We show that the presence of an oscillating electromagnetic field can induce a new avoided crossing between true crossing electronic energy surfaces of molecules without actual absorption or emission of photons. This avoided-crossing energy gap and the field-dressed energies and states are functions of the field intensity, frequency, and polarization. Thus the elastic and inelastic probabilities across these energy regions can be controlled by tuning these field parameters. This mechanism can be used to enhance or suppress field-free transitions by orders of magnitude. More importantly, the field can open up new inelastic channels so that the field-induced transitions, free of any competing field-free transitions, can be readily detected. We apply these new effects to molecular dissociation and predissociation and to atomic (ionic) and molecular collisions. The field-induced probabilities of these processes are studied as functions of the (quasi) molecular electronic energies, relative velocity or vibrational energies, laser field frequency and intensity. It is shown that far-away nonresonant states can contribute significantly to the field-induced avoided crossing and transitions. We give approximate but accurate formulas which enable rapid calculation of all these effects. Our method of solution of the charge-field interaction includes the stationary perturbation theory in the weak-field limit. Our modified Landau-Zener formulas of transition probability include the time-dependent perturbation results, the adiabatic limit, and the field-free limit. Improvements over earlier methods of solving the adiabatic eigenvalue problem are given, especially for charge systems with definite "parities." It is shown that the radiative-induced predissociation of ${\mathrm{I}}_2$ in the B $0^{+}u\left({}_{}{}^3{}_{}{}^{}\Pi \right)$ state into the repulsive $1u\left({}_{}{}^1{}_{}{}^{}\Pi \right)$ state can broaden its vibrational spectrum and quench its fluorescence. The same mechanism can be used to increase the enrichment of laser isotope separation of ${\mathrm{Br}}_2$ involving the same states. Formulas fór field-induced predissociation rate per second without or with tunneling are given. In these cases, the small laser-induced coupling controls the large internal energy flow as fluorescence or as kinetic energy. In other situations such as dissociation and collisions, the laser field is also a means of switching on the exchange of electronic or vibronic energies internally and/or externally as kinetic energy. All these are achieved at no expense of photon energy since no actual photo-absorption or -emission is involved in these nonresonant processes.

The collision-induced absorption and emission coefficients for electric-dipole forbidden atomic transitions are calculated for weak radiation fields. The approximations used are valid for $\hslash \omega$ near $\hslash {\omega }_0$, the atomic energy differences. The example case of $S-D$ transitions induced by a spherically symmetric perturber (e.g., a noble-gas atom) is treated in detail and compared to measurements. The case of "radiative collisions," in which both colliding atoms change their state, is included in the theory and is also compared to experiment.

It is theoretically shown that detector quantum-noise-free measurement is feasible by a joint moment (JM) method which utilizes many photodetectors. The quantum/shot noise disappears in the statistical moments of JM photon counting. The statistical error in the JM measurement is calculated for light with Gaussian statistics and a Lorentzian spectrum and compared with that in the usual factorial moment method which utilizes a single photodetector. The JM measurement is shown to be useful for the measurement of very weak light with a wide spectrum.

Direct evidence is reported that associated with laser-produced plasma for metallic targets, the self-generated magnetic field consists of two identifiable parts having different radial and background pressure dependences as well as propagation speeds. For background pressures greater than about 0.1 mTorr and probe distances greater than 5 mm, two independent $\dot{B}$ signals are observed. The ${\dot{B}}_1$ field is laser driven and originates from a stream of electrons ($T_e\sim 10$ eV) moving counter to the incident laser beam. The ${\dot{B}}_2$ field originates from the Korobkin effect and is associated with the expanding plasma. For the experiments reported here the magnetic fields are ${10}^3$ G or less.

The front of an intense relativistic electron beam has been used to reflect a counterstreaming electromagnetic wave ($f_i=9.3\mathrm{}$ GHz, $P_i=250\mathrm{}$ kW). A doubly-Doppler-shifted reflected wave with a pulse duration on the order of a nanosecond has been produced with a sixfold increase in frequency, a 13-dB power gain, and a doubling of wave energy. The output has been analyzed with a multichannel grating spectrometer and found to have a spectral width $\frac{\Delta \lambda }{\lambda }$ of ∼5%. The reflected-wave frequency was tunable over a range of ∼±20% by simply varying the external magnetic field, and over a much broader range by simultaneously changing the beam rise time. All these observations are in good agreement with a simple theoretical model of beam-front scattering. This mechanism represents a new kind of short-pulse, high-power, tunable source of millimeter (and probably submillimeter) wavelength radiation, and it could be immediately useful as an electron-beam velocity diagnostic.

A discussion is given of density expansions for transport coefficients for moderately dense gases. The arguments for the occurrence of logarithms of the density $n$ in this expansion are reviewed, and are verified by explicit calculations. We present a relatively simple method for computing part of the coefficient of the first $\ln n$ term appearing in these expansions, and compare our results with the computer results obtained by Pomeau et al. for hard-sphere molecules.

The effect of relativistic electron-mass variation on the propagation of electron plasma waves is considered. Including thermal dispersive effects, a variational principle is used to find the possible final states of the linearly unstable modes. It is shown that dispersion will limit the nonlinear steepening predicted by the coldfluid approach.

We report the measurement of $\mathrm{nd}\to \mathrm{}(n+1\mathrm{})p$ intervals in sodium Rydberg states with $n=30-32\mathrm{}$. The measurements were made using a microwave-resonance technique which utilizes selective field ionization. Fine-structure intervals of the $p$ state are reported and shown to continue the ${\left(n^{*}\right)}^{-3\mathrm{}}$ scaling law, where $n^{*}=n-\delta$ is the effective quantum number and $\delta$ is the quantum defect. Quantum defects for the $p$ states are derived and compared to spectroscopic measurements.

The $Z^3$ correction to the differential cross section for ejection of electrons from argon by $\alpha$ particles is estimated by adapting the theory of Ashley, Ritchie, and Brandt for the $Z^3$ effect on stopping power. Results are compared with the difference between cross sections for ionization by $\alpha$ particles and equivalentvelocity protons. For ejected electron energies between 40 and 190 eV, good agreement is obtained between the model and experiment. The model predicts a significant enhancement of the cross section for ejection of low-energy electrons by $\alpha$ particles which is not observed.

Proposed and performed experiments on the Doppler-free two-photon absorption of two coherent laser beams are discussed. The coherent phenomenon in experiments follows directly from basic quantum mechanics. It is shown that, to excite the coherent absorption, the laser beams need not be spatially or temporally separated.

The data of Weiner, Langley, and Ford on both the sum and difference of coexisting densities of S${\mathrm{F}}_6$ are found to be consistent, within a range of 2% in reduced temperature of $T_c$, with the series of terms (revised and extended scaling) predicted by renormalization group calculations. The hypothesis that the relatively small range of applicability of this series is due to a crossover to Van der Waals behavior is supported by further analysis.

It is argued that the very narrow, low-energy ${}_{}{}^1{}_{}{}^{}D_{}^o{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ $d$-wave shape resonances in the $e^{-}$-F system reported by Ormonde must be artifacts. Evidence that this is so is drawn from numerical Hartree-Fock calculations, from construction of effective local potentials, from calculations with model polarization potentials, and from extensive configuration-interaction/stabilization computations. No evidence of such resonance behavior is found in any of these calculations.

The close-coupling (CC) calculations reported by Ormonde for $e^{-}$ + F scattering have been repeated using independent CC computer programs. No evidence of very narrow, low-energy shape resonances is observed in the ${}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}D_{}^o{}_{}{}^{}$ $d$ waves.

The critical properties recently discovered in binary mixtures of ionic fluids are partly reduced to those of the uncharged fluid binary mixture. It is shown, for instance, that although the direct correlation functions are not short ranged, an Ornstein-Zernike expression for the static concentration fluctuations can still be obtained.

An argument is presented to assess the convergence of Larsson's calculation on the ground state of Li towards the exact nonrelativistic energy. For an assessment of the convergence of the Fermi contact term, higher numerical percision in Larsson's wave function is necessary.

The structure and properties of ${\mathrm{H}}_3^{+}$ ions in magnetic fields with strengths of the order of ${10}^9$-${10}^{10}$ G have been studied by means of a variational method. It is found that there is a rapid change in the configuration of the ${\mathrm{H}}_3^{+}$ ion from its equilateral triangular structure to a linear chain, around a magnetic field $B_c=2.35\mathrm{}\times {10}^9$ G. The exchange contribution increases with the magnetic field, and its effect on $B_c$ is to lower its value. The vibrational frequencies of ${\mathrm{H}}_3^{+}$, about its ground-state structure increase with the field strength and undergo a rapid change near $B_c$. The oscillator strengths for the electronic transition stay nearly constant in the range 0-4.7 × ${10}^{10}$ G of the magnetic field strength studied.

In two previous papers, the quantum number $k\equiv n+l$ was considered as an energy-ordering quantum number for the excited states of 42 atoms and ions, which can be regarded as being composed of a single excited valence electron outside closed shells. It was shown that the energy levels of the valence electron are energy ordered according to the (increasing) values of $k$, and moreover within each $k$ group or $k$ band, there is a definite and generally constant sequence of $l$ values for each atom or ion, as the electronic energy is increased within the $k$ band; this sequence has been called the "$l$ pattern." Altogether 42 spectra involving 1155 levels were included in the previous investigation. Of these 1155 levels, 120 show a small deviation from $k$ ordering, and these have been called "$k+\lambda$ exceptions." In the present work, a thorough analysis of these $k+\lambda$ exceptions has been made, and it has been found that in the vast majority of the cases, the $k+\lambda$ exceptions arise from the fact that the angular momentum $l$ is too large, and is close to or larger than the limiting angular momentum $l_1$ for which a "phase transition" occurs from $k$ ordering to hydrogenic (H) ordering, which is similar to the phase transition which arises when the ionicity $\delta \equiv Z-N$ ($N$ being the number of electrons) is too large, and exceeds the "limiting ionicity" ${\delta }_1$. A diagram showing the regions of validity of $k$ and H ordering as a function of the angular momentum $l$ and the atomic number $Z$, i.e., the curve of $l_1$ vs $Z$, has been obtained. A tentative explanation of the phase diagrams of $\delta$ vs $Z$ and $l$ vs $Z$ is discussed, i.e., the reason why too large a value of $\delta$ or $l$ will destroy the $k$ ordering phase of the spectrum.

Calculations are presented of the $E1\mathrm{}$ amplitude expected in forbidden $M1\mathrm{}$ transitions of Cs if parity conservation is violated in the neutral weak $e-N$ interaction, as proposed in a number of gauge models, including that of Weinberg and Salam. Valence electron wave functions are generated as numerical solutions of the Dirac equation in a Tietz central potential, and are used to calculate excited-state lifetimes, hfs splittings, and Stark $E1\mathrm{}$ transition amplitudes. These are compared with experiment and are in good agreement. Contributions to the $6{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ $g$-factor anomaly and to the forbidden $6{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-7\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ and $6{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-8\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ transitions from relativistic effects, Breit interaction, interconfiguration interaction, and hfs mixing are calculated, and it is found that this theoretical description is not entirely adequate. The parity-nonconserving $E1\mathrm{}$ amplitude ${\mathcal{E}}_{\mathrm{PN}}$ for the $6{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-7\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ and $6{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-8\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ transitions is evaluated. The results ${\mathcal{E}}_{\mathrm{PN}}\mathrm{}(6S-7S)=i3.50\mathrm{}\times {10}^{-11\mathrm{}} Q_W\left|{\mu }_B\right|$ and ${\mathcal{E}}_{\mathrm{PN}}\mathrm{}(6S-8S)=i1.48\mathrm{}\times {10}^{-11\mathrm{}}{Q}_W\left|{\mu }_B\right|$ are obtained. With a measured value of the $M1\mathrm{}$ amplitude ${\mathfrak{M}}_{\mathrm{expt}}$ and the Weinberg value $Q_W=-99\mathrm{}$, we find a circular dichroism $\delta =1.64\mathrm{}\times {10}^{-4\mathrm{}}$ for the $6{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-7\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ transition.

Analytic expressions for relativistic screened Coulomb radial wave functions, including bound-state energy eigenvalues as well as bound and continuum wave-function shapes and normalizations, are given explicitly as series in $\lambda \simeq \alpha Z^{\frac{1}{3}}$. The method employed is a direct generalization of an approach previously used for the nonrelativistic case. The analytic expansions which we obtain are compared with exact numerical solutions of the Dirac equation for relativistic Hartree-Slater potentials. Low-, intermediate-, and high-$Z$ cases are considered for a wide range of energies and angular momenta. In general, excellent agreement is found for both inner bound states and for relativistic continuum states.

Within the frame of the infinite-nuclear-mass approximation a differential inequality for the square root of the one-electron density is derived. This linear differential inequality is structured like a one-particle Schrödinger equation and leads to results on the analytic behavior of the electron density $\rho$ in the region far from the nuclei. A domain determined by the potential and the ionization energy is given where $\rho$ is subharmonic. For atoms it is shown that the spherically averaged electron density is a convex monotonically decreasing function outside some sphere whose radius depends on the ionization energy and the electron nuclear attraction. Furthermore, an upper bound for the electron density is given in terms of Whittaker functions which decreases exponentially and is exact for the $s$ states of the H atom. It compares favorably with the results given in the literature.