We show both theoretically and experimentally that fluctuations of a weak probe beam are increased above the coherent-state shot-noise level as the beam interacts with a strong degenerate pump beam in an atomic vapor. The origin of this noise amplification process is the two-beam-coupling process between the pump beam and the vacuum sidebands of the probe beam. The major contribution to this excess noise arises from the quantum fluctuations of the atomic medium that are induced by the pump beam. We believe that this mechanism can be important in preventing the reduction of noise below the quantum-noise limit in experiments that utilize atomic vapors.

This paper describes our first-principles derivation of the Hamiltonian for the calculation of the bound states for a particle with a spatially varying mass in an arbitrary potential well. Our approach is based on the Feynman path-integral technique and results in a Hermitian form of the Schrödinger equation that conserves current at the boundary. We deduced the correct operator ordering for the Hamiltonian and found a correctional term that can be viewed as an effective potential.

The expression for the light-scattering intensity is deduced using the general perturbation expansion for a stationary solution of the Liouville equation. The principal importance of translational symmetry for coherent spectroscopy is rigorously shown. The expressions for the degenerate four-wave mixing (DFWM) signal intensity as well as for its polarization are derived in the case of fast translational relaxation (Dicke narrowing). The instructive relationship between the index of refraction, the absorption spectrum, and the DFWM is established.

A calculation of the vacuum-polarization contribution to the hyperfine splitting for hydrogenlike atoms is presented. The extended nuclear charge distribution is taken into account. For the experimentally interesting case ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}_{}^{82+}{}_{}{}^{}$ we predict a Δλ=-1.6 nm shift for the transition wavelength of the ground-state hyperfine splitting.

High-resolution measurements of the photoinduced L x-ray spectrum of metallic uranium were performed with a transmission-type bent-crystal spectrometer. Linewidths of 32 L x-ray emission lines were extracted. Nonlifetime broadening effects, such as multiple-vacancy configuration states and multiplet splitting, that influence the line profiles are discussed.

A pair of closely lying states of opposite parity and the same total electronic angular momentum (J=10) at 19797.96 ${\mathrm{cm}}^{\mathrm{-}1}$ in dysprosium is experimentally investigated with the goal of evaluating parameters relevant to parity and parity–time-reversal violation experiments. An atomic beam apparatus is used. The states of interest are populated with a sequence of two laser pulses, and a third laser pulse and fluorescence detection are used to probe the state population. Their lifetimes are determined from the dependence of the fluorescence signal on the time delay between the pump and probe pulses. The lifetime of the even-parity state was also measured by a different method involving detection of cascade fluorescence. Spectroscopy of radio-frequency E1 transitions between the opposite-parity states is performed when one of the states is populated and the population of the other is probed. This determines precise energy separations between various isotope and hyperfine structure components, and allows extraction of the corresponding isotope shift and hyperfine structure parameters. Electric polarizability is determined from radio-frequency line shapes in the presence of a dc electric field. As part of the preparation of a parity violation experiment, level-crossing signals which occur when various Zeeman components of the closest hyperfine components (isotope 163, F=10.5; initial separation 3.1 MHz) are brought together in the presence of collinear electric and magnetic fields were studied. These measurements provide an independent determination of the E1 matrix element between the opposite-parity states. In addition, lifetimes, isotope, and hyperfine structure of other dysprosium states are obtained and a number of narrow autoionization resonances (Γ<10 ${\mathrm{cm}}^{\mathrm{-}1}$) are observed.

The radiative correction to the Lamb shift of order ${\mathrm{\alpha }}^2$(Zα${)}^5$m induced by the light-by-light scattering insertion in external photons is obtained. This contribution turns out to be equal to -0.122(2)${\mathrm{\alpha }}^2$[(Zα${)}^5$/(π${\mathit{n}}^3$)](${\mathit{m}}_{\mathit{r}}$/m${)}^3$m. Combining this contribution with our previous results we obtain the complete correction of order ${\mathrm{\alpha }}^2$(Zα${)}^5$m induced by all diagrams with closed electron loops. This correction is 37.3(1) kHz and 4.67(1) kHz for the 1S and 2S states in hydrogen, respectively.

Local-density-approximation calculations of atomic structure are useful for the description of atoms and ions in plasmas. The large number of different atomic configurations that exist in typical plasmas leads one to consider the expression of total energies in terms of a Taylor series in the orbital occupation numbers. Two schemes for computing the second derivative Taylor-series coefficients are given; the second, and better one, uses the linear response method developed by Zangwill and Soven [Phys. Rev. A 21, 1561 (1980)] for the calculation of optical response in atoms. A defect in the local-density approximation causes some second derivatives involving Rydberg orbitals to be infinite. This is corrected by using a modified local-density approximation that had previously been proposed [Phys. Rev. B 2, 244 (1970)].

Metastable multiply charged argon ions produced in, and extracted from, an electron cyclotron resonance ion source were captured from the beam into an electrostatic (Kingdon) ion trap by rapidly pulsing the potential of the central wire relative to the cylinder. The ions were selected on a charge-to-mass ratio basis before capture. Photons emitted in magnetic-dipole and electric-quadrupole transitions from levels with lifetimes exceeding 5 ms were selected by wavelength and recorded vs ion storage time in the trap. Also, ions were counted after ejection following a preselected storage time in the trap, using a microchannel plate detector. These signals were studied as a function of the pressure of typical residual gases. Extrapolation to zero pressure enabled the extraction of the lifetimes τ of metastable levels from four different configurations of the type ${\mathit{ns}}^2$${\mathit{np}}^{\mathit{k}}$ with n=2 or 3 and k=3, 4, or 5. Our experimental results are τ(${\mathrm{Ar}}^{2+}$, 3${\mathit{s}}^2$3${\mathit{p}}^4$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$)=159.7±9.7-38.4 ms, τ(${\mathrm{Ar}}^{3+}$, 3${\mathit{s}}^2$3${\mathit{p}}^3$ ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$)=243±73-79 ms, τ(${\mathrm{Ar}}^{9+}$, 2${\mathit{s}}^2$2${\mathit{p}}^5$ ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{1/2}$)=8.53±0.24-0.17 ms, and τ(${\mathrm{Ar}}^{10+}$, 2${\mathit{s}}^2$2${\mathit{p}}^4$ ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$)=14.8±1.1-0.48 ms. Both statistical errors and a possible error associated with a systematic correction are given for each measurement. These results are compared with the predictions of theoretical calculations, many previously untested. The basis of the measurement technique is discussed in some detail. The technique is expected to be applicable to ions in a large range of charge states from a variety of low-energy ion sources, and to levels with transitions from the near-infrared to the deep-ultraviolet or soft-x-ray range.

A generalization of Weinberg’s nonlinear quantum theory is used to model a reported violation of the predictions of orthodox quantum theory.

We discuss the evaluation of matrix elements of spin-dependent operators expressed in terms of products of up to four U(n) generators. Such operators arise in connection with spin-orbit, spin–other-orbit, and spin-spin interaction operators in the Pauli-Breit Hamiltonian discussed recently by Gould and Battle [J. Chem. Phys. 98, 8843 (1993); 99, 5983 (1993)]. Those authors point out the need for closed-form expressions suitable for numeric calculations. In this work we enumerate the many factors which arise in molecular configuration interaction and complex-atom electronic-structure calculations. We also present numerical examples to illustrate the use of the methods.

An exact formal Kohn-Sham scheme is derived with the help of perturbation theory. Through the introduction of a basis set this Kohn-Sham scheme can be used to perform, in principle, exact Kohn-Sham calculations. As a demonstration, only zeroth- and first-order terms in the underlying perturbation theory are considered. As a result an exact basis set ‘‘exchange-only’’ method is obtained. The presented perturbation theory expansions of the exchange-correlation energy and potential may serve as a starting point for the development of new approximate exchange-correlation functionals based on Kohn-Sham orbitals and eigenvalues and may be used to check conventional exchange-correlation functionals. The formal structures of the ab initio and the introduced density-functional treatment of electronic systems are compared.

A dipole radiative rate for metastable antiprotonic helium is estimated using an existing Born-Oppenheimer wave function and the velocity form of the transition matrix element. This rate is 4.7 times faster than the one computed using the length form. It is suggested that the velocity form gives a rate that is easier to reconcile with experiment, as interpreted with accepted notions about exotic atom formation.

Natural radiative lifetimes of the states in the highly perturbed 5${\mathit{d}}^{10}$np ${}_{}{}^2{}_{}{}^{}$P sequence in neutral gold, Au i, for n=6–9, as well as of four of the perturbing 5${\mathit{d}}^9$6s6p ${}_{}{}^2{}_{}{}^{}$P states, have been measured. This was done by direct excitation from the ground state with short-pulse vacuum-ultraviolet laser light and time-resolved detection of the laser-induced fluorescence. We found the lifetimes to be τ(6p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{1/2}$)=6.2(2) ns, τ(6p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$)=4.7(2) ns, τ(7p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{1/2}$)=6.4(7) ns, τ(7p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$)=5.3(7) ns, τ(8p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{1/2}$)=63(3) ns, τ(8p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$)=24(2) ns, τ(9p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{1/2}$)=28(2) ns, and τ(9p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$)=75(4) ns. For the perturbing states (two states of each term have been observed) we found τ${(}^2$${\mathit{P}}_{1/2}$, 60 983.05 ${\mathrm{cm}}^{\mathrm{-}1}$)=17.5(10) ns, τ${(}^2$${\mathit{P}}_{1/2}$, 62 540.65 ${\mathrm{cm}}^{\mathrm{-}1}$)=6.7(7) ns, τ${(}^2$${\mathit{P}}_{3/2}$, 58 826.30 ${\mathrm{cm}}^{\mathrm{-}1}$)=2.1(15) ns, and τ${(}^2$${\mathit{P}}_{3/2}$, 63 005.62 ${\mathrm{cm}}^{\mathrm{-}1}$)=2.7(15) ns. Furthermore, we have investigated the hyperfine structure of the 6p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$ state.

The transverse relaxation of the muon spin in muonium due to electron spin exchange with a polarized spin-1/2 medium is investigated. Stochastic calculations, which assume that spin exchange is a Poisson process, are carried out for the case where the electron spin polarization of the medium is on the same axis as the applied field. Two precession signals of muonium observed in intermediate fields (B>30 G) are shown to have different relaxation rates which depend on the polarization of the medium. Furthermore, the precession frequencies are shifted by an amount which depends on the spin-nonflip rate. From the two relaxation rates and the frequency shift in intermediate fields, one can determine (i) the encounter rate of muonium and the paramagnetic species, (ii) the polarization of the medium, and most importantly (iii) the quantum-mechanical phase shift (and its sign) associated with the potential energy difference between electron singlet and triplet encounters. Effects of spin-nonflip collisions on spin dynamics are discussed for non-Poisson as well as Poisson processes. In unpolarized media, the time evolution of the muon spin in muonium is not influenced by spin-nonflip collisions, if the collision process is Poissonian. This seemingly obvious statement is not true anymore in non-Poissonian processes, i.e., it is necessary to specify both spin-flip and spin-nonflip rates to fully characterize spin dynamics.

We perform LCAO (linear combination of atomic orbitals) calculations for the ground state of the Yukawa potential V(r)=-(${\mathit{e}}^2$/r)${\mathit{e}}^{\mathrm{-}\mathit{q}\mathit{r}}$ as a function of the screening parameter q. We obtain the best variational result so far for the ground-state energy ${\mathit{E}}_0$ as a function of q. We also obtain the critical exponents of both the probability density at the origin and the ground-state energy as functions of (q-${\mathit{q}}_{\mathit{c}}$), where ${\mathit{q}}_{\mathit{c}}$ is the critical q above which V(r) does not have a bound state. The use of the critical exponents permits the so far most precise determination of ${\mathit{q}}_{\mathit{c}}$, ${\mathit{q}}_{\mathit{c}}$=1.190 612 27±0.000 000 04. We also show that it is possible to use the LCAO calculations as a tool to determine the analytical form of very precise variational wave functions. We obtain, in such a way, the wave function ψ=(${\mathit{e}}^{\mathrm{-}\mathit{a}\mathit{r}}$-${\mathit{e}}^{\mathrm{-}\mathit{b}\mathit{r}}$)/r+${\mathit{e}}^{\mathrm{-}\mathit{b}\mathit{r}}$/(r+α). This variational wave function has a bound-unbound transition at ${\mathit{q}}_{\mathit{c}}$=1.190 610 74.

We present an experimental study of the entangled two-photon polarization states in type-II optical parametric down-conversion. It is interesting to see that the polarization entanglement depends on the detection spectral bandwidth, i.e., the bandwidth of the spectral filters placed in front of the detectors. The entanglement is also dependent on the length of the down-conversion crystal. A simple quantum model is provided to explain these phenomena.

Positronium formation in positron-hydrogen collisions is studied by the coupled-channel method based on the hyperspherical-coordinate representation. The coupled equations are solved by the diabatic-by-sector method expanding the scattering wave function in terms of sector adiabatic states associated with H(n=1–3) and Ps(n=1,2) in the separated-atom limit. In the energy range of the Ore gap, even the two-state expansion shows a good convergence, and both the formation and the elastic cross sections agree well with the existing elaborate variational calculations. As the collision energy exceeds the Ore gap, the contribution from the level associated with H(n=2) becomes significant. The present s-wave formation cross section does not show the resonance structures, which were predicted recently by some theoretical calculations, above the ionization threshold of the hydrogen atom.

The maximum-entropy formalism is used to obtain approximations to the spherically averaged electron-pair density h(u) in terms of the first few interelectronic moments. This method leads to the least biased results by the information not used. In particular, tight analytical and numerical approximations to the electron-electron repulsion energy ${\mathit{E}}_{\mathit{e}\mathit{e}}$ and to the central electron-pair density h(0) are obtained. Chebyshev inequalities are also applied to obtain bounds on h(u), showing the complementarity of both methods. For illustration, the accuracy of the bounds and approximations obtained are studied by means of Hylleraas-type wave functions.

Term energies are determined for the ground state and n=2 singlet states of heliumlike ions with nuclear charges in the range 4≤Z≤92. These calculations are based on the relativistic no-pair Hamiltonian which includes both the Coulomb interaction and the retarded Breit interaction. Single-particle wave functions are expanded in a B-spline basis constructed from Dirac-Coulomb orbitals restricted to a finite cavity. The Hamiltonian matrix is evaluated and Davidson’s method is used to determine the lowest few eigenenergies and eigenfunctions for each angular symmetry. Quantum electrodynamic corrections are also calculated. We find good, but not precise, agreement between theory and experiment for the Kα x-ray energies. It is argued that high-precision x-ray measurements for highly charged ions are needed to further test the theory.