Azimuthal asymmetry in elastic scattering has been measured for electron collisions with laser-excited, polarized ($3P$) Na atoms. An observation of this asymmetry in the elastic channel is reported for incident electron energies in the range of 1 to 10 eV at polar scattering angle 135°. Data with selected magnetic sublevels provide a stringent test for available calculations where even the most successful one, the convergent close-coupling calculation, has difficulties at the large scattering angles.

In view of recent successful evaporative cooling experiments reaching temperatures in the nK range, we discuss ground-state two-body inelastic and three-body decay rates of dilute cold atomic gas samples at ultralow temperatures. We present theoretical low-temperature two-body decay rates in alkali-atom systems using recently obtained information on two-body potentials. The rates show an oscillating structure as a function of temperature and magnetic field which can be understood in terms of the interference of initial and final radial waves.

The effect of plasma fluctuations on transverse spatial coherence of x-ray lasers is investigated. Hose type (random) transverse displacements of the x-ray lasing medium induced by pump-laser nonuniformities are considered in detail. Such displacements lead to decreased transverse coherence via reduced gain discrimination from mode coupling. This effect may be related to a previously reported insensitivity of transverse coherence to laser length in neonlike selenium at 206 and 210 Å [Trebes et al., Phys. Rev. Lett. 68, 588 (1992)]

We have measured the index of refraction in the region of a coherent population trapping resonance in a cesium vapor cell with an interferometric technique. We find very high normal dispersion (up to $\frac{\mathrm{dn}}{\mathrm{df}}=9.7\mathrm{}\times {10}^{-12\mathrm{}}$ ${\mathrm{Hz}}^{-1\mathrm{}}$) at low absorption. From our spectra we obtain very small group velocities below $\frac{c}{3000}$. This corresponds to a delay time of more than 200 ns for a cesium cell 20 mm in length, equivalent to more than 60 m of propagation in vacuum.

We report high harmonic generation from a 248.6-nm KrF laser giving harmonic orders up to the 37th (67 Å) in a helium gas jet and the 35th (71 Å) in neon, for laser intensities up to 4 × ${10}^{17}$ W/${\mathrm{cm}}^2$ in 380-fs pulses. These observations are interpreted using theoretical modeling that identifies the ion species ${\mathrm{He}}^{+}$, ${\mathrm{Ne}}^{+}$, and ${\mathrm{Ne}}^{2+}$ as the sources of the highest harmonics.

A system of two identical atoms sharing a photon with a high-$Q$ resonator mode is studied by a nonperturbative formalism. As opposed to previously considered models, here the interatom coupling is shown to result from competing effects of vacuum Rabi splitting and photon exchange via off-resonant modes. Strong suppression of interatom excitation transfer is predicted at both near- and far-zone separations.

Starting from a constrained-search formulation of current-density-functional theory, we obtain rigorous scaling and virial relations for the kinetic, exchange, and correlation energy functionals of electronic systems in strong magnetic fields.

Circular dichroism has been detected in the polarization of the fluorescence resulting from the decay of excited calcium ions. Synchrotron radiation was used to both ionize and excite calcium atoms from their ground state, and the photoejected electron was detected in coincidence with the polarized fluorescent photon. By introducing a degree of left, then right circularly polarized light into the incident photon beam the circular dichroism could be measured. The analysis of the results was carried out using recent developments of the statistical tensor method, and it was possible to determine the sign of the phase difference between the outgoing waves.

The number-phase uncertainty relation based on the Pegg-Barnett Hermitian phase operator formalism is discussed for generalized squeezed states of the harmonic oscillator. The corresponding number-phase uncertainty product is calculated for the magnitudes of the squeeze and displacement parameters ranging from 0 to 3/2 in the former case and from 0 to 4 in the latter case for the first few classes of generalized squeezed states (m=0, 1, and 2) and for different values of their combined phases. It is found that for a given magnitude of the squeeze parameter, the number-phase uncertainty product tends to the fixed limiting value m+1/2 when the magnitude of the displacement parameter tends to infinity. On the other hand, for a fixed magnitude of the displacement parameter, the uncertainty product grows indefinitely as the magnitude of the squeeze parameter increases. It is also observed that the number-phase uncertainty product tends to zero for few-photon generalized squeezed states (when the magnitudes of both squeeze and displacement parameters tend to zero) so that, according to the Pegg-Barnett Hermitian phase formalism, it is possible to have generalized squeezed states with a number-phase uncertainty product smaller than 1/2.

We study the ħ perturbation expansion of the quantum Wigner equation. It leads to a unified formulation of semiclassical approximations based on the phase-space representation of quantum mechanics. We derive the O(${\mathrm{ħ}}^2$) quantum corrections to the finite-temperature Bose and Thomas-Fermi phase-space distributions. Both reduce, in the high-temperature limit, to the known quantum corrections of the classical Gibbs-Boltzmann probability density. Within this approach, moreover, we obtain a very simple derivation of the extended Thomas-Fermi theory. Finally, the limits of applicability, the convergence problems, and the possibility of improving or defining new semiclassical approximations are discussed.

A model problem consisting of two isolated particles with a mutual interaction depending upon retarded and advanced positions and constrained to one-dimensional motion is analyzed herein. This system has a number of features in common with a previously considered one-particle double-delay model problem. The equations of motion have closed-form solutions and the systems are both deterministic and causal. In both cases, standard low-order approximations to the exact problem, in general, have spurious solutions, which must be recognized and removed in order to extract the physically meaningful parts and to proceed reasonably with quantization. In addition, the two-particle system has specific characteristics. The center-of-momentum motion separates out. The dependence of the solutions on the mass ratio of the two particles can be examined. Further, not only does the relative motion have the ordinary solution, in which the two particles move out of phase, it can also have an extraordinary solution, in which they move in phase with each other. Finally, the total generalized linear momentum and Hamiltonian can be evaluated and seen to be constants of the motion.

A proposal for an experimental realization of Bohm’s spin-1/2 particle version of the Einstein-Podolsky-Rosen experiment is described. Two ${}_{}{}^{199}{}_{}{}^{}\mathrm{Hg}$ atoms, each with nuclear spin 1/2, are produced in an entangled state with total nuclear spin zero. Such a state is obtained by dissociation of dimers of the ${}_{}{}^{199}{}_{}{}^{}\mathrm{Hg}_2^{}{}_{}{}^{}$ isotopomer using a spectroscopically selective stimulated Raman process. The measurement of nuclear spin correlations between the two atoms in this entangled state is achieved by detection of the atoms using a spin state selective two-photon excitation-ionization scheme. The experiment will not only close the detector efficiency loophole, but in addition will permit enforcement of the locality condition.

We propose a measure of entanglement between two subsystems of arbitrary (but finite) number of levels. This measure is invariant under unitary transformations of the subsystems and varies between 0 (product states) and 1 (maximum entangled states). The case of two two-level systems is worked out explicitly, where the known complementarity between one- and two-particle interference results in a very natural way from a sum rule. Generalizations to more than two subsystems are discussed. Here we show that for three particles there cannot exist a pure state that is completely characterized by three-particle entanglement alone. For the example of the Greenberger-Horne-Zeilinger (GHZ) state, an experimental setup is proposed, in which its corresponding two-particle entanglement would show up.

The properties of the quantum vacuum in a one-dimensional cavity with a moving wall are studied. We present a method to obtain an exact solution for the classical electromagnetic potential of a cavity with arbitrary wall motion. This method is applied to a system with a wall oscillating at a harmonic of the cavity resonance frequency. Two factors entirely determine the long-time solution of an undamped system: the points in time at which the wall returns to its initial position, and the direction the wall was displaced in between these points in time. In each of the resonant systems we examined, wave packets in the field energy density formed that become narrower and grow in intensity as time increases. This is the case even when the oscillation frequency of the wall is equal to the fundamental cavity resonant frequency, despite the fact there is no net energy growth in the field of such systems. The number of wave packets, and the long-time limit to the value of the energy density in between the wave packets, are determined by the two factors mentioned above.

The energy levels of the Sr 5snd${\mathrm{}}^{1,3}$${\mathit{D}}_2$ Rydberg series have been measured using an autoionization scheme, which provides an excellent opportunity for the application of the multichannel quantum-defect theory (MQDT) to their spectra. MQDT parametrizations of the ${}_{}{}^{1,3}{}_{}{}^{}$${\mathit{D}}_2$ bound-state Rydberg series are presented, including calculated term values for these series. Furthermore, it is found that MQDT wave functions that are derived from experimentally determined level energies are capable of predicting such wave-function-sensitive properties as natural radiative lifetimes of Sr 5snd${\mathrm{}}^{1,3}$${\mathit{D}}_2$ Rydberg states.

Sub-Doppler excitation spectra of HD have been recorded in the range 92–98 nm with the use of a narrow-band and tunable extreme ultraviolet laser in combination with a molecular beam. Frequencies of 147 transitions to the B${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{u}}^{+}$, C${\mathrm{}}^1$${\mathrm{\Pi }}_{\mathit{u}}$, and EF${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{g}}^{+}$ states have been calibrated with an average absolute accuracy of 0.035 ${\mathrm{cm}}^{\mathrm{-}1}$. The data have been analyzed in the framework of a semiempirical deperturbation model involving mutual couplings between nearby lying levels of the B${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{u}}^{+}$ and C${\mathrm{}}^1$${\mathrm{\Pi }}_{\mathit{u}}$ states. Also, symmetry-breaking effects, i.e., interactions with EF${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathit{g}}^{+}$ gerade states, were inferred from the data.

The hyperfine constants A and B for magnetic dipole and electric quadrupole interaction in the ${}_{}{}^9{}_{}{}^{}$${\mathit{S}}_4$ ground state of unstable ${}_{}{}^{150}{}_{}{}^{}\mathrm{Eu}_{}^{+}{}_{}{}^{}$ ions have been determined with high precision in an optical microwave double-resonance experiment. The ions were produced by nuclear reactions at the ISOLDE facility at CERN, collected on a foil, reevaporated, and stored in a Paul ion trap. Three of eight possible hyperfine transitions between different F sublevels have been observed with well resolved Zeeman substructure in a residual magnetic field. Analysis of the transition frequencies and extensive second-order hyperfine correction yield values of A=559 010 325(40) Hz, B=-926.2(3.0) kHz. A preliminary value for the nuclear quadrupole moment Q ${(}^{150}$${\mathrm{Eu}}^{+}$)=1.264(23) b has also been obtained.

We show that a paramagnetic atom with spin polarization S, in an electric field E, will have an anapole moment in the direction E×S, with magnitude of order α${\mathit{Ea}}_0^4$. There is a corresponding toroidal magnetic field inside the atom in the direction r×(E×S), with strength of order αE. As an example, we evaluate exactly the toroidal field and its anapole moment for hydrogenic atoms to first order in E, using both the Schrödinger and Dirac equations. We also use the calculated electric polarizabilities to estimate the toroidal magnetic fields and anapole moments for the ground states of the alkali-metal atoms and for Rydberg states. We show that the Stark-induced toroidal magnetic fields of atoms will have no influence on their hyperfine structure. However, they can change the direction of the nuclear spins of electron-spin polarized molecules.

A pump-and-probe approach was used to investigate polarization quantum beats resulting from hyperfine interactions in the resonant 4p${\mathrm{}}^2$${\mathit{P}}_{3/2}$ level of ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$. Coherent time evolution of the electronic polarization was observed over eight radiative lifetimes of the 4p${\mathrm{}}^2$${\mathit{P}}_{3/2}$ level. Analytical expressions for the resulting polarization beat signals were fitted to the data to determine the magnetic-dipole constant, A=3.325(15) MHz, and the electric-quadrupole constant, B=3.230(23) MHz. These results represent an improvement of about one order of magnitude over previous measurements.

We have remeasured the optical oscillator strengths of eight noble-gas resonance lines in the vacuum-ultraviolet region. The measurements use a 900-eV collimated electron beam to excite the atoms, and the transmission of the emitted radiation is measured as a function of the gas density. In the method of self-absorption used here, the measured oscillator strengths are proportional to the distance between the electron beam and the fixed aperture of the spectrometer-detector system. We investigated and eliminated a possible systematic effect in the determination of the absorption length due to deflections of the electron beam. These measurements are performed at higher energies than our previous experiments at 100 eV in order to keep the electron-beam path better defined and aligned with the electron-gun apertures. The measured absolute oscillator strengths are He I (58.4 nm), 0.2700±0.0076 (2.8%); He I (53.7 nm), 0.0737±0.0023 (3.1%); Ne I (74.4 nm), 0.010 95±0.000 32 (2.9%); Ne I (73.6 nm), 0.1432±0.0038 (2.6%); Ar I (106.7 nm), 0.0580±0.0017 (2.9%); Ar I (104.8 nm), 0.2214±0.0068 (3.1%); Kr I (123.6 nm), 0.1775±0.0050 (2.8%); and Kr I (116.5 nm), 0.1416±0.0041 (2.9%).