We study the Compton-scattering contribution to the double ionization of helium within the $A^2$ approximation. We present results for the final-photon energy distribution for incoming photon energies of 6 and 20 keV using two alternative forms for the $A^2$ operator, named in the literature as the length and velocity forms. It is shown that, although there is a form dependence of the results, these differences tend to cancel at the level of the total cross section as the incoming photon energy increases. Our results support the conclusion that the asymptotic limit for the ratio of double-to-single ionization by Compton scattering is about 0.8%.

Photoassociation of ultracold lithium atoms into bound vibrational levels of the $A{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ excited state is used to probe the $X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ ground-state interaction potential of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}_2^{}{}_{}{}^{}$ and ${}_{}{}^7{}_{}{}^{}\mathrm{Li}_2^{}{}_{}{}^{}$. It had been predicted that the $s$-wave photoassociation signal strength would pass through a minimum as a function of vibrational level for positive $s$-wave scattering length. We report the observation of this novel effect, and use the location of the minimum to precisely determine the singlet $s$-wave scattering length for both isotopes. The sensitivity of this technique is demonstrated by distinguishing the minima for collisions involving ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ atoms in different hyperfine states.

The double Auger (DA) decay of a $K$ hole has been observed directly by detecting the two emitted electrons in coincidence. The hole was created in ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$ following the electron-capture decay of ${}_{}{}^{37}{}_{}{}^{}\mathrm{Ar}$. The probability of DA decay, per Auger decay, with the two electrons both having an energy greater than 250 eV was found to be 3.7±0.2%. The DA probability was found to decrease exponentially as the energy partitioning between the two electrons changed from the asymmetric case ($E_1\gg E_2$) to the symmetric case ($E_1\approx E_2$). The DA probability accounts for the bulk of the intensity of high charge states previously measured in ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$.

We have measured the Compton double-to-single ionization ratio of helium using an ion time-of-flight spectrometer along with monochromatized synchrotron radiation of 57 keV. This photon energy is high and probes the Compton ionization alone, since the photoionization makes only a negligible contribution to the total cross section. Comparing our result, which is (1.25±0.3)%, with theoretical calculations and measurements at lower energies shows that this energy is most likely still not high enough to confirm the value of the asymptotic high-energy limit experimentally.

High harmonic generation in the presence of a static electric field is analyzed theoretically by an extension of the zero-range potential model treatment of Becker et al. [Phys. Rev. A 50, 1540 (1994)]. For ${\mathrm{H}}^{-}$ and a C${\mathrm{O}}_2$ laser of 5 × ${10}^{10}$ W/${\mathrm{cm}}^2$ intensity, a static electric field of 100 kV/cm is shown to produce a plateau from the 3rd to the 23rd harmonic in which neighboring even and odd harmonics are of comparable intensity. Furthermore, odd harmonics on the plateau are one or more orders of magnitude more intense than in the absence of the static electric field. Dependence of emission rates on laser intensity and results for harmonic generation by Ar are also presented.

Laser-cooled ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ atoms have been confined in three-dimensional spatially periodic potentials that are nearly conservative. The potentials were formed from the intersection of four laser beams far-detuned from the optical resonance. By adjusting the relative orientations of the beams, lattices with primitive translation vectors larger than the laser light wavelength were created. We achieved an effective temperature of ∼80 μK through adiabatic reduction of the confining potential strength, and prepared ensembles with effective temperatures of ∼1.8 μK by initially confining atoms in weak potentials.

An axial magnetic field applied to vertical-cavity surface-emitting lasers induces emission of elliptically polarized states. The characteristic switching between orthogonal linearly polarized states with no magnetic field becomes a switching between elliptically polarized states with low ellipticity for weak magnetic fields. Stronger magnetic fields induce time-dependent solutions with two main peaks in the optical spectrum, with orthogonal elliptically polarized basis states. Strong magnetic fields induce rotating linearly polarized emission.

We have studied the behavior of cesium atoms cooled in six-beam "gray" optical molasses. Cooling occurs for a laser detuned to the blue side of the $6S_{\frac{1}{2}}$, $F=3\mathrm{}\to 6P_{\frac{3}{2}}$, $F^{\prime }=2\mathrm{}$ transition, and a Sisyphus-type effect accumulates the atoms in states not coupled to the light. We measure a minimum temperature of 1.1±0.1 μK at low atomic density. The typical cooling time is on the order of 1 ms. A linear dependence of the temperature versus atomic density is found with a slope of ∼0.6 μK/(${10}^{10}$ atoms/${\mathrm{cm}}^3$).

Selleri’s model of photodetection based on variable detection probability is analyzed. The results of an experiment that discriminates between the predictions of Selleri’s model and quantum mechanics are presented [Bell’s Theorem and the Foundations of Modern Physics, edited by A. van der Merwe, F. Selleri, and G. Tarozzi (World Scientific, Singapore, 1992); in Wave-Particle Duality, edited by F. Selleri (Plenum, New York, 1992)]. © 1996 The American Physical Society.

We use the common eigenvectors ‖ζ〉 of two particles’ center-of-mass position ${\mathit{X}}_{\mathit{c}}$=${\mathrm{\mu }}_1$${\mathit{X}}_1$+${\mathrm{\mu }}_2$${\mathit{X}}_2$ and mass-weighted relative momentum ${\mathit{P}}_{\mathit{r}}$=${\mathrm{\mu }}_2$${\mathit{P}}_1$-${\mathrm{\mu }}_1$${\mathit{P}}_2$, as well as the eigenvectors ‖η〉 of the other pair commutative operators X=${\mathit{X}}_1$-${\mathit{X}}_2$ and P=${\mathit{P}}_1$+${\mathit{P}}_2$ to solve the dynamics of two coupled oscillators. The coupling involves both interbond potential and kinetic coupling. This approach seems to be simple, convenient, and natural. © 1996 The American Physical Society.

Weak-interaction contributions to hyperfine splitting and the Lamb shift in hydrogen and muonium are discussed. The problem of sign of the weak-interaction contribution to HFS is clarified, and simple physical arguments that make this sign evident are presented. It is shown that weak-interaction contributions to HFS in hydrogen and muonium have opposite signs. A weak-interaction contribution to the Lamb shift is obtained. © 1996 The American Physical Society.

Sequential stationary phase, i.e., the replacement of a multidimensional stationary phase evaluation by an ordered set of lower-dimensional stationary phase integrations, is applied to uniformly asymptotic path integral forms for the semiclassical propagator. The results are useful formulas for computing trajectory indices (generalized Maslov indices) in any quantum representation for general types of time-dependent Hamiltonians. Index connecting relations that relate the indices for the different representations are also obtained. We also demonstrate a general canonical structure for the semiclassical phase indices that arises naturally through the application of sequential stationary phase. © 1996 The American Physical Society.

Based on the previously proposed notions of action operators and of quantum integrability, frequency operators are introduced in a fully quantum-mechanical setting. They are conceptually useful because another formulation can be given to unitary perturbation theory. When worked out for quantum spin systems, this variant is found to be formally equivalent to canonical perturbation theory applied to nearly integrable systems consisting of classical spins. In particular, it becomes possible to locate the quantum-mechanical operator-valued equivalent of the frequency denominators that may cause divergence of the classical perturbation series. The results that are established here link the concept of quantum-mechanical integrability to a technical question, namely, the behavior of specific perturbation series. © 1996 The American Physical Society.

Utilizing a recently found solution to the problem of a spontaneously radiating atom with an extended center-of-mass wave function [K. Rza̧żewski and W. Żakowicz, J. Phys. B 25, L319 (1992)] it is shown, for nonrelativistic atomic velocities, that the field density matrix is a statistical mixture of parts corresponding to emission from different positions within the wave packet. © 1996 The American Physical Society.

We investigate the time T a quantum computer requires to factorize a given number dependent on the number of bits L required to represent this number. We stress the fact that in most cases one has to take into account that the execution time of a single quantum gate is related to the decoherence time of the quantum bits (qubits) that are involved in the computation. Although exhibited here only for special systems, this interdependence of decoherence and computation time seems to be a restriction in many current models for quantum computers and leads to the result that the computation time T scales much stronger with L than previously expected. © 1996 The American Physical Society.

A relativistic oscillator whose period is independent of its energy is of great fundamental importance in both relativistic classical mechanics and relativistic quantum mechanics. In this work theoretical and computational investigations of such a constant period oscillator are reported, with emphasis on basic mathematical and physical properties of the oscillator. © 1996 The American Physical Society.

The theory of discrete Wigner functions and of discrete quantum-state tomography [U. Leonhardt, Phys. Rev. Lett. 74, 4101 (1995)] is studied in more detail guided by the picture of precession tomography. Odd- and even-dimensional systems (angular momenta and spins, bosons, and fermions) are considered separately. Relations between simple number theory and the quantum mechanics of finite-dimensional systems are pointed out. In particular, the multicomplementarity of the precession states distinguishes prime dimensions from composite ones. © 1996 The American Physical Society.

Two-color resonance ionization spectroscopies of Pb, even parity, J=0, 1, and 2 levels were performed and their term values were analyzed with multichannel quantum defect theory. We have observed 6pnp(1/2,1/2${)}_0$ (28≤n≤50), 6p7p(3/2,3/2${)}_0$, 6pnp(1/2,3/2${)}_1$ (14≤n≤27), 6pnp(1/2,3/2${)}_2$ (42≤n≤54), and 6pnf 1/2[5/2${]}_2$ (28≤n≤51). Fitting multichannel quantum defect theory (MQDT) parameters to minimize deviation between the observed and theoretical energy values, we determined quantum defects ${\mathrm{\mu }}_{\mathrm{\alpha }}$ and unitary matrix elements ${\mathit{U}}_{\mathit{i}\mathrm{\alpha }}$ for J=0, 1, and 2 even-parity levels. Calculating theoretical energy values and determining their assignment with MQDT, we assigned observed levels and predicted unobserved levels and perturbers. Admixture coefficients for perturbing levels of J=0, 1, and 2 were calculated in order to ensure their assignments. © 1996 The American Physical Society.

This paper comprises a comparison of experimental methods used for determining fine-structure splittings in negative atomic ions. The comparison is based on experimental data for the fine-structure splittings of the 4${\mathit{p}}^5$${\mathrm{}}^2$P term of ${\mathrm{Se}}^{\mathrm{-}}$ and 5${\mathit{p}}^5$${\mathrm{}}^2$P term of ${\mathrm{Te}}^{\mathrm{-}}$ obtained by single-photon detachment and three-photon detachment in a Raman coupling scheme. The result for the J=3/2-1/2 splitting in ${\mathrm{Se}}^{\mathrm{-}}$ is found to be 2278.2(2) ${\mathrm{cm}}^{\mathrm{-}1}$, while the J=3/2-1/2 splitting in ${\mathrm{Te}}^{\mathrm{-}}$ is 5004.6(5) ${\mathrm{cm}}^{\mathrm{-}1}$. A variety of experimental approaches to fine-structure measurements are briefly discussed. In many atomic negative ions the perspectives for improvements in the determination of fine-structure splittings are in the range of two to three orders of magnitude. © 1996 The American Physical Society.

A renormalized expression for the gauge invariant set of three second-order bound self-energy graphs is obtained. A nontrivial extra counterterm is found that is important for cancellation of infrared divergences. Also, a different type of infrared divergences specific to the bound-state QED is discussed and its cancellation is traced explicitly. The expression obtained is convenient for the application of the partial-wave renormalization technique. © 1996 The American Physical Society.