Very short optical pulses, traveling in sharp-line resonant absorbers without change of shape, are investigated with a new approximation technique. Instead of employing the long-pulse or slowly varying envelope assumption, we have developed a method of approximation based on a series expansion in powers of a small parameter which is related to the electric field strength. The principal advantages of the method are its ability to treat very short pulses, and the simplicity with which it can be extended, both from lower to higher levels of approximation, and from one type of steady-state pulse to another. In this paper we use the approximation method to study very short pulses which require retention of the second-derivative terms in the Maxwell envelope and phase equations. Corrections to the well-known McCall-Hahn results are easily found to first order in the small parameter. As expected, the corrections begin to be important only for picosecond and shorter pulses.

We discuss the phenomenon of a pretransitional enhancement in the optical rotatory power of the isotropic phase of cholesteric liquid crystals. The effect is viewed theoretically as the modulation of dielectric properties of the isotropic liquid by chiral orientational correlations which destroy local inversion symmetry in a way that produces circular birefringence. De Gennes's theory of short-range order is applied to derive a quantitative result. This is experimentally tested with a system of "chiral-nematic" liquid crystals, achieving good rapport in the pretransition region. The existence of chiral orientational order in the isotropic phase is confirmed.

A beginning is made towards determining the energy of dense and strongly interacting quantum liquids at 0 °K, starting all the way from the interparticle potential. Liquids ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ as well as neutron-star interiors approximate such a system. Since expansions do not converge either in powers of the interaction nor in the density, $n$-body clusters have to be calculated for all $n$ and to all orders in the potential. Working within a simplified model, a method is suggested for estimating $n$-body contributions to the binding energy. The method is far simpler than more-direct methods thus far employed, which can be used only for low values of $n$. The method is verified and illustrated by comparison with these existing calculations of two-, three-, and four-body energies. A discussion is also given of the steps remaining to be taken from where this paper leaves off. Possible "pairing" and "super" properties are outside the scope of this paper.

The sixth frequency moment of the spectral functions of both the longitudinal and transverse current correlations along with their self-parts has been derived for a system of particles interacting through a two-body potential. The first two frequency moments of the spectral function of the energy-density fluctuation, and the first four frequency moments of the spectral function of the kinetic-energy-density fluctuation-correlation functions have also been derived. Numerical estimates for the fourth and sixth frequency moments of the spectral function of the longitudinal current correlations have been made for liquid argon. From this some information about the behavior of the contributions of triplet and quadruplet correlation functions to the frequency moments of liquid argon have been obtained. Numerical estimates have also been made for the first four frequency moments of the kinetic-energy-density fluctuation-correlation function in the long-wavelength limit for liquid argon.

An attractive $\delta$-function potential is introduced in a Fermi gas. The contribution to the liquid-impurity correlation function of bound states is calculated exactly in a Green's-function formalism. The exact results are compared with those obtained in a self-consistent approximation and the range of validity of the latter is discussed.

The investigation of bound or restricted diffusion in a steady magnetic field gradient on the NMR Hahn spin-echo experiment is extended to samples with cyllndrical boundaries. The restricted self-diffusion coefficient $D^{\prime }\mathrm{}\left(t\right)=-12\mathrm{}\ln \frac{\left[\frac{A(t,G)\mathrm{}}{A(t,0\mathrm{})\mathrm{}}\right]}{{\gamma }^2{G}^2{t}^3}$ is defined in terms of the spin-echo experiment, where $A(t,G)\mathrm{}$ is the echo amplitude and $t=2\mathrm{}\tau$ is the time between the 90° rf pulse and the echo. Values of $D^{\prime }\mathrm{}\left(t\right)\mathrm{}$ for times from 30 to 200 msec are reported for water in arrays of fused-glass tubes with inside diameters of 50, 37, 27, and 10 μm, and a comparison of these data, which were measured with the gradient perpendicular to the tube axes, is made with a theory developed by Neuman. In general, the agreement is good for the 50- and 37-μm samples. Larger discrepancies, which increase with decreasing tube diameter, were observed for the 27- and 10-μm samples; but, by considering the magnitude of the error in $D^{\prime }$ that results from an inaccurate determination of the tube diameter, these discrepancies can partially be reconciled. Moreover, we show that the restricted self-diffusion coefficient as a function of the angle $\theta$ between the tube axis and the magnetic field gradient is given by $D^{\prime }\left(\theta \right)={(D_{\parallel }^2{cos}^2\theta +D_{\perp }^2{\mathrm{sing}}^2\theta )}^{\frac{1}{2}}$, where $D_{\parallel }$ and $D_{\perp }$ are, respectively, the diffusion coefficients measured parallel and perpendicular to the tube axis.

It has recently been suggested that a radiative correction of relative order $\alpha \ln \alpha$ may contribute to the $1s2s{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-1\mathrm{}{s}^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ magnetic dipole transition of the heliumlike ions. The low-frequency contributions to the correction are evaluated and shown to vanish.

The critical behavior of an Ising model of classical spins in a transverse field $H$ is derived for dimension $d=4-\epsilon$ using an $\epsilon$ expansion based on the Wilson renormalization group. To first order in $\epsilon$ the model exhibits a line of critical points $T_c\mathrm{}\left(H\right)\mathrm{}$ with the same fixed point and critical exponents as in previous studies of the Wilson effective Hamiltonian.

Our recently published variational treatment of the $R$-matrix method for multichannel scattering requires computations involving unsymmetric matrices. An alternative derivation by Schlessinger and Payne has shown that the method can be reformulated in terms of symmetric matrices. Special techniques applicable to symmetric matrices simplify the computations and improve numerical accuracy.

Two explanations have been proposed for an apparent discrepancy between theoretical prediction and experimental measurement of third-sound attenuation. One of these proposes a new "macroscopic quantum uncertainly principle," and the other proceeds via nonlinear, anharmonic effects due to zero-point fluctuations. We argue that neither suggestion is acceptable.

Using the known direct-correlation functions for one- and three-dimensional fluids with hard-core repulsion, the convergence of the roots of the moment expansion for successive truncations has been investigated. The estimate given by the lowest-order truncation is not reliable, and usually at least eight moments are required to obtain accurate values for the decay of pair correlations.

The present paper applies the method of high-intensity quantum electrodynamics developed earlier to several problems of current experimental interest. In this paper the intensitydependent shifts and widths of atomic levels are calculated and applied to a given transition near resonance. The technique is demonstrated with three examples: the multiphoton ionization of atomic cesium and hydrogen in atomic beams and third-harmonic production in an atomic vapor. It is found that the multiphoton-ionization rate in a relatively weak laser beam (of order ${10}^8$ W/${\mathrm{cm}}^2$) is determined by the intensity-dependent level width ($6f$ configuration) as well as the interference of the fine-structure states, and that the rates for hydrogen, in a much more intense beam (of order ${10}^{12}$ W/${\mathrm{cm}}^2$) are determined by both the intensity-dependent widths and shifts a$\stackrel{\mathrm{`}}{\mathrm{s}}$ well as the wave-function renormalization constants. The agreement of these two examples of calculations with the experiments done recently is satisfactory. For third-harmonic production the role of two-photon resonance is emphasized, and the dependence of the generated third-harmonic intensity on the intensity and frequency of the fundamental is discussed. Near resonance, the ratio of third-harmonic intensity to fundamental intensity saturates.

The magnetic-dipole and electric-quadrupole hfs interaction constants of 11-h ${}_{}{}^{193m}{}_{}{}^{}\mathrm{Hg}$ in the $6s6p{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ state were determined from the observation of four level crossings. Previous studies relied on the observation of a single level crossing (W. W. Smith) and on optical spectroscopic data. The results, with second-order hyperfine, Zeeman, and cross Zeeman-hyperfine corrections are $A=-2399.60\mathrm{}\left(3\right)\mathrm{}$ MHz and $B=-655.6\mathrm{}\left(18\right)\mathrm{}$ MHz. The calculated hfs anomaly ${}_{}{}^{193m}{}_{}{}^{}\Delta _{}^{199}{}_{}{}^{}$ is 1.055(1)%, and the resulting electric-quandrupole moment is 1.2(1) b. The isotope shift is redetermined by the new hfs results.

Extensive calculations have been carried out to obtain the quadrupole shielding or antishielding factors $R\left(\mathrm{nd}\right)\mathrm{}$ for the lowest excited $\mathrm{nd}$ states of the alkali-metal atoms. In all cases except for lithium, and appreciable net antishielding [$R\left(\mathrm{nd}\right)<0\mathrm{}$] is found. For Li and Na, $R\left(\mathrm{nd}\right)\mathrm{}$ is approximately equal to the total ionic shielding or antishielding factor ${\gamma }_{\infty }$, as a result of the fact that the $\mathrm{nd}$ wave function $v_0\mathrm{}\left(\mathrm{nd}\right)\mathrm{}$ for these atoms is essentially hydrogenic, and hence the overlap between $v_0\mathrm{}\left(\mathrm{nd}\right)\mathrm{}$ and the core wave functions $u_0\mathrm{}\left(\mathrm{nl}\right)\mathrm{}$ and their perturbations $v_1(nl\to l^{\prime })$ is very small. For Li, ${\gamma }_{\infty }$ is positive, and accordingly $R\cong 0.25$, whereas for Na, ${\gamma }_{\infty }$ is negative (antishielding), and correspondingly $R\cong -3.9\mathrm{} \mathrm{to} -4.8\mathrm{}$, in going from $3d$ to $5d$. For the heavier alkali-metal atoms, namely, K, Rb, and Cs, $R\left(\mathrm{nd}\right)\mathrm{}$ is generally antishielding, but with much smaller absolute values than for Na. Thus $R\left(\mathrm{nd}\right)\mathrm{}$ lies generally in the range from -0.2 to -0.5. The values obtained for Rb are the most reliable, and range from -0.48 for Rb $4d$ to -0.20 for Rb $6d$. For K and Cs, the values of $R\left(\mathrm{nd}\right)\mathrm{}$ obtained are less reliable, because of the sensitivity of the valence wave functions $v_0\mathrm{}\left(\mathrm{nd}\right)\mathrm{}$ to the details of the effective one-electron potential $V_{\mathrm{eff}}\mathrm{}\left(r\right)\mathrm{}$.

The significance of retardation effects in photon emissions and absorptions is emphasized in the calculation of self-energy. It is explicitly demonstrated that inclusion of such effects leads to a finite answer for the shifts of atomic energy levels in a nonrelativistic theory without cutoff. Ambiguities that exist in the mass renormalization in the nonrelativistic approach are pointed out. Such ambiguities vanish from the relativistic theory. Explicit calculation is carried out in the case of hydrogen by utilizing the Coulomb Green's function. The advantage of the present approach in calculating self-energy shift in high-$Z$ hydrogenic ions is suggested.

The $M_{4,5}$ emission spectra from ${\mathrm{Gd}}_2$${\mathrm{O}}_3$ and ${\mathrm{Yb}}_2$${\mathrm{O}}_3$ have been obtained in fluorescence on a double-crystal spectrometer. The profiles differ from the $M_{4,5}$ emission spectra excited by electron impact. These differences are due to resonance radiation and substantiate the interpretation given by Bonnelle and Karnatak. The $M\alpha$ emission line was found to lie above (in energy) the $M_5$-absorption resonance line in ${\mathrm{Yb}}_2$${\mathrm{O}}_3$, which is in contrast to ${\mathrm{Gd}}_2$${\mathrm{O}}_3$ and general experience. It is suggested that this observation is a result of the discrete nature of the absorption lines. With the help of estimated binding energies for the final configurations $5p_{\frac{1}{2},\frac{3}{2}}^{5}4f^7$, the photoelectron spectrum of ${\mathrm{Gd}}_2$${\mathrm{O}}_3$ is discussed.