The free-free absorption coefficient for ${\mathrm{Ar}}^{-}$ is calculated at radiation wavelengths of 2000 and 20000 Å for various temperatures. Electron correlation corrections to the Hartree-Fock approximation are obtained by using many-body perturbation theory. Comparison is made with other theoretical methods and experiment.

The matrix element for Rayleigh scattering by atomic $K$-shell electrons is evaluated in the limit of high photon energies at finite momentum transfers $\Delta$. The limiting form of the matrix element $\overline{M}$ is derived from its relativistic expression at finite energies $\mathfrak{M}$ in which the one-electron Green's function $G$ is replaced by its nonrelativistic approximation $G_0$ with adequately modified parameters. The expression obtained for $\overline{M}$ is exact in $\Delta$ and the atomic number $Z$, and is equivalent to the one found by Goldberger and Low. The evaluation of the matrix element is carried out in momentum space for the case of a Coulomb atomic field. Exact integral representations are used for $G_0$ and the ground-state eigenspinors. The integration of $\mathfrak{M}$ is carried out analytically as far as possible and at one stage the high-energy limit is taken. For one $K$-shell electron, when electron spin-flip is possible, $\overline{M}$ is expressed in terms of three real amplitudes $H$, $K$, and $L$, whereas the matrix element for the closed $K$ shell, ${\overline{M}}_K$, depends only on $H$. The amplitudes are obtained as one-dimensional integrals over Appell functions $F_1$. They simplify considerably in the case of forward scattering, and the connection of their imaginary parts with absorption cross sections is discussed. Expansions of the forward amplitudes in powers of $a=\alpha Z$ are also given. Further, a connection between $H$ and the nonrelativistic form factor is established, and the asymptotic behavior of $H$ with respect to $\Delta$ is derived. Then, a description is given of the numerical methods used. $H$ is computed for $0\le \frac{\Delta }{am}\le 15$ and $1\le Z\le {\alpha }^{-1\mathrm{}}$. Of the electron spin-flip amplitudes only $K$ is computed for forward scattering ($L$ vanishes in this case). The numerical results are discussed and comparison is made with other works. The validity of the high-energy result ${\overline{M}}_K$ at lower photon energies is considered. Finally, the magnitude of the Rayleigh matrix element ${\overline{M}}_K$ is compared with the one for Delbrück scattering.

We present a third-order perturbation calculation of line shapes in laser spectroscopy based on the density-matrix formalism. The new feature of this theory is the inclusion of the Gaussian spatial structure of the laser beams. We study the linewidth as a function of relaxation and transit times. A shift is found when the wave fronts are not flat. General line-shape formulas are given as well as approximate formulas valid in various domains.

Pb atoms were excited and studied by optical techniques using signal averaging and phase sensitive detection. Cross sections for the quenching of the ${}_{}{}^3{}_{}{}^{}P_1^o{}_{}{}^{}$ excited state of Pb were measured by observing the reduction of the atomic fluorescence as a function of foreign gas pressure. The cross sections for the following quenchers measured at 900°K were (in ${\mathrm{\AA }}^2$) for ${\mathrm{N}}_2$, 18; CO, 27; ${\mathrm{CO}}_2$, 63; and for ${\mathrm{CH}}_4$, 55 with an estimated uncertainty of ± 20%. Upper limits on the quenching cross sections of Ne, Ar, Kr, Xe, ${\mathrm{H}}_2$, and ${\mathrm{D}}_2$ were also measured.

The use of an active cell located outside the laser cavity has allowed us to observe the Autler-Townes effect under well-defined conditions. The splitting is proportional to the square root of the density of energy flux. An experimental value of the transition probability for the line at $\lambda =3.51\mathrm{}$ μm is proposed.

The lowest Rb metastable autoionizing level has been identified by a rf resonance measurement of the g factors of the various hyperfine sublevels. Of the two lowest-lying metastable state assignments, $4p^5\left({}_{}{}^2{}_{}{}^{}P\right)5\mathrm{}s5\mathrm{}p\left({}_{}{}^3{}_{}{}^{}P\right){}_{}{}^4{}_{}{}^{}D_{\frac{7}{2}}^{}{}_{}{}^{}$ and $4p^{5}4d\left({}_{}{}^3{}_{}{}^{}F\right)5\mathrm{}s{}_{}{}^4{}_{}{}^{}F_{\frac{9}{2}}^{}{}_{}{}^{}$, only components of the ${}_{}{}^4{}_{}{}^{}D_{\frac{7}{2}}^{}{}_{}{}^{}$ were observed in the metastable beam. The atomic-beam resonance method employed resembles traditional methods except that it exploits the differential metastability of the fine-structure levels instead of magnetic deflection for state selection.

A nonperturbative analysis is given for an $n$-level atom or molecule dressed by a Stark field and in single-photon or multiphoton (near) resonant interaction with coherent optical field modes, which may be intense. All the field amplitudes and phases may have nonadiabatic time variation. New formulas for probability amplitudes of states with finite lifetimes are given for atom-field levels swept or optical Stark shifted through resonance or into close approach. One of these includes the Landau-Zener formula as a special case. Power broadening is contained in these formulas. They are useful for both weak- and strong-field interaction. Further, it is shown that many familiar single-photon coherent transient phenomena have their analogs in the intense-field and the multiphoton domains. Two new effects, pulse-shape dependence in final transition probability and population inversion due to the nonadiabatic passage of an asymmetric pulse, are demonstrated with numerical results for the process $\mathrm{Na}\mathrm{}\left(3s\right)+2\mathrm{}\hslash \omega \to \mathrm{Na}\mathrm{}\left(5s\right)\mathrm{}$. Finally, double resonance (single-photon and/or multiphoton) is analyzed, with discussion of adiabatic following and a derivation of a formula for level crossing. Generalization of an earlier procedure for solving the adiabatic eigenvalue problem of the whole atom-field system is given.

Stark broadening and shift measurements of ionized helium resonance lines from a fully ionized helium plasma are reported. Electron densities in the range from 2 × ${10}^{17}$ to 6 × ${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$ and temperatures between 40 000 and 45 000 K are achieved in the reflected shock of an electromagnetically driven $⊺$ tube. All observed Hell resonance lines are emitted optically thick by a nearly homogeneous plasma slab and self-reversed by a very thin, cooler boundary layer. Profiles of the first resonance line, Hell $\lambda 304$ ÅA, are measured photoelectrically, yielding asymptotic Stark wings (20 ± 20)% below those predicted by Kepple's calculations and showing marked blue shifts of 0.07 ± 0.05 ÅA which may be due to plasma polarization. Photographic wavelength measurements of the first three series members $\lambda 304$, $\lambda 256$, and $\lambda 243$ ÅA are performed relative to the same lines from a Tanaka discharge. Despite some irreproducibilities in the resulting shifts, blue shifts of about 0.04 ÅA at densities near or slightly below 4 × ${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$ can be deduced.

Using hyperspherical coordinates and a Born-Oppenheimer-type expansion, the potential curves of ${\mathrm{H}}^{-}$ that converge to the $n=1\mathrm{}$ and $n=2\mathrm{}$ thresholds of hydrogen are obtained. From the computed potential curves, the properties of bound states, Feshbach resonances, and shape resonances are conveniently studied.

This work reports the multiphoton ionization of cesium atoms, via resonance with the $6F$ level, by interaction with a single transverse and longitudinal mode neodymium-glass laser beam. At a low rate of ion production, when the laser frequency is tuned through resonance, the laser intensity necessary to create a constant number of ions passes through a minimum, as expected, for a three-photon energy equal to the unperturbed $6S\to 6F$ transition energy. But for a higher ionization rate, involving larger laser intensities, a departure from expectation is observed which is interpreted as a consequence of an energy shift of the transition. The level shifts are demonstrated in another way by their strong effect on the experimental order of nonlinearity of the interaction, $K_{\mathrm{expt}}$. A sharp variation of $K_{\mathrm{expt}}$ is observed when the energy shift of the $6S\to 6F$ transition exactly compensates the wavelength detuning of the laser. The latter method gives shift values which are found to be independent of the large variations of the interaction volume under conditions of resonance. Both methods give a linear dependence of the shifts on the laser intensity. Identification of these shifts with energy shifts of the $6S\to 6F$ transition is subject to theoretical reservations and needs further experimentation.

Energy profiles are calculated for photons scattered twice from stationary electrons in a cylindrical sample of infinite radius. Both double-Compton (inelastic) and one-Rayleigh (elastic), one-Compton events are treated. Klein-Nishina, Thomson, and isotropic differential cross sections are employed. It is found that at the energies typically used in $\gamma$-ray experiments, the different cross sections result in significantly different energy profiles and angular distributions, while at x-ray energies the form of the cross section is (as expected) considerably less important. Sample thickness and choice of primary scattering angle are found to have major effects on the shapes of the double-scattered profiles.

Total probabilities, angular distributions, and energy profiles of multiply scattered radiation are calculated using Monte Carlo techniques. It is found that use of either the Klein-Nishina or the polarization-dependent Thomson cross section can result in significant departures from the angular distributions and energy profiles obtained with the polarization-averaged Thomson cross section. The radius of the incident photon beam appears to have a substantial influence on multiple scattering probabilities and angular distributions for finite cylindrical samples. Criteria are established for estimating under what experimental conditions a sample may be considered effectively "infinite," so that earlier analytic results become applicable. Triple and higher-order scattering are found to be generally insignificant for finite cylinders.

One-, two-, three-, and four-photon resonances in the $N=6,7, \mathrm{and} 9$ states of $\mathrm{He}_4^{}{}_{}{}^{+}$ have been observed with a fast atomic beam. The locations, amplitudes, widths, and rf Stark shifts of these resonances are discussed along with the prospects for exploiting multiphoton fast-beam spectroscopy as a means for measuring the fine structure of $\mathrm{He}_4^{}{}_{}{}^{+}$ to high precision.

The absorption spectra of the negative ions of chlorine and bromine have been observed in shock-heated vapors of CsCl and CsBr, respectively. The photodetachment cross sections of ${\mathrm{Cl}}^{-}$ and ${\mathrm{Br}}^{-}$ have been measured from their threshold values down to 2000 ÅA. The results are found to be in good agreement with the calculated values of Robinson and Geltman.

The new excimer emission bands from laser-excited and discharge-excited alkali-noble-gas systems we recently reported are observed in absorption for Cs and Rb, with noble-gas densities between 1 and 10 amagats. The absorption bands observed correspond to transitions from the unbound $\Sigma$ molecular ground state to bound or free $\Sigma$ and $\Pi$ excited states which are correlated with low-lying $S$ and $D$ excited alkali atoms, so that the corresponding atomic transitions are forbidden. Quantitative reduced absorption coefficients ($k_{\nu }$ divided by the vapor densities) are derived from the observed spectra and have peak values of the order of 4 × ${10}^{-38\mathrm{}}$ ${\mathrm{cm}}^5$ for the heaviest noble gas, xenon. A comparison is made with the spectra that would be expected from the adiabatic potential curves recently calculated by Pascale and Vandeplanque, with the conclusion that they have exaggerated the repulsion in certain excited $\Sigma$ states.

Formulas are presented for the angular distribution of photoelectrons produced on absorption of circularly polarized photons by randomly oriented, optically active (chiral) molecules or molecular negative ions. Results are presented to order ${\alpha }^3$. The results for nonchiral molecules can be recovered by setting the appropriate coefficients equal to zero. These findings suggest measurement of the angular distribution difference for absorption of left and right circularly polarized photons, whose leading term behaves as $2B_{e}cos\theta$, where $B_e$ is a coefficient appropriate for the electric dipole ($E1\mathrm{}$) process and $\theta$ is the angle between the direction of the emerging beam of photoelectrons and the direction of incidence of the photon beam. The integrated cross-section difference behaves as $8\pi (A_m+\frac{C_m}{3})$, where these coefficients are appropriate for the electric-dipole, magnetic-dipole ($E1\mathrm{}M1\mathrm{}$) interference; this term is responsible for the circular dichroism of the molecule in the region of continuous absorption.

A self-consistent set of equations is derived for an atomic central potential such that the energy given by the orbitals for the potential is minimized. It is shown that this effective potential behaves like $\frac{-e^2}{r}$ for large $r$ values. The equations have been solved for carbon, neon, and aluminum, and the resulting total energies exceed the Hartree-Fock total energies by less than 0.005%. The theory leads to an effective, local, central exchange potential analogous to the $X\alpha$ potential.

We present the results of the first calculation of the spectral distribution of emitted photons following $K$-$\mathrm{MM}$ radiative-Auger transitions in the free argon atom. The calculation is based on second-order perturbation theory, and the total transition rate found to be $\frac{2.68\times {10}^{-4\mathrm{}}}{\hslash }$ eV, or 4% of the calculated $K{\beta }_{1,3}$ rate of $\frac{6.7\times {10}^{-3\mathrm{}}}{\hslash }$ eV. The calculated rate and photon spectrum agree fairly well with the experimental data of Keski-Rahkonen and Utriainen. Difficulties which preclude a direct comparison between theory and experiment are discussed, especially the effects of the spectrometer response function on the experimental data. The need for more high-resolution data is emphasized.

We examine the effect of including phase-coherent coupling between a driving laser field and a gas of multilevel molecules ($N=20,40\mathrm{}$) on a nontransient time scale. Although multiphoton enhancement of upper energy-level populations is known to be negligible for systems containing a small number of levels ($N=3,4\mathrm{}$), such coherent enhancements increase strongly as a function of the number of consecutive radiatively coupled levels, and may play a significant role in recently observed laser-induced chemical reactions.

We introduce a generalized version of the Volterra-Wiener functional expansion and show its fruitfulness in the treatment of nonlinear stochastic processes. As an application we derive in a simple way the statistical properties of the single-mode laser radiation both in the steady state and in the transient regime. Besides deriving already known results with good accuracy, we give for the first time the transient correlation function for the photon number.