The factorization method of Bar-Shalom, Klapisch, and Oreg [Phys. Rev. A 38, 1773 (1988)] is extended to relativistic-distorted-wave cross sections for ionization by electron impact. This leads to a very great simplification for complex ions. In particular, when mixing is confined to the states in a complex (having the same set of n values, parity, and J value), the ionization cross section takes the form of a summation over states of the product of a readily calculated quantity that depends only on target-ion properties, such as mixing coefficients and angular momenta, and a cross section having exactly the same form as a hydrogenic cross section except that the radial functions should be calculated using the appropriate potential for the ion being considered. Similar results are obtained for intermediate coupling using LS-coupling notation and for totally nonrelativistic calculations. Only slightly more complicated formulas apply when mixing is included outside a complex. It is also noted that similar expressions apply for photoionization. Sample numerical results are obtained and compared with relativistic calculations of Moores and Pindzola [Phys. Rev. A 42, 5384 (1990)]. Quite good agreement is obtained when mixing is included among the same set of states.

We report the results of a series of pulsed and cw laser experiments which measure spontaneous and effective lifetimes of the Cs(5DJ) levels and investigate excitation-transfer collisions involving Cs(5DJ) atoms and ground-state-cesium perturbers. With cw excitation of the dipole-forbidden but electric-quadrupole-allowed 6S1/2→5D5/2 transition, we monitor the ratio of sensitized to direct fluorescence, i.e., I5D3/2→6P1/2/I5D5/2→6P3/2. A rate-equation analysis of these data yields values for the Cs(5D5/2)+Cs(6S)→Cs(5D3/2)+Cs(6S) excitation-transfer rate, and for the rate of quenching of Cs(5D) by ground-state perturbers. The role of out-of-multiplet quenching is discussed at length, and we have demonstrated that quenching by ground-state atoms dominates over that by cesium dimers under these conditions. In the pulsed-laser experiments, the temporal evolution of the 5DJ→6S and cascade 6PJ′→6S fluorescence was observed following either direct forbidden-line pumping of one fine-structure level, or indirect excitation of both fine-structure levels (i.e., molecular excitation followed by predissociation). Analysis of the buildup and decay rates of the various levels as a function of cesium density yields values for the natural lifetimes of the Cs(5DJ) levels, as well as for the excitation transfer and quenching rates. Best values for the lifetimes and cross sections for Cs-Cs collisions obtained from these combined experiments are τ5D=1250±115 ns, σ5/2→3/2=36±8 Å2, and σ5D=30±3 Å2. In addition, numbers for the 6P level-quenching cross sections due to collisions with Cs atoms and Cs2 molecules, respectively, were obtained: σ6P(Cs)=6.6±3.0 Å2 and σ6P(Cs2)=863±260 Å2. In the discussion, we show how these new values can be used to reconcile the seemingly discrepant results of several previous studies.

The Auger decay anisotropy parameter ${\mathrm{\alpha }}_2$ of angular distribution has been calculated for the ${\mathit{M}}_{45}$-NN transitions in Kr and ${\mathit{M}}_{45\mathrm{-}}$NN and ${\mathit{N}}_{45\mathrm{-}}$OO transitions in Xe atoms using the multiconfiguration Dirac-Fock model in intermediate coupling with configuration interaction. For transitions involving many contributing partial waves and leading to the strongly mixed final ionic states in intermediate coupling, the effects of relativity and spin-orbit interaction are found to be quite important for the calculations of ${\mathrm{\alpha }}_2$ values. The existing discrepancies between theory and experiment are largely removed by the present relativistic intermediate coupling calculations.

An investigation has been made, for the case of octupole transitions, of the dependence of the partial-collision strength on the orbital angular momentum of the colliding electron. It is shown that, similar to the dipole and quadrupole transitions, the sum over partial-collision strengths is asymptotic to a geometric series of common ratio ${\mathit{E}}_{\mathit{j}}$/${\mathit{E}}_{\mathit{i}}$, where ${\mathit{E}}_{\mathit{i}}$ and ${\mathit{E}}_{\mathit{j}}$ are the initial and final energies of the colliding electron, respectively. For large incident energies (${\mathit{E}}_{\mathit{j}}$/${\mathit{E}}_{\mathit{i}}$∼1) the convergence of the sum to the geometric series is rather slow, since the geometric-series method only starts to become valid for large values of angular momentum. This difficulty is overcome by developing an alternative method in which the approximation is made that ${\mathit{E}}_{\mathit{j}}$/${\mathit{E}}_{\mathit{i}}$=1. An analytic formula is then obtained to estimate the contribution to the total-collision strength from large values of angular momentum. Results of partial- and total-collision strengths are presented for direct electric octupole transitions in ${\mathrm{Ca}}^{+}$ and ${\mathrm{Sr}}^{+}$.

Kinetic electron-emission yields γ from swift ion penetration of solids are proportional to the (electronic) stopping power γ∼β${\mathit{S}}^{\mathrm{*}}$, if the preequilibrium evolution of the charge and excitation states of the positively charged ions is taken into account. We show that the concept of the preequilibrium near-surface stopping ${\mathit{S}}^{\mathrm{*}}$ can be applied successfully to describe the dependence of the ion-induced electron yields on the projectile atomic number ${\mathit{Z}}_{\mathit{P}}$ and on the charge states ${\mathit{q}}_{\mathit{i}}$ of the incoming ions. We discuss the implementation of this concept into Schou’s transport theory after having presented a summary of recent results on the projectile- and charge-state dependence of forward and backward electron yields ${\gamma }_{\mathit{F}}$ and ${\gamma }_{\mathit{B}}$ and the Meckbach factor R=${\gamma }_{\mathit{F}}$/${\gamma }_{\mathit{B}}$. A simple extension of the yield equations is proposed and several assumptions are justified by investigating the ‘‘transport factor’’ β, the energy spectrum of directly ejected recoil electrons and the evolution of ionic charge state inside solids. Estimates of the energy-loss fraction leading to electron emission and the effective charges of the ions near the surface allow a quantitative description of the ${\mathit{Z}}_{\mathit{P}}$ dependence of the electron yields.

Proton-induced L x-ray spectra of heavy elements have been recorded with a Si(Li) x-ray spectrometer of accurately determined resolution function. The intrinsic widths of the Ll and L${\mathrm{\alpha }}_1$ lines were obtained by a nonlinear-least squares fitting procedure. L${\mathrm{\alpha }}_1$ widths agree with relativistic independent-particle-model (IPM) calculations, but Ll widths fall some 10–30 % below predictions. This indicates a strong influence of many-body effects on the decay of the 3s hole state; a similar influence is already well established for the 2s state. Relative intensities of the weak, electric-dipole-forbidden lines Lt and Ls are in good accord with IPM calculations.

The lifetime of the 3${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$–3s3p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ intersystem transition of magnesium has been measured by different authors; however, a noticeable discrepancy appears mostly between two groups of measurements. We have measured the ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ decay time constant in a metastable atomic beam with a combined laser-microwave excitation technique, based on the 1.5-m downstream detection of the fine-structure transition ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{1\mathrm{-}}^3$${\mathit{P}}_0$ (at 601 GHz) with and without laser optical pumping. Due to the decay of the ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ state, a population difference between ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ and ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$ levels arises before the interaction of the microwave radiation with the atomic beam allowing the observation of the ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{1\mathrm{-}}^3$${\mathit{P}}_0$ magnetic dipole transition; its intensity is then related to the ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ decay time constant. Afterwards, the ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ state is entirely depopulated through optical pumping just outside the beam exit. The microwave-induced transition intensity in this case is independent of the ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ decay constant, with all of the other parameters of the experiment being unchanged. The ratio between the microwave-induced transition probabilities in the two cases is sensibly dependent on the ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ lifetime, allowing a determination of its value unaffected by the knowledge of absolute parameters such as atomic flux and detection efficiency, whose evaluation at a sufficient degree of precision may be unreliable. The result of our measurement is τ${(}^3$${\mathit{P}}_1$)=5.1±0.7 ms, which is in good agreement with a group of experimental data previously reported in the literature and with theoretical predictions.

A finite-basis-set method is used to calculate relativistic and nonrelativistic binding energies of an electron in a static Coulomb field and in magnetic fields of arbitrary strength (0<B≤${10}^{13}$G). The basis set is composed of products of Slater- and Landau-type functions, and it contains the exact solutions at both the Coulomb limit (B=0) and the Landau limit (Z=0). Relativistic variational collapse is avoided and highly accurate results are obtained with the basis set. The relativistic corrections obtained for intense magnetic fields (B≳${10}^9$G) differ from the previous relativistic calculations based on the adiabatic approximations. It is found that the sign of the relativistic correction changes from negative to positive near B≊${10}^{11}$ G for the ground state and near B≊${10}^{10}$ G for the 2${\mathit{p}}_{3/2}$(μ=-3/2) excited state of hydrogen. The method is checked to be very accurate by means of the virial theorem, sum rules, and the relativistic low-B limit where comparison can be made with perturbation results. In the nonrelativistic limit of the Dirac equation, our results agree with other accurate nonrelativistic calculations available and with our own calculations based on the Schrödinger equation, which converge to more significant digits than previous calculations for the whole range of magnetic fields.

Microwave transitions between the neighboring levels that belong to the ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$, ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$, and ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$ Rydberg series of ytterbium are studied for the principal quantum number ranging from 33 to 57. The term values and the quantum defects are determined by means of the general Rydberg-Ritz formula. The determined quantum defects show large linear energy dependence. The Zeeman effect measured for three ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ and one ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$ Rydberg states under a weak external magnetic field is discussed.

We report observation of laser excitation of a narrow, magnetic-dipole-allowed, infrared transition in a single trapped ion. Quantum jumps of a ${\mathrm{Ba}}^{+}$ atom were observed using a diode laser tuned in resonance with the excited-state 5d ${}_{}{}^2{}_{}{}^{}$${\mathit{D}}_{3/2}$–5d ${}_{}{}^2{}_{}{}^{}$${\mathit{D}}_{5/2}$ transition at 12.48 μm. Single-ion resonance line shapes were obtained and a transition frequency of ν=24 012 033±11 MHz was determined. Calculated quantum jump rates of the D-D transition for the applied laser spectral brightness yield agreement with experimentally observed values.

Classically chaotic systems possess a proliferation of periodic orbits. This phenomenon was observed in a quantum system through measurements of the absorption spectrum of a hydrogen atom in a magnetic field. This paper gives a theoretical interpretation of the bifurcations of periodic or closed orbits of electrons in atoms in magnetic fields. We ask how new periodic orbits can be created out of existing ones or ‘‘out of nowhere’’ as the energy changes. Hamiltonian bifurcation theory provides the answer: it asserts the existence of just five typical types of bifurcation in conservative systems with two degrees of freedom. We show an example of each type. Every case we have examined falls into one of the patterns described by the theory.

The energy difference of triplet and singlet states due to exchange coupling, the energy levels, the ground binding state, and the wave functions is calculated for a hydrogen molecule in an ultrahigh magnetic field when the distance between the Landau levels eħH/mc exceeds the Coulomb unit (Rydberg) ${\mathit{me}}^4$/2${\mathrm{ħ}}^2$. The results are asymptotically exact at the interatomic distance R, which is large compared with the atomic size and for high magnetic fields. It is shown here that the triplet electron term has a minimum at large interatomic distances corresponding to the formation of the ground state of a stable ${\mathrm{H}}_2$ molecule. For the hydrogen molecule in an ultrahigh magnetic field, the energy of the singlet state also has a deep minimum at R<1, which is much higher than the triplet one and may be a metastable state only.

The sodium ${\mathit{D}}_2$ transition is resonantly excited by π-polarized, narrow-band laser radiation. The line polarization of the resulting fluorescence detected normally to the plane containing the electric-field vector of the radiation and its propagation direction, as well as the atomic beam, is measured as a function of radiation intensity and tuning. The data are compared to calculations from a quantum-electrodynamic theory which includes all participating energy states in the hyperfine representation. The quantitative agreement is very good.

When light from a laser is fully absorbed by an ideal detector, the detected current exhibits a fluctuation called here ‘‘photonic noise.’’ The spectral density of Iintensity noiseR, defined as the difference of the photonic-noise spectral density and a term corresponding to the shot-noise level, is negative for sub-Poissonian statistics. The usefulness of the relative-intensity-noise concept is that it is independent of any linear attenuation. A simple circuit theory of intensity noise based only on energy conservation and the Nyquist formula (zero-point fluctuation) leads to expressions of the spectral densities that agree with quantum theory even for sub-Poissonian photon statistics. When the optical gain and loss are frequency independent, the circuit theory reduces to a corpuscular theory that keeps track of the time rates of change of electron and photon numbers treated as continuous variables. Consideration is given to laser diodes in which the rate of electron-photon conversion depends nonlinearly on both the carrier and photon densities. The cross-spectral density between electrical-voltage and relative photonic fluctuations is independent of internal or external optical losses. Standard rate equations are inaccurate in the case of gain compression. Very general yet simple formulas for intensity noise are applied to room-temperature GaAs laser diodes, using recently calculated optical parameters.

Properties of the radiation fields in negative binomial states are investigated. The density matrix of the field is related to the density matrix ${\mathrm{\rho }}_{\mathit{c}}$ of the chaotic field via ${\mathit{a}}^{\mathit{s}}$${\mathrm{\rho }}_{\mathit{c}}$${\mathit{a}}^{\mathrm{°}\mathit{s}}$. Various quasiprobability distributions and the thermofield representation for negative binomial states of the field are derived. The production of negative binomial distribution in a number of nonlinear processes is demonstrated.

In this paper we theoretically investigate the behavior of a two-level atom in a lossless cavity driven by an external field. Using classical electrodynamics to describe the external field while quantizing the cavity field, we find that the cavity field is excited to a coherent state whose amplitude is equal to that of the external field, but shifted 180° in phase. This results in the disappearance of the atomic resonance fluorescence (i.e., the atom stops interacting with the fields). When we quantize the external field the effect persists. A fully quantized dressed-state approach provides some helpful insight and a nice analogy to another problem in which the resonance fluorescence vanishes.

The effect of squeezing on the degenerate parametric oscillator is studied. It is shown that when the ordinary-vacuum reservoir is replaced by a squeezed-vacuum reservoir, the maximum 50% limit of the second-order squeezing inside the cavity can be crossed. It is also shown that the mean number of photons increases considerably. An exact steady-state solution for the Fokker-Planck equation for the field mode is also presented. The photon distribution for the intracavity field and the higher-order variances have been obtained by using the solution of this equation.

We report experimental observation of multiphoton resonances and Bloch-Siegert shifts in a strongly driven classical two-level system. The system is an optical ring resonator, and the levels are two orthogonal linear polarizations. The Rabi frequency and the Bloch-Siegert shift were measured for both the one- and three-photon cases. Satisfactory agreement was achieved with theory developed for a quantum two-level system. The experiment demonstrates that these coherence phenomena can be observed in a purely classical system.

We analyze the collapse and revival phenomenon in the energy exchange of two field modes initially prepared in a Fock state, as well as their coherent superposition in the process of k-photon down-conversion with quantized pump. The influence of the presence of a Kerr-like medium is discussed.

In a finite ladder of states excited stepwise by a (laser) field with linearly increasing detunings described by the SU(2) group, loss rates are introduced that vary linearly with level number. The dynamical group of the model is identified to be scrR⊗SL(2,openC), with scrR an overall exponential dissipation factor. By using the representation theory of the SL(2,openC) group, the transition probability of flipping from one state to another is obtained in a simple formula generalizing the Majorana formula, which is valid for the coherent excitation only. For the case of the time-dependent driving field a SU(2), SU(1,1) coherent-state path-integral formalism is developed that leads to a Riccati equation for the matrix elements of the evolution operator.