The linear response of an arbitrary electronic system is considered within the framework of the density-functional theory. An integral equation determining the density induced by an external perturbation is derived. The independent-particle response function for an inhomogeneous system appearing in this equation is obtained in a form convenient for numerical calculations. The equation is applied to the calculation of dipole polarizabilities of spherically symmetric atoms and ions. Results for the rare-gas atoms obtained by means of the local-density approximation are in good agreement with experimental values, except for the case of He. Polarizabilities are also evaluated for the alkali-metal ions, the alkaline-earth and other closed-shell metallic atoms.

In calculating $K$-shell-hole production when an ion collides with an atom, account must be taken of the fact that processes involving electrons other than the $K$-shell electron can occur. For example, after making a $K$-shell hole an $L$-shell electron may be knocked into it, or an $L$-shell vacancy may be produced and the $K$-shell electron promoted to that vacancy in the "Fermi sea" of the target-atom orbitals. In 1973 a theorem was proved by one of the present authors demonstrating that all these multielectron processes cancel in an independent-particle model for the target atom. In this paper it is shown that the same thing occurs for hole production by charge transfer to the ion. The authors demonstrate that multihole production does not obey this simple rule and that the probability for multihole production is not the product of independent single-electron probabilities. The correct expressions that should be used for these processes are given, together with new results for charge-transfer processes accompanied by hole production.

Ejected-electron spectra of Yb and Ba are presented. In both spectra, structure was seen which is attributable to autoionization to ground and excited states of $M^{+}$ ($M=\mathrm{Ba}\mathrm{or}\mathrm{Yb}$), and to Auger decay of highly excited $M^{*+}$ states to the ground state of $M^{2+}$. In Yb, Auger decay was also observed to populate excited states of $M^{2+}$. Both spectra are strongly affected by a collective resonance in the excitation of a $5p$ electron. For energies above the $5p$ ionization threshold, two-step autoionization to $M^{2+}$ was found to be dominant.

Freely suspended films of the material DOBAMBC ($p$-decyloxybenzylidene-$p^{\prime }$-amino 2-methyl butyl cinnamate), which has a layered ferroelectric liquid-crystalline phase (the chiral smectic $C$ phase), are created across a rectangular hole in a glass microscope cover slide. The films are quantized in thickness, being one, two, three, or more monomolecular (smectic) layers thick. In the tilted smectic $C$ phase, the films exhibit a net spontaneous electric polarization parallel to the smectic layers and in the plane of the film. A unique determination of the polarization, the Frank elastic constants, and the associated viscosities is made by comparing intensities of quasielastic Rayleigh-scattered light from orientational fluctuations of the molecular director in the presence and absence of an applied electric field. Measurements are performed on films three smectic layers thick as a function of temperature near the $C-A$ transition. The relevence of our results to the theories of the classical two-dimensional $\mathrm{XY}$ transition will be discussed.

Analysis of the electrons ejected during the autoionization of the $\mathrm{Ba}{\left(6\mathrm{}{p}_{j}20s_{\frac{1}{2}}\right)}_J$ states shows that for all but the ${\left(6\mathrm{}{p}_{\frac{3}{2}}20s_{\frac{1}{2}}\right)}_1$ state the electrons have ∼2.5 eV of kinetic energy, implying autoionization to the ground ${\mathrm{Ba}}^{+}6s_{\frac{1}{2}}$ state. However, in the autoionization of the anomalously wide ${\left(6\mathrm{}{p}_{\frac{3}{2}}20s_{\frac{1}{2}}\right)}_1$ state, roughly two-thirds of the electrons have an energy of 0.2 eV and one-third have an energy of 2.5 eV, implying that the anomalous width of the $6p_{\frac{3}{2}}20s_{\frac{1}{2}}$ state is due to autoionization to the excited ${\mathrm{Ba}}^{+}6p_{\frac{1}{2}}$ state.

The authors have observed an anomalous emission feature from a dense (∼ ${10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$) barium vapor illuminated with a ${\mathrm{N}}_2$ pumped dye laser (peak intensity ∼ 1 MW ${\mathrm{cm}}^{-2\mathrm{}}$). The input laser wavelength was 552.5 nm, 1 nm shorter in wavelength than the barium $6s^2{}_{}{}^1{}_{}{}^{}S-6s6p{}_{}{}^1{}_{}{}^{}P$ resonance transition. In the forward direction strong emission was observed emerging from the barium vapor in the form of an conical shell of half-angle ∼2° at ∼1% of the incident laser intensity. The emission was broad in wavelength (3 nm) and peaked 1 nm longer in wavelength than the Ba $6s^2{}_{}{}^1{}_{}{}^{}S-6s6p{}_{}{}^1{}_{}{}^{}P$ transition. Self-focusing of the laser beam by the barium vapor was observed under the same conditions. Although the emission is intense, an adequate explanation of this phenomenon has yet to be found.

Some time ago Bloch and Nordsieck, working in a model in which the spectrum of the radiation field is cut off beyond some low frequency ${\omega }_1$, showed that the transition probability for scattering, summed over final photon states, is approximately that which would be obtained if the interaction of the projectile with the radiation field were neglected entirely. Here, within the context of a nonrelativistic treatment of the scattering process, the sum rule is generalized through the inclusion of corrections of first order in ${\omega }_1$. These corrections can be interpreted in terms of a simple classical picture. In the course of the derivation, a lowfrequency approximation for the transition amplitude is obtained which contains as special cases the perturbative result of Low for single-photon bremsstrahlung and the more recently derived approximation for scattering in a low-frequency laser field.

Pulsed nuclear-magnetic-resonance measurements have been performed on ${}_{}{}^{83}{}_{}{}^{}\mathrm{Kr}$ in natural krypton gas at room temperature in a 2.114-T field. The spin-lattice relaxation time $T_1$ has been measured as a function of density $\rho$ (in amagat), with the result $\frac{1}{T_1}=\rho (2.13\mathrm{}\pm 0.05)\times {10}^{-3\mathrm{}}$ ${\mathrm{s}}^{-1\mathrm{}}$. $T_1$ has also been calculated by using the theories of Adrian and Staub. These results demonstrate that the nuclear quadrupole interaction is the relevant relaxation mechanism and that the inclusion of exchange interactions is necessary for an adequate description of collisions between rare-gas atoms. As a by-product, the chemical shift of the ${}_{}{}^{83}{}_{}{}^{}\mathrm{Kr}$ resonance frequency has been remeasured, confirming previous results.

The effect of photon correlations on two- and three-photon ionization via two near-resonant levels is discussed in terms of the resolvent-operator formalism. It is shown that under certain circumstances the ionization probability for a chaotic light can be enhanced by a factor larger than $N!$ compared to the ionization probability for a coherent light. The dependence of this enhancement factor on the interaction time, the average intensity, the detunings of the photon frequency from the near-resonant levels, and the separation between the two near-resonant levels is discussed.

The radiative lifetime of $1s2s{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ ${\mathrm{Li}}^{+}$ ions has been measured by a comparison of the count rate of spontaneous decay photons (210 Å) to a laser-induced fluorescence signal proportional to the total number of metastable ions. The ions were confined in a rf-quadrupole trap, and the fluorescence signal used was the intercombination transition $1s2p{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ to $1s^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ at 202 Å. The ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ state was populated from ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ by absorption of laser photons at 5485 Å. The result is ${\tau }_r=58.6\mathrm{}\pm 12.9$ sec (95% confidence level); theory predicts ${\tau }_r=49.1\mathrm{}$ sec.

The collisional and radiative processes leading in a glow discharge to quenching and and excitation transfer in the $n=3\mathrm{}$ helium sublevels are investigated by means of a laser perturbation method. Laser-induced population perturbations are solutions of coupled rate equations, the coefficients of which are related to radiative coefficients and collisional excitation cross sections. An accurate numerical method of data analysis (the "identification method") is developed in which the rate coefficients are determined so as to minimize the difference between experimental curves and those calculated from the model. In the pressure and current intensity investigated, $P<\mathrm{}10\mathrm{}$ Torr, $i<\mathrm{}50\mathrm{}$ mA, only radiative and atom-atom collision processes contribute to quenching and excitation transfer in the $n=3\mathrm{}$ levels. Numerical identification of the $n=3\mathrm{}$ experiments provides a nearly complete set of rate coefficients and thermally averaged cross sections. In particular, $3{}_{}{}^1{}_{}{}^{}P\rightleftarrows 3{}_{}{}^1{}_{}{}^{}D$ excitation transfers predominate over the $3{}_{}{}^3{}_{}{}^{}P\rightleftarrows 3{}_{}{}^3{}_{}{}^{}D$ ones. This results from the near-resonant character of the He-He* inelastic collision processes.

The $H\alpha$ line is analyzed in a dense plasma of $N_e\approx {10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$ produced in a $z$-pinch discharge. The line is shifted by up to 9 Å to the red, and the profile is strongly modulated. This modulation is attributed to the effect of collective fields of different frequency distributions, one being of the order of ${\omega }_{\mathrm{pi}}$. The shift is density dependent and agrees with available theoretical calculations.

$K$-x-ray nuclear-satellite cross sections are reported for ${}_{50}{}^{120}{}_{}{}^{}\mathrm{Sn}$, ${}_{65}{}^{165}{}_{}{}^{}\mathrm{Ho}$, ${}_{69}{}^{169}{}_{}{}^{}\mathrm{Tm}$, ${}_{73}{}^{181}{}_{}{}^{}\mathrm{Ta}$, ${}_{79}{}^{197}{}_{}{}^{}\mathrm{Au}$, ${}_{82}{}^{208}{}_{}{}^{}\mathrm{Pb}$, and ${}_{83}{}^{209}{}_{}{}^{}\mathrm{Bi}$ bombarded with 17.5-22.5-MeV $\alpha$ particles. Depending on target and energy, between 19 and 92% of these cross sections or those of ${}_{82}{}^{206}{}_{}{}^{}\mathrm{Pb}$ and ${}_{82}{}^{207}{}_{}{}^{}\mathrm{Pb}$ can be related to known nuclear decays in the recoils. Also deduced was the number of $K$-shell vacancies per reaction as a function of atomic number, which varies from 0.1 to 1.7, with pronounced minima at the shell closures $Z=50\mathrm{} \mathrm{and} 82$. The system ${}_{73}{}^{181}{}_{}{}^{}\mathrm{Ta}$+$\alpha$ at 18.5-and 20.5-MeV bombarding energy is studied in an x-ray-$\gamma$ coincidence experiment selecting the ($\alpha$,$2n$) reaction channel. A general procedure for complete cascade analysis is formulated. It emerges that (101±13)% and (105±8)% of the satellite intensity at 18.5 and 20.5 MeV, respectively, originate in converted transitions in the excited recoil. This accuracy shows that the study of converted continuum transitions by nuclear x-ray satellites is made possible by use of the algorithm for cascade analysis developed here. Also given are a decay scheme of ${}_{75}{}^{184}{}_{}{}^{}\mathrm{Re}$, hitherto unknown, and a number of new transitions completing the decay scheme of ${}_{75}{}^{183}{}_{}{}^{}\mathrm{Re}$.

Angular distributions of photoelectrons from resonant two-photon ionization of sodium have been measured. Excitation and ionization were carried out with two pulsed lasers, one with a frequency resonant with the $3s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\to 3p{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ transition. The hyperfine levels in the intermediate state were excited coherently; hyperfine coupling affects the photoelectron distributions through a dependence on the time interval between excitation and ionization. The results are analyzed to give values of three microscopic parameters: the ratio of the radial dipole matrix elements for the production of $l=0\mathrm{}$ and $l=2\mathrm{}$ final states from the $3p$ level, the difference of the phase shifts of the outgoing electron in the final channels, and a parameter which expresses the depolarizing effect of the nuclear spin on the intermediate state. The phase-shift difference agrees with extrapolated bound-state data, but the final state has more $s$ character than theoretical quantum-defect calculations suggest.

The interference effect produced by two independent sources can be understood in terms of the detection process, owing to the inability of the detector to know from which of the two sources the photons come. Detection based on the Compton effect seems to be a powerful method for recording the interference between high-frequency coherent fields. It is shown that by taking advantage of the uncertainty over the photon momenta, the scattering probability for an electron in an interference fringe is very high when the electrons are not relativistic. When the fields have the same frequency in the laboratory system, relativistic electrons can "see" the interference only when the angles between the fields are very small. In general, relativistic electrons see interference when the fields are suitably shifted in frequency in the laboratory system.

Photon emission by an atom in the metastable $2S$ state in a weak static electric field is examined within the context of bound-state quantum electrodynamics. Low's method is applied to obtain the expansion in terms of Coulomb wave functions of the propagation function for an electron interacting with the nuclear Coulomb field, the applied electric field, and the quantized radiation field. For a weak applied field, and to lowest relative order in $\frac{\alpha }{\pi }$, the $2S$-state resonant contribution to the propagation function can be factorized to provide the basis for a calculation of the angular distribution of single-photon radiation and lifetime of the excited state. A numerical evaluation is given, which takes into account effects of electric dipole, magnetic dipole, and magnetic quadrupole emission, relativistic corrections, and finite level widths.

The authors have studied the fine-structure splittings in the $F$ sequence of states in the cesium atom using high-resolution laser spectroscopy. The experiments were performed with a single-mode laser acting on the transitions from the lowest $D$ state to the different $F$ doublets. The Doppler broadening was reduced to about 20 MHz by means of the techniques of collimated atomic beams. For populating the $D$ state, a further laser acting on the transition from the ground state to the second excited $P$ state was used. About 10% of the $P$-state atoms decay to the $5{}_{}{}^2{}_{}{}^{}D$ levels. All the studied $F$ states were found to be inverted, with splittings as follows: $\Delta E\left(10\mathrm{}{}_{}{}^2{}_{}{}^{}F\right)=-873.2\mathrm{}\left(2.0\right)\mathrm{}$ MHz, $\Delta E\left(11\mathrm{}{}_{}{}^2{}_{}{}^{}F\right)=-667.2\mathrm{}\left(2.0\right)\mathrm{}$ MHz, $\Delta E\left(12\mathrm{}{}_{}{}^2{}_{}{}^{}F\right)=-522.0\mathrm{}\left(3.0\right)\mathrm{}$ MHz, $\Delta E\left(13\mathrm{}{}_{}{}^2{}_{}{}^{}F\right)=-416.0\mathrm{}\left(3.0\right)\mathrm{}$ MHz, $\Delta E\left(14\mathrm{}{}_{}{}^2{}_{}{}^{}F\right)=-336.8\mathrm{}\left(1.0\right)\mathrm{}$ MHz, $\Delta E\left(15\mathrm{}{}_{}{}^2{}_{}{}^{}F\right)=-276.3\mathrm{}\left(1.0\right)\mathrm{}$ MHz, $\Delta E\left(16\mathrm{}{}_{}{}^2{}_{}{}^{}F\right)=-229.3\mathrm{}\left(1.0\right)\mathrm{}$ MHz, and $\Delta E\left(17\mathrm{}{}_{}{}^2{}_{}{}^{}F\right)=-190.5\mathrm{}\left(2.0\right)\mathrm{}$ MHz. The results are compared with recent theoretical calculations. A further result of the present investigation is the hyperfine structure of the $5{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2},\frac{5}{2}}^{}{}_{}{}^{}$ states of ${}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}$. For the magnetic dipole interaction constant $a$ and the electric quadrupole interaction constant $b$ the following values were obtained: $a\left(5\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\right)=+48.6\mathrm{}\left(2\right)\mathrm{}$ MHz, $b\left(5\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\right)=0.0\mathrm{}\left(8\right)\mathrm{}$ MHz, $a\left(5\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}\right)=-21.2\mathrm{}\left(1\right)\mathrm{}$ MHz, $b\left(5\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}\right)=0.0\mathrm{}\left(1.0\right)\mathrm{}$ MHz. The inversion of the $5{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$ state is especially noteworthy, but can be explained as due mainly to strong polarization effects.

An atomic-beam magnetic-resonance technique has been used to measure the differential Stark splitting between "flop-in" Zeeman levels in the ground-state hyperfine structure of naturally occurring gallium. Precision measurements of the shift were made at several electric fields up to 200 kV/cm and various rf power levels. A significant rf dependence was observed, and it was necessary to extrapolate to zero rf power to obtain the final result. The shift was determined to be 500(16)×${10}^{-10\mathrm{}}$ Hz/${\mathrm{}(\mathrm{V}/\mathrm{c}\mathrm{m})\mathrm{}}^2$, including systematic uncertainties in the electric field value and the filling factor. This can be interpreted as a tensor polarizability of 667(21)×${10}^{-10\mathrm{}}$ Hz/${\mathrm{}(\mathrm{V}/\mathrm{c}\mathrm{m})\mathrm{}}^2$ or $2.700\left(0.84\right)\mathrm{}\times {10}^{-4\mathrm{}}{a_0}^3$. The shift increases the magnetic splitting between the $M_F=-1\mathrm{}$ and the $M_F=-2\mathrm{}$ sublevels. The theoretical and experimental results are compared and found to agree well to within the stated errors.

The phenomenon of nonlinear second-harmonic generation of laser radiation in $n$-InSb contained inside a rectangular waveguide is investigated. The nonlinearity arises through the ponderomotive force on electrons. The power conversion efficiency is resonantly enhanced at some optimum values of waveguide density and size such that $2{\beta }_1={\beta }_2$, i.e., $\frac{n^2{\pi }^2}{b^2}+(m^2-4)\frac{{\pi }^2}{a^2}=\frac{3\omega p^2}{c^2}$; ${\beta }_1$ and ${\beta }_2$ are the propagation constants of fundamental and second-harmonic modes, $a$ and $b$ are the $x$ and $y$ dimensions of the waveguide, and $n$ and $m$ are integers. For a typical 1-kW C${\mathrm{O}}_2$ laser the second-harmonic efficiency takes on values as high as 1%.

The analytical solution for the spectrum of resonance fluorescence from a collective system of two atoms is presented. It is shown that the spectrum is a decreasing function of frequency in the neighborhood $\omega -{\omega }_L=\pm 2\Omega$ ($\Omega$ is the Rabi frequency) for moderately large $\Omega$ and exhibits resonant structure only for extremely large $\Omega \approx 100\gamma$. For moderately large $\Omega$ the resonant contributions at $\omega -{\omega }_L=\pm 2\Omega$ are destroyed by the nonresonant contributions; hence the additional structures at $\pm 2\Omega$ can be resolved only by filtering the nonresonant contributions.