A microwave-resonance optical detection technique has been used to study the charge exchange reaction in which 49-keV protons incident on nitrogen and hydrogen molecules form hydrogen atoms in the $n=3\mathrm{}$ state. Hydrogen atoms formed in the $n=3\mathrm{}$ state in the charge exchange cell pass through a radio-frequency field, and the Balmer-$\alpha$ light emitted by the atoms is monitored. Measurements are made with the microwave electric field both perpendicular and parallel to the direction of the proton beam and for light polarized both parallel and perpendicular to the beam direction. Through a detailed analysis of the observed resonances, the partial cross sections for capture into each of the angular momentum states ($L$ and $M_L$) are determined. The population of any state in the $n=3\mathrm{}$ manifold can be calculated from these cross sections.

Using the Muckermann-V potential surface for F${\mathrm{H}}_2$, the contribution of the single-step direct-process portion to state—to—"all"-states reactive scattering is examined as a function of collision energy. The use of the orbital angular momentum space distribution is found to explain favorably the structures of angular distributions. Not only sideways—but also backward-peaked state-to-state (and thus state—to—all-states) angular distributions are shown to occur due dominantly to impact-parameter collisions other than head-on ($L=0\mathrm{}$) collisions. It is found that the structures of state—to—all-states angular distributions contributed by the (single-step) direct reaction remain consistently backward peaked (at 180°) at all collision energies studied. The increase of collision energy is seen to cause only the broadening of the angular distribution. This differs from the observation that shows sideways-peaked scattering at a certain collision energy, thus indicating that the observed sideways scattering may have been caused by other than the single-step direct-reaction process, if the potential surface which we used is reliable.

The method of distorted-wave Born approximation has been highly successful in treating fewnucleon transfer reactions in nuclear physics. Considering its relatively recent introduction to molecular reactions, it is of great interest to examine its validity in various applications. In the present study we limit ourselves to the study of product rotational state distributions in the atom—diatomic-molecule reactive scattering F+${\mathrm{H}}_2$→HF+H. It is found that the predicted first peak positions in the product rotational state distributions are in reasonable correlation with observation. The trend of the peak position shift toward the lower rotational angular momentum state of product molecule with the enhancement of the product-state vibrational manifold is also predicted to be in good correlation with observation. From the present study, we find that angular momentum matching plays a significant role in characterizing the product rotational state distributions. The peak position in the distribution is found to occur where the angular momentum match is most favorable.

Pure elastic scattering ($J=0\mathrm{}\to J^{\prime }=0\mathrm{}$ and $J=1\mathrm{}\to J^{\prime }=1\mathrm{}$), rotational excitation ($J=0\mathrm{}\to J^{\prime }=2\mathrm{}$ and $J=1\mathrm{}\to J^{\prime }=3\mathrm{}$), and average elastic (pure elastic plus rotational excitation) cross sections of the hydrogen molecule by 1—200-eV positrons are computed by using the adiabatic approximation in which the Glauber-type eikonal amplitude for a fixed molecular orientation is considered as input. Both differential and total scattering cross sections are calculated. Momentum-transfer cross sections are also obtained. Two different model effective potentials for positron—hydrogen-molecule interactions have been considered. Effects of positronium formation channel are neglected. Comparison is made with the recent measurements as well as with the available theoretical calculations. Below the positronium formation threshold average total elastic-scattering cross sections are found to reproduce the experimental data quite accurately. Electron and positron scattering cross sections at intermediate energies are compared. The effects of polarization interaction are found to be significant even at 200 eV.

Relativistic effects on a modified version of Rutherford's scattering cross section are considered up to first-order in the Born approximation for relativistic velocities in the binary-encounter approximation (BEA). The predicted cross sections with protons as projectile are lower than the previous theoretical values at low energies and are seen to be in better agreement with measurements. An approximate relativistic correction factor which accounts for orbital electrons only is compared with exact Dirac corrections, within the BEA model.

The first precise ground-state dipole moment of CaCl was measured by using the molecular-beam laser-microwave double-resonance method. From the study of two vibrational states the vibrational dependence $\mu ={\mu }_0+{\mu }_1(v+\frac{1}{2})$ was determined. The result is ${\mu }_0=4.257\mathrm{}\left(3\right)\mathrm{}$ D and ${\mu }_1=0.016\mathrm{}\left(3\right)\mathrm{}$ D (with statistical standard deviation in the last digit given in parentheses). The determination of the dipole moment from measured Stark shifts of individual hyperfine levels required diagonalization of the complete energy matrix. Problems in the application of the Rittner ionic model to the alkalineearth monohalides are discussed.

The probability of preparing multilevel atoms in high-lying levels by multiphoton excitation using one or more laser pulses can be increased by suitably tailoring the pulse amplitudes and frequencies. Few, if any, systematic methods designed specifically for multilevel excitation have been proposed. We present in this paper specific pulses and phase modulations which give specific degrees of inversion of multilevel atoms in analytic form.

Quadrupole-allowed and collision-induced fundamental band absorption in ${\mathrm{H}}_2$ has been studied at densities between 1.3 and 2.7 amagats and at high resolution (0.009 ${\mathrm{cm}}^{-1\mathrm{}}$). The absorption dips observed for several $Q$- and $S$-branch transitions are asymmetric about the center frequency. The asymmetry is attributed to collisional phase shifts, and a simple expression for the dip line shape is developed. When this dip line-shape function is combined with a Galatry profile for the narrow quadrupole absorption features, the data can be satisfactorily fitted. The resulting width and phase-shift parameter values for each dip feature are consistent with one another and with the assumptions used in the derivation of the line-shape function.

The relative transition probabilities $\frac{K{\beta }_3}{K{\beta }_1}$, $\frac{K{\beta }_2}{K{\beta }_1}$, $\frac{K{O}_{23}}{K{\beta }_1}$, $\frac{K{P}_{23}}{K{\beta }_1}$, $\frac{K{\beta }_5}{K{\beta }_1}$, and $\frac{K{\beta }_4}{K{\beta }_1}$ are measured by Ge spectroscopy for the atoms having $Z=70, 78, 82, \mathrm{and} 92$. In contrast to previous data, the results exhibit smooth $Z$ dependences and agree closely with Scofield's relativistic Hartree-Fock calculations. A tentative observation of the $K{M}_1$ transition is reported.

The influence of the dynamic Stark effect on photoelectron angular distributions for two-photon-resonant three-photon ionization of sodium by way of the $4{}_{}{}^2{}_{}{}^{}D$ fine-structure components has been investigated. Owing to the dynamic Stark shift of the atomic transition frequency, the angular distributions expected at low laser intensities were modified as different transitions were intensity tuned into and out of resonance with the laser frequency. The distributions are in good qualitative agreement with theory.

The time-dependent Schrödinger equation for the coherent interaction of a multilevel molecular system with an intense electromagnetic field is transformed with a new rotating-frame transformation into a frequency-dependent representation in which much of the information relevant to multiphoton excitation is contained in a time-independent interaction matrix, the solution of which follows by standard eigenvalue techniques. The flexibility of this transformation and simplicity of the resulting approximation (the general rotating-frame approximation) make it a powerful tool for solving the multiphoton dynamics of many-level systems. Extension to interactions with several laser fields is straightforward. The theory is illustrated by application to the model of Schek, Jortner, and Sage [Chem. Phys. 59, 11 (1981)] for the multiphoton dissociation of a diatomic molecule. The results from the general rotating-frame approximation are in good agreement with the exact results obtained by numerical integration of the full time-dependent Schrödinger equation. The implications for treatment of multiphoton absorption and dissociation of polyatomic molecules are discussed.

Six lifetimes and eight collisional quenching cross sections ${\sigma }^{\mathrm{}\left(0\right)\mathrm{}}$ for the $3s_5$, $3s_4$, $3s_3$, $3s_2$, $4d_6$, $4d_5$, $4d_4$, and $4s_1^{\prime \prime \prime }$ states in the $2p^{5}5s$ and $2p^{5}4d$ configurations of neon have been measured using laserinduced time-resolved fluorescence spectroscopy and a weak radio-frequency discharge. Two-step excitation sequences are driven by synchronously pulsed but separately tuned dye lasers. Considerable care is exercised to avoid spurious effects arising from polarized radiation, cascades, and light trapping. The resulting lifetimes vary from 39(4) to 81(6) ns, while the measured cross sections range from 25(4) to 56(4) ${\mathrm{\AA }}^2$. The results are in good agreement with past measurements and theory.

A new finite-volume variational method (FVVM) devised for ab initio calculation of molecular continuum wave functions is presented. It is a generalization of Kohn's FVVM which appeared in the same paper [W. Kohn, Phys. Rev. 74, 1763 (1948)] as the well-known principle for phase shifts. In FVVM, the inner-region continuum wave functions are expanded onto a finite basis set. A symmetrization of the Hamiltonian matrix is realized by introducing a set of unknown logarithmic derivatives $b$ at the surface boundary. This leads to a generalized system of eigenequations in terms of the unknowns, namely, the expansion coefficients and eigenvalues $b$. The proposed method combines the respective advantages of $R$-matrix and eigenchannel theories in the sense that the system of eigenequations is solved only once and that the eigenfunctions so obtained are uniformly convergent at the surface boundary, where collision information may be extracted by matching. As a model calculation, we use FVVM to calculate eigenphases and cross sections for the photoionization of ${{\mathrm{H}}_2}^{+}(1\mathrm{}{\sigma }_g\to E{\sigma }_u)$. Very encouraging results are obtained that demonstrate the numerical feasibility of the method.

The nonrelativistic first-Born-approximation matrix element for the photoionization and electron impact of a single electron from a molecule with no restriction on its shape, including retardation effects and with rotational energy resolution, is evaluated within the framework of the Born-Oppenheimer approximation. Angular distributions of ejected electrons are cylindrically symmetric about the propagation direction of the photon or electron source if the light is circularly polarized or if no attempt is made to simultaneously measure the scattered and ejected electrons in electron-impact ionization. If plane polarized light is used, retardation effects destroy the cylindrical symmetry about the light propagation direction. If the scattered electron in electron-impact ionization is detected in coincidence with the ejected electron then the angular distribution of ejected electrons shows cylindrical symmetry about the momentum-transfer direction. Use of an LCAO-MO (linear combination of atomic orbitals representation of molecular orbitals) basis for both bound and continuum one-electron orbitals leads to selection and propensity rules for rotational excitation.

A theory of saturation spectroscopy is developed which accounts for effects of level degeneracy. The theory can be applied to those situations in which a pump laser field of arbitrary strength and polarization acts between two manifolds of degenerate or nearly degenerate atomic levels, while a probe laser field of arbitrary strength and polarization acts between a coupled manifold of levels. As such, this theory of "three-level" systems could, in principle, include effects arising from level degeneracy, optical pumping, atomic motion, transient laser fields, different polarizations and strengths for pump and probe fields, and atomic transit across the laser fields. The present calculation, however, is limited to a study of optical pumping and field polarization effects for pump fields of arbitrary strength and weak probe fields interacting with a single velocity subclass of atoms. Probe absorption line shapes clearly display the effects of pump-field strength (Rabi splittings), pump-field polarization (positions and number of Rabi-split resonance peaks), pump-field detuning (positions of resonance peaks), and optical pumping (relative strengths of the resonance peaks). The calculation is carried out with the use of an irreducible tensor basis for the atomic density matrix although a standard ($m$-basis) calculation is included in an appendix.

F $\mathrm{KVV}$ Auger emissions were measured with NaF, Mg${\mathrm{F}}_2$, A1${\mathrm{F}}_3$, and Teflon [${\left(\mathrm{C}{\mathrm{F}}_2\right)}_n$], which were induced by photoionization. Chemical effects were reflected in line broadening and change in intensity ratios of the spectra emitted from singly and doubly ionized initial states, $|K^1{L}^0〉$ and $|K^1{L}^1〉$. Reduction in Auger peak intensities which originated from $|K^1{L}^1〉$ is in the order of the covalencies of the fluorides or the natural widths of F $L$ shells. This is caused by the refilling of a F $L$-shell vacancy by one of the ligand electrons prior to Auger emission.

The quantum noise of an injection-locked laser oscillator is analyzed by the operator Langevin equation. The problem is also treated by the Fokker-Planck equation and the same results are obtained in the same regimes of applicability. The steady-state solution of the Fokker-Planck equation gives the probability distribution of amplitude and phase, the Langevin equation arrives more directly at the spectrum of amplitude and phase. The phase of the injection-locked oscillator is related to the phase of the injection signal and thus constitutes a measurement of phase. In the limit of complete inversion and zero internal loss of the laser resonator, the associated uncertainty is twice that dictated by the uncertainty principle. This result is interpreted by comparing it with the uncertainty introduced by a linear amplifier which can perform a simultaneous measurement of amplitude and phase.

The quantum theory of the degenerate parametric amplifier is usually treated in the parametric approximation where the pump field is treated classically. In this paper we present a fully quantized theory of this nonlinear optical device using a path-integral approach. A perturbation series, the first term of which corresponds to the parametric approximation, is employed to evaluate explicitly the coherent-state propagator. The question of the validity of the parametric approximation is considered and the conditions under which this approximation is justified are elucidated. Finally, certain correlation functions for the signal-mode operators are calculated that are needed to study squeezed states. It is shown that the quantum nature of the pump field tends to decrease the squeezing.

We investigate delay-induced chaos in an optically bistable system which has a symmetry with respect to the exchange of two circular polarizations. Roughly speaking, the output of the system bifurcates in the following way as the input light intensity increases: (1) symmetric steady state, (2) asymmetric steady state, (3) asymmetric periodic oscillation, (4) asymmetric chaos, and (5) symmetric chaos. The first bifurcation is a well-known symmetry-breaking transition. It is shown that the last bifurcation through which the symmetry is recovered can be viewed as a crisis of chaos, which has been defined by Grebogi et al. as a sudden change of strange attractor. By changing system parameters, we find three distinct types of the crises in the experiment with an electronic circuit which simulates the difference-differntial system equation. Before and after the crises, waveforms characteristic of each type are observed. In a simple two-dimensional-map model, we can find all three types of crises. It is also found that the types of crises are determined by the nature of unstable fixed (or periodic) points which cause the crises by colliding with the chaotic attractors. The symmetry-recovering crises seem to be general phenomena appearing in nonlinear systems with some symmetries.

We report on studies on optical bistability from coherently driven $\Lambda$-type three-level atoms in a Fabry-Perot resonator. The nonlinear mechanism relies on transverse optical pumping and is due to population trapping in a coherent superposition of the ground-state sublevels. If, under appropriate conditions, a zero-field level-crossing resonance (Hanle resonance) occurs in the atomic system, the optical device is shown to display dispersive or absorptive bistability. Our theoretical studies are based on numerical solutions of the corresponding three-level Bloch equations in the presence of optical feedback. Experiments are performed on the $D_1$ line in a sodium-filled Fabry-Perot resonator using transverse optical Zeeman pumping of the ${}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ ground state. The measurements are found to be in fair agreement with the theoretical predictions from our simple model.