The binary isotropic collision-induced scattering spectra of the gaseous tetrafluoromethane has been measured in absolute units in the 50–150 ${\mathrm{cm}}^{\mathrm{-}1}$ frequency range. Corresponding theoretical intensities taking into account multipolar polarizabilities have been calculated in a semiclassical way. From a comparison with experiment, the independent components of dipole-quadrupole and dipole-octupole polarizability tensors have been estimated. They have been compared with those previously deduced from depolarized spectrum and with recent theoretical ab initio calculations.

The conventional Hartree and Hartree-Fock approaches for bound states are generalized to treat atomic collision processes. All the single-particle orbitals, for both bound and scattering states, are determined simultaneously by requiring full self-consistency. This generalization is achieved by introducing two Ansätze: (a) the weak asymptotic boundary condition, which maintains the correct scattering energy and target orbitals with correct number of nodes, and (b) square integrable amputated scattering functions to generate self-consistent field (SCF) potentials for the target orbitals. The exact initial target and final-state asymptotic wave functions are not required and thus need not be specified a priori, as they are determined simultaneously by the SCF iterations. To check the asymptotic behavior of the solution, the theory is applied to elastic electron-hydrogen scattering at low energies. The solution is found to be stable and the weak asymptotic condition is sufficient to produce the correct scattering amplitudes. The SCF potential for the target orbital shows the strong penetration by the projectile electron during the collision, but the exchange term tends to restore the original form. Potential applicabilities of this extension are discussed, including the treatment of ionization and shake-off processes.

Relative differential cross sections (DCS's) have been measured for 4 to 200 eV ${\mathrm{e}}^{+}$-${\mathrm{CH}}_4$ quasielastic scattering (elastic scattering plus rotational and vibrational excitations) from 30° to 135° in a crossed-beam experiment. The observed DCS behavior, including diffraction effects at low energies, is very similar to that found earlier for ${\mathrm{e}}^{+}$-Ar elastic scattering. Comparisons between (${\mathrm{e}}^{+}$,${\mathrm{e}}^{\mathrm{-}}$)-(${\mathrm{CH}}_4$,Ar) DCS measurements suggest that observed diffraction effects may be correlated with the sign of the net interaction potential and the degree of spherical symmetry of the target.

The differential cross section for Compton scattering ${\mathrm{d}}^2$σ/dΩdE in germanium (Z=32) was measured using the sensitive volume of a Ge detector as the scatterer and another Ge detector for detection of the scattered radiation, at an incident energy of 59.537 keV and a scattering angle of about 170°. The application of the coincidence technique and the requirement of a constant energy sum yield a clear spectrum in a broad energy range. Detailed analyses of the processes involved in the detector-to-detector scattering were made, including various double-scattering processes. Calculations show that bremsstrahlung of photoelectrons dominates at low energies, while all double-scattering processes weakly contribute to the coincidence rates. The influence of Compton-Rayleigh and Rayleigh-Compton scattering on Compton data is relatively stronger at high energy, while an approximate proportionality of Compton-Compton and single Compton spectra at scattering angles close to 180° was obtained, assuming the impulse approximation. Single and double Compton scattering on stationary electrons at 180° have been shown to produce photons of exactly the same energy. The measured differential cross sections for Compton scattering and results of calculations based on the impulse approximation are in fair agreement.

We examine finite basis set implementations of complex scaling procedures for computing scattering amplitudes and cross sections. While ordinary complex scaling, i.e., the technique of multiplying all interparticle distances in the Hamiltonian by a complex phase factor, is known to provide convergent cross-section expressions only for exponentially bounded potentials, we propose a generalization, based on Simon's exterior complex scaling technique, that works for long-range potentials as well. We establish an equivalence between a class of complex scaling transformations carried out on the time-independent Schrödinger equation and a procedure commonly referred to as the method of complex basis functions. The procedure is illustrated with a numerical example.

Wannier theory predicts an infinite threshold exponent for the breakup of three charged particles if two of the particles have equal charges and the ratio of the charge of one of these to the charge of the third particle has the value (-4). We show that the Wannier picture of ridge propagation remains valid and that the threshold law changes to the form σ∝${\mathrm{E}}^{\mathrm{-}1\mathrm{/}6}$exp(-κ/${\mathrm{E}}^{1\mathrm{/}6}$). The classical and quantum results differ, which is in contrast to the generic Wannier case. We show that the classical limit of the threshold law explains the threshold behavior obtained numerically by classical trajectory calculations.

The angular distribution of the 360.2-eV Auger transition in ${\mathrm{N}}_2$, which is attributed to an ${\mathrm{N}}_2^{2+1}$${\prod }_{\mathrm{g}}$ final state, is measured and calculated. Calculations predict a sharper distribution than what is measured. The angular distribution of the 363.5-eV Auger transition, attributed to an ${\mathrm{N}}_2^{2+1}$${\prod }_{\mathrm{u}}$ final state, is nearly isotropic in the laboratory frame. This is believed to be caused by metastable vibrational levels of the final state. The final state of the 358.7-eV transition was found to be nondissociative, and its angular distribution could not be measured by our experimental technique. The peak in the ${\mathrm{N}}^{+}$ fragment-ion spectrum at about 3.9 eV is assigned to the ${}_{}{}^3{}_{}{}^{}\sum _{\mathrm{g}}^{\mathrm{-}}{}_{}{}^{}$ dissociative state of ${\mathrm{N}}_2^{2+}$.

Argon ${\mathrm{L}}_{2,3}$-${\mathrm{M}}_{2,3}$${\mathrm{M}}_{2,3}$ Auger-electron spectra were measured in coincidence with Kα fluorescent x rays in studies of K-shell vacancy decays at several photon energies above the K threshold and on the 1s→4p resonance. The complex spectra recorded by conventional electron spectroscopy are greatly simplified when recorded in coincidence with fluorescent x rays, allowing a more detailed analysis of the vacancy cascade process. The resulting coincidence spectra are compared with Hartree-Fock calculations, which include shake-up transitions in the resonant case. Small energy shifts of the coincident electron spectra are attributed to postcollision interaction with 1s photoelectrons.

The structure of Massey parameters Δ(${\mathrm{Z}}_1$,${\mathrm{Z}}_2$) for (N,l,m)-(N+1,l+1,m) nonadiabatic couplings in the (${\mathrm{Z}}_1$,e,${\mathrm{Z}}_2$) system (${\mathrm{Z}}_1$,${\mathrm{Z}}_2$ are the nuclear charges) is investigated as a function of the ratio ζ=${\mathrm{Z}}_2$/${\mathrm{Z}}_1$. It is found that Δ(ζ) exhibit deep minima in certain regions Δ${\mathrm{\zeta }}_{\mathrm{LZ}}$, associated with the coalescence of the loci of Q- and I-type branching points of adiabatic energy surfaces in the complex plane of internuclear distance. The positions of these minima, as well as the extension of the regions Δ${\mathrm{\zeta }}_{\mathrm{LZ}}$ in which the I-type (Landau-Zener) coupling prevails, are evaluated analytically. The implications of this phenomenon for the low-energy collision dynamics are briefly discussed.

Theoretical electron transfer cross sections for 1.3–130 eV/amu singly charged ions colliding with Rydberg atoms (n=28, m=2) in a magnetic field up to 4 T are presented. Both paramagnetic and diamagnetic interactions are taken into account for the initial state and the collision. Cross sections are calculated within the classical trajectory Monte Carlo model. A method to create a classical ensemble of electrons in a nonseparable Hamiltonian allows the initial quantum stationary states to be modeled. The effect of the magnetic field on electron capture is analyzed in terms of the field-induced alteration of the initial state, as well as the direct influence on the collision dynamics.

Total energy loss by high-energy protons colliding with surfaces at grazing angles is investigated in terms of the collision parameters. A quantum formulation for binary collisions between the projectile and the free-electron gas is developed. Detailed results are obtained by using a first-order perturbation theory, and they are compared with two other stopping mechanisms, plasmon excitations and ionization of bound electrons. The range of importance of each mechanism is established in terms of the projectile velocity and its incidence angle. It is concluded that at high impact velocities the stopping due to binary collisions with the free-electron gas is dominant.

We have used the time-of-flight technique to measure the energy loss for 51-keV argon ions scattered grazingly from a smooth highly oriented pyrolytic graphite surface. The energy loss has been measured for several impact angles and two charge states, q=2+ and q=16+. Our data indicate that the image charge acceleration in the front of the surface, which increases the effective impact angle of the projectile, affects the energy loss. After correcting for this effect, the energy loss does not depend on the initial charge state of the projectile but increases with increasing the angle of incidence. This indicates a full neutralization of the projectile before it reaches the distance of the closest approach. The experimental results agree approximately with predictions of a modified Firsov model.

We consider the quantum dynamics of a neutral atom Bose-Einstein condensate in a double-well potential, including many-body hard-sphere interactions. Using a mean-field factorization we show that the coherent oscillations due to tunneling are suppressed when the number of atoms exceeds a critical value. An exact quantum solution, in a two-mode approximation, shows that the mean-field solution is modulated by a quantum collapse and revival sequence.

We investigate the low-lying excitations of Bose-Einstein condensate of confined alkali-metal atoms, with repulsive interaction. Vortex excitation energy of the condensate containing a large number of atoms is estimated semiclassically. We also investigate the asymptotic form of the low-energy quasiparticle excitation of the condensate in the presence of a vortex, in the large-N limit. The dispersion relation remains the same as that of a condensate without a vortex, except the z component of angular momentum of the modes is shifted by the angular momentum of the vortex. The first-order correction of the energy eigenvalues due to finite-size effects is calculated.

We show that two independent Bose-Einstein condensates, each initially containing a well-defined number of atoms, will appear coherent in an experiment that measures the beat note between these condensates. We investigate the role played by atomic interactions within each condensate in the time evolution of their relative phase.

We examine the solitary-wave behavior of eigenstate solutions to various nonlinear Schrödinger equations (NLSE's) in an arbitrary number of dimensions and with a general potential. These eigenstate solutions are the only wave functions that can rigorously preserve their shape. We show that solitary-wave motion is only possible if the nonlinearity is decoupled from the absolute position of the wave packet and if the potential in the moving frame differs by at most a linear term from that for the eigenstate problem. If these conditions are satisfied then the motion is along the fully classical trajectory, although the nonlinear term may introduce an additional acceleration. We comment on the implications of these results to the study of the behavior of Bose-Einstein condensed atoms in harmonic trapping potentials, for which the relevant NLSE is the Gross-Pitaevskii equation. Numerical simulations are presented for harmonic and anharmonic potentials in one dimension to illustrate our results.

We study the properties of a spin-polarized Fermi gas in a harmonic trap, using the semiclassical (Thomas-Fermi) approximation. Universal forms for the spatial and momentum distributions are calculated, and the results compared with the corresponding properties of a dilute Bose gas.

We analyze the influence of long-range dipole-dipole interactions between atoms with Zeeman substructure on atomic polarization-gradient cooling at low laser power. The system we consider is a cloud of N atoms driven by two counterpropagating linear cross-polarized laser beams (lin⊥lin configuration) on a – transition. In the semiclassical regime we derive analytical results for the change of the cooling force due to collisions and for the diffusion coefficient in the far-field approximation. For the energy regime where the center-of-mass motion is characterized by oscillations in the optical potentials, we estimate the effect of these far-field collisions on the motion-induced sideband structure of the resonance fluorescence spectrum by using a white-noise approximation for the background light field. This gives a qualitative signature of the heating mechanism in such systems.

We use recently measured cold photoassociation and two-photon data to extract the singlet and triplet accumulated radial phases of interacting ground-state lithium atoms. Using the resulting values we predict scattering lengths, Feshbach resonances, and exchange decay rates for cold collisions between ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ and ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ atoms that are of interest for the possibility of sympathetic cooling of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ and for the coexistence of the bosonic and fermionic quantum-degenerate phases of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ and ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$. In addition, we calculate scattering lengths and exchange decay rates for cold collisions between identical lithium isotopes in different hyperfine states. These quantities are used to examine the possibilities of coexisting ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ Bose condensates and of evaporatively cooling coexisting ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ subsystems.

A theory of Bragg scattering of atoms is presented in which atoms are scattered by counterpropagating optical fields having different frequencies. It is shown that, for this geometry, the system reduces to that encountered in the pump-probe spectroscopy of two or multilevel systems. As a result, one can tune the Bragg resonances by varying the frequency difference between the optical fields. The possiblity of using these techniques to construct an atom-beam splitter, whose output arms are separated in momentum space by a hundred photon momenta, is discussed.