A comprehensive theoretical study of the charge transfer to hydrogen 1s, 2s, and 2p states and excitation to helium 2 ${}_{}{}^1{}_{}{}^{}S$ and 2 ${}_{}{}^1{}_{}{}^{}P$ states in p-He collisions in the 1–100 keV energy region is presented. This study is the first demonstration of the application of the recently developed atomic-orbital–molecular-orbital matching procedure to two-electron collision systems. In this method the time-dependent electronic wave function is expanded in terms of traveling atomic orbitals of the two collision centers at large internuclear separation which is matched to the solution in the inner region where it is expanded in terms of molecular orbitals without translation factors. It is shown that the results from the present theoretical method are in good agreement with experimental measurements of (1) total charge-transfer cross sections to 1s, 2s, and 2p states, (2) charge-transfer probabilities at small impact parameters or large scattering angles, and (3) excitation cross sections to 2 ${}_{}{}^1{}_{}{}^{}S$ and 2 ${}_{}{}^1{}_{}{}^{}P$ states above 20 keV.

The technique of two-photon excited fluorescence has been used to measure the cross section for the 3p ${\mathrm{}}^3$$P_2$,1,0←2p ${\mathrm{}}^3$${\mathrm{P}}_2$ transition in atomic oxygen. Excitation was monitored by observing fluorescence at 845 nm from the 3p ${\mathrm{}}^3$$P_2$,1,0→3s ${\mathrm{}}^3$${\mathrm{S}}_1$ transition. Spontaneous Raman scattering from ${\mathrm{H}}_2$ was used to calibrate the fluorescence collection system. The spatial and temporal profiles of the exciting dye-laser pulses were carefully measured in a mildly focused excitation geometry, allowing the integrated two-photon absorption coefficient to be measured absolutely. The integrated absorption coefficient is the product of an atomic quantity, ${\mathcal{J}}_{J\mathcal{’}}$${\sigma }_0^{\mathrm{}\left(2\right)\mathrm{}}$(J’←2), and the second-order correlation function of the laser field, $G^{\mathrm{}\left(2\right)\mathrm{}}$. The experimental value of this coefficient is ${\mathcal{J}}_{\mathrm{J}\mathcal{’}}$${\mathrm{\sigma }}_0^{\mathrm{}\left(2\right)\mathrm{}}$(J’←2)${\mathrm{G}}^{\mathrm{}\left(2\right)\mathrm{}}$ =(2.66±0.80)×${10}^{\mathrm{-}35}$ ${\mathrm{cm}}^4$. If chaotic photon statistics are assumed (i.e., $G^{\mathrm{}\left(2\right)\mathrm{}}$=2), excellent agreement with the calculations presented in the companion paper is obtained. The cross section for photoionization by a third, identical 226-nm photon has been determined by measuring the absolute number of ions produced per laser pulse. The excited-state photoionization cross section is ${\sigma }_{\mathrm{pi}=(5.3\mathrm{}\pm 2.0)\times {10}^{\mathrm{-}19}}$ ${\mathrm{cm}}^2$.

Two-photon absorption cross sections for transitions from the O${(\mathrm{}}^3$P) ground electronic state to the 3p ${}^3$P, 4p ${}^3$P, and the autoionizing ${\mathrm{O}}^{+}$(${\mathrm{}}^2$D)3p’ and ${\mathrm{O}}^{+}$(${\mathrm{}}^2$P)3p’’ states have been calculated by explicit evaluation of the perturbation-theory summation using matrix elements calculated from configuration-interaction wave functions and sum rules to correct for truncation. The role of different contributions in the summation has been analyzed. For the 3p ${}^3$P state, a cross section of ${\mathcal{J}}_{J\mathcal{’}}$${\sigma }_0^{\mathrm{}\left(2\right)\mathrm{}}$(J’←J) of (1.319±0.2)×${10}^{\mathrm{-}35}$ ${\mathrm{cm}}^4$ has been obtained, which is in excellent agreement with the experimental value for the quantity ${\mathcal{J}}_{J\mathcal{’}}$${\sigma }_0^{\mathrm{}\left(2\right)\mathrm{}}$(J’←2)$G^{\mathrm{}\left(2\right)\mathrm{}}$ =(2.66±0.80)×${10}^{\mathrm{-}35}$ ${\mathrm{cm}}^4$, given in the companion paper, if the photon statistical factor, $G^{\mathrm{}\left(2\right)\mathrm{}}$, is evaluated in the chaotic field limit ($G^{\mathrm{}\left(2\right)\mathrm{}}$=2).

This work reports the five-photon ionization of the ${\mathrm{H}}_2$ molecule via the four-photon transitions (E,F ${\mathrm{}}^1$${\Sigma }_g^{+}$, $v_E$=1,2,3)←(X ${\mathrm{}}^1$${\Sigma }_g^{+}$, v=0), in the ${10}^{11}$-W/${\mathrm{cm}}^2$ laser-intensity range. The resulting ${\mathrm{H}}^{+}$- and ${\mathrm{H}}_2$${\mathrm{}}^{+}$-ion spectra exhibit essentially the Q(J) resonances, and the ratio [${\mathrm{H}}^{+}$]/[${\mathrm{H}}_2$${\mathrm{}}^{+}$] is found to increase drastically with the vibrational quantum number $v_E$. The photoelectron energy spectra are dominated by the peak corresponding to the five-photon ionization of ${\mathrm{H}}_2$ leading to ${\mathrm{H}}_2$${\mathrm{}}^{+}$ ions in the $v_{+}$=$v_E$ vibrational level. The photodissociation of ${\mathrm{H}}_2$${\mathrm{}}^{+}$ is found to be the only process which forms ${\mathrm{H}}^{+}$. In addition, we report—for the first time, to our knowledge—the absorption by a molecule of an extra photon above the ionization potential, when the laser intensity is increased up to 7×${10}^{11}$ W/${\mathrm{cm}}^2$.

We report an application of our previously developed model for determining the probabilities P(${\alpha }_N$,$N_A$) of emitting $N_A$ Auger electrons and the probabilities P(${\alpha }_N$,${\beta }_N$→${\gamma }_N$) of the radiative transitions ${\beta }_N$→${\gamma }_N$ during the cascade decay process following the creation of an arbitrary distribution ${\alpha }_N$ of N vacancies among the nl subshells of an atomic system. Particular emphasis has been given to the effects of single inner-shell vacancies, which may be created by energetic charged-particle collisions or by x-ray photoionization. Results of calculations are presented for single inner-shell electron ionization of iron ions from the neutral atom through the heliumlike ionization state, taking into account all of the Auger, Coster-Kronig, and electric dipole radiative transitions which can occur during the inner-shell vacancy-cascade process. The importance of the multiple ionization which results from Auger electron emission and of the x-ray satellite line radiation which is produced by the radiative decay of multiple-vacancy states is investigated for inner-shell electron ionization by electron collisions and by photon impacts.

Collective emission in a resonant cavity was observed between Ba Rydberg levels. The superradiant decays were controlled by varying the distance of the mirrors of the cavity. The superradiant character of the emission was checked by studying the variation of pulse height versus delay. The dependence between pulse height and delay was explained by modified Maxwell-Bloch equations.

A formulation has been developed for the evaluation of the matrix representation, in sets of ‖${\mathrm{SM}}_S$${\mathrm{LM}}_L$), ‖${\mathrm{SLJM}}_J$), or ‖${\mathrm{JIFM}}_F$) functions (as required), of the complete atomic Hamiltonian operator consisting of the electronic, the SL-nonsplitting (specific mass, mass variation, Darwin, spin-spin contact, and orbit-orbit) correction terms, and the fine- (spin-orbit and spin-spin dipole) and hyperfine-structure (magnetic dipole, electric quadrupole, and magnetic octupole) interactions. This formulation may be easily implemented in a computer program, appropriate for the accurate evaluation of the energy levels of any atomic system.

New experimental results for the doubly excited quartet levels in B?ize -2 roman III— have been obtained using the beam-foil excitation technique. Both wavelengths and lifetimes are reported and the wavelength accuracy is higher than that in most previous investigations. A remeasurement of the 2s2p ${\mathrm{}}^4$$P^o$ –2$p^2$ ${\mathrm{}}^4$P transition yields a wavelength of 1702.1±0.1 Å, which confirms the most accurate theoretical value 1701.8 Å. The important 2s3s ${\mathrm{}}^4$S–2s3p ${\mathrm{}}^4$$P^o$ transition has been observed for the first time. The new findings are discussed in relation to recent calculations.

The multiphoton ionization of atomic hydrogen is studied by means of photoelectron spectroscopy. The order of nonlinearity of the ionization process via the 3p resonance is measured for intensities in the ${10}^{11}$-W/${\mathrm{cm}}^2$ range, revealing that the three-photon excitation step is rate limiting. What may be the first measurement on ‘‘above-threshold ionization’’ (ATI) of atomic hydrogen is reported, performed as a function of the real momentary light intensity. Agreement between the measured relative ATI yield and the theoretically predicted one is within 10%. Possibilities to extend the measurements into the regime where perturbation theory breaks down are investigated by means of a two-color experiment.

We report a study of the Sturmian expansion of Green’s function and its convergence properties in the complex energy plane. We take as a model for our study multiphoton ionization of hydrogen. Convergence difficulties arise from the fact that the stationary wave of the outgoing photoelectron contains both outgoing and ingoing parts, whereas the Sturmian functions have outgoing wave character and so do not provide an expansion of the ingoing part of the photoelectron wave. We show how this difficulty can be overcome. We have tested the method for N-photon ionization of hydrogen when (N-1)-photon ionization is possible, with N=2–5, and for three-photon ionization when ordinary photoionization is possible.

The dynamics of a cw pumped, multimode dye laser system have been experimentally investigated by measuring the mode correlation times $t_{\mathrm{mode}}$, the second-order dimension $D_2$ of the attractor of the system, and the corresponding second-order entropy $K_2$. Dynamical instabilities have been observed as discontinuous changes of $t_{\mathrm{mode}}$, $D_2$, and $K_2$ at distinct values of the spectral power density P/Δλ. Over the whole investigated range of P/Δλ, the analysis of the experimental data yields sufficient conditions for deterministic chaos. The dimensionality of the system and its degree of chaos have been found to depend on the spectral power density. The contributions of stochastic and of chaotic processes to the limited mode correlation time have been unraveled.

Spectra with extremely narrow lines are observed, under suitable conditions, in double-modulation electron spin resonance, carried out in systems with inhomogeneously broadened lines. The saturation curve of these lines is experimentally determined. It is shown, in terms of the response to resonant multiple irradiations, that the observed spectrum corresponds to a three-photon process. We demonstrate that the very narrow line shape is not related to the $T_2$ relaxation time of the single spin packet but rather to the longitudinal relaxation time of the spin system. Furthermore, we explain how the average over the Larmor frequencies of the single spin packets does not broaden the observed line. Connections of this phenomenon with the longitudinally detected electron spin resonance are pointed out. According to the interpretation given here, this effect turns out to be very useful and simple in determining the longitudinal relaxation time.

Conservation of commutator brackets imposes constraints on the response of linear systems. From these constraints the minimum uncertainties of in-phase and quadrature field components in linearized parametric and oscillator systems can be determined. In this paper, a cavity containing a ‘‘degenerate parametric wall’’ is analyzed and the resulting equations are found to be identical with those of a saturated oscillator. The ideal parametric wall resonator has lower noise than the saturated oscillator. Feedback is put onto an oscillator formed by the parametric wall, and onto the saturated oscillator, by degenerate heterodyne (homodyne) detection of the oscillator output. It is shown in both cases that the field fluctuations incident upon the photodetector in the feedback loop are ‘‘squeezed,’’ i.e., the photodetector current fluctuation level is below shot noise. A semiclassical analysis arrives at the same expression for the detector current fluctuations in the limit of a highly saturated oscillator, thus permitting an alternative interpretation of these results. However, a quantum nondemolition measurement via a nonlinear interferometer ‘‘extracts’’ the squeezed states, predicted by the quantum analysis, from the feedback loop. This result has no semiclassical interpretation.

Relationships between density matrices and densities or between operators and local potentials are considered for model problems defined by the introduction of basis sets. Some properties depend only on the space spanned by the basis while others depend on a particular choice of basis functions. Linear-dependency conditions play a critical role. In a model problem defined by a basis with all products linearly independent, the effect of any operator can be reproduced by a local potential, but any complete basis must have linearly dependent products. A one-electron density matrix or single-determinant wave function can be determined from the density (or experimental measurements sensitive only to the density) in the model problem defined by a basis with linearly independent products, but not otherwise. A simple example illustrates some of the general results.

A quantum theory of degenerate four-wave mixing is presented in which the atomic medium consists of stationary four-level atoms, each with three degenerate excited states, and the interacting light beams are allowed to be in different states of polarization. This vector-field theory differs from the scalar-field theory of Reid and Walls [Phys. Rev. A 31, 1622 (1985)] in that there are new atomic variables in the Langevin equations which are related to the induced coherence between the upper atomic states. It is found, for the assumed set of atomic levels, that this seemingly different mechanism of four-wave-mixing gain does not circumvent the degrading effect of spontaneous emission on squeezing obtainable via degenerate four-wave mixing. The theory is applied to both forward and backward degenerate four-wave mixing with nearly collinear geometry, and specialized to the case in which the polarization states of the two pump modes are mutually orthogonal. It is found that for both forward and backward configurations, the range of pump intensity for which squeezing can be achieved in the vector-field case is larger than that in the scalar-field case, and the maximum amount of squeezing obtainable at a particular pump detuning is comparable in both cases.

The frequency dependence of the second hyperpolarizability (γ) of ${\mathrm{CH}}_4$ has been measured in the visible (477<λ<672 nm) by means of gas-phase electric-field-induced second-harmonic generation (ESHG). No resonances due to vibrational overtones are observed. Comparison of the ESHG results with the results of several other third-order nonlinear-optics experiments indicates that vibrational contributions to ${\gamma }_{{\mathrm{CH}}_4}$ are negligible.

The problem of periodicity windows appearing within the chaotic domain of the hybrid bistable device is considered. New results concerning the frequency-locked waveforms are presented in relation to their stability and their long-lived transients. We also present numerical and experimental results concerning new periodicity windows for a small range of values of the delay (1<${\tau }_D$<7). These waveforms appear to be the continuous-time counterparts of the discrete cycles predicted by the one-dimensional model.

We study the transient fluorescence spectra of two-level atoms driven by a strong optical field when the atoms are initially prepared in pure dressed states of the atom-field Hamiltonian. Spectra obtained here differ qualitatively from those observed in the steady state. In the case of steady-state resonant excitation, a three-peaked spectrum symmetric about the laser frequency is obtained; with pure-dressed-state preparation, the symmetry of the spectrum about the driving field is broken—one side peak is initially enhanced and the other is initially suppressed. Furthermore, the temporal oscillations of fluorescence intensity observed in previous calculations of transient fluorescence spectra appropriate to atoms prepared in a superposition of dressed states [J. H. Eberly et al., J. Phys. B 13, 217 (1980)] are suppressed when pure-dressed-state preparation is considered.

We consider the nonlinear propagation of an intense short pulse of polarized light through a molecular medium with ground- and excited-state absorption, excited-state emission, and fluorescence from the excited state to the ground state and possibly to a lower-lying excited state. We incorporate the effects of saturation, field-induced alignment, and rotational diffusion of the molecules in the medium. Our approach uses a slowly varying envelope approximation for the light propagation and rate equations for the effective parallel and perpendicular (and higher-multipole) population components of the molecular states. The time dependence of the anisotropy of the fluorescence occurring after preparation of the medium by the intense short pulse is determined. We can treat propagation through an optically nonthin medium wherein the intensity of the pulse decreases while propagating through the medium. An example of a 100-ps pulse propagating through a sample of Rhodamine-6G is presented. We compare our method with others used to describe intense-short-pulse propagation in molecular media.

The use of four pulsed rf fields for the excitation of multiphoton resonances in a two-level system is investigated. A general theoretical description of the experiment is provided based on the Floquet formalism and application of basic conservation laws to the overall transition process. The predictions of the theory are compared with computer simulations of the time evolution of the magnetization according to the exact time-dependent Hamiltonian. It is shown that N-photon resonances occur when the fields are applied at frequencies ±kω and ±lω from the Larmor frequency, where k and l are positive integers having no common factors and where 0≤k<l, k+l=N. For any resonance k photons are taken from the outer field pair and l are taken from the inner field pair. A total of 2[(l+k)!]/(k!l!) mutually interfering transition pathways exist for the overall process and the resultant magnitude of the effective N-photon field is very sensitive to the relative initial phases of the rf fields. The spiral motion observed for multiphoton resonances induced by double-frequency irradiation is absent here when the field intensities are symmetrical. In addition, the fraction of total applied rf intensity available for multiphoton pumping is considerably greater than for two fields. Phase cycling to enhance detection of multiphoton effects and multiphoton spin locking are considered.