vanish in the high-intensity spectrum due to complete depletion of the initial state by the first pulse.

We present a general nonperturbative formalism and an efficient and accurate numerical technique for the study of the angular distributions and partial widths for multiphoton above-threshold detachment in two-color fields. The procedure is based on an extension of our recent paper [D. A. Telnov and S.-I Chu, Phys. Rev. A 50, 4099 (1994)] for one-color detachment, and the many-mode Floquet theory [T. S. Ho, S.-I Chu, and J. V. Tietz, Chem. Phys. Lett. 96, 464 (1983)]. The generalization of this procedure is performed for both cases of commensurable and incommensurable frequencies of the two-color fields. The procedure consists of the following elements: (i) Determination of the resonance wave function and complex quasienergy by means of the non-Hermitian Floquet Hamiltonian formalism. The Floquet Hamiltonian is discretized by the complex-scaling generalized pseudospectral technique recently developed [J. Wang, S.-I Chu, and C. Laughlin, Phys. Rev. A 50, 3208 (1994)]. (ii) Calculation of the angular distribution and partial widths based on an exact differential formula and a procedure for the rotation of the resonance wave function back to the real axis. The method is applied to a nonperturbative study of multiphoton above-threshold detachment of ${\mathrm{H}}^{\mathrm{-}}$ by 10.6-μm radiation and its third harmonic (the commensurable case). The results show strong dependence on the relative phase δ between the fundamental frequency field and its harmonic. For the intensities used in calculations (${10}^{10}$ W/${\mathrm{cm}}^2$ for the fundamental frequency, ${10}^8$ and ${10}^9$ W/${\mathrm{cm}}^2$ for the harmonic), the total rate has its maximum at δ=0 and minimum at δ=π. However, this tendency, though valid for the first several above-threshold peaks in the energy spectrum, is reversed for the higher-energy peaks. The energy spectrum for δ=π is broader, and the peak heights decrease more slowly compared to the case of δ=0. The strong phase dependence is also manifested in the angular distributions of the ejected electrons.