The ostensible correctness of the Mihara-Puff theory of the structure factor for liquid helium-four and well-known sum-rule expressions are combined to suggest two limiting forms for the dynamic structure factor. One of them is exact in the limit $k\to \infty$ and has the form proposed by Hohenberg and Platzman. We show that it should provide information about Bose condensation if inelastic neutron scattering can be done for $k>\mathrm{}40\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$. The other is a simple phenomenological form which applies to the range $3 {\AA }^{-1\mathrm{}}<k<\mathrm{}8\mathrm{} {\AA }^{-1\mathrm{}}$ and is shown to describe successfully the scattering experiments of Cowley and Woods.

Some comments on a recent paper of Dashen, Ma, and Bernstein on an $S$-matrix formulation of statistical mechanics are made and, in particular, an alternate form of one of their main results (which was obtained by Watson in 1956) is discussed.

The impact-broadening operator $\Phi$ for the hydrogen line ${\mathrm{H}}_{\alpha }$ is calculated by solving numerically for the $S$ matrices using the straight-line classical-path approximation. All contributing multipoles in the perturber- (free-electron-) atom interaction [$V\left(t\right)\mathrm{}$] are included; time ordering of the operators in the $S$ matrices is retained. The matrix elements are compared with previous approximations based on the same model; the effects on the ${\mathrm{H}}_{\alpha }$ line profile are considered.

The entropy is determined of a quantum-mechanical system whose statistical state is characterized by a Wigner distribution function that is Gaussian in form. It is found to depend only on the variance of the distribution function. This enables us to study quantum mechanically the approach to equilibrium of coupled harmonic-oscillator chains, a system for which a classical treatment has been given recently by Robertson and Huerta.

Experimental cross sections for the electron-impact vibrational excitation of ${\mathrm{CO}}_2$ are compared with the theoretical calculation in the Born approximation. It is found that the optically forbidden mode (100) can be exicted through the polarization interaction, whereas the dipole interaction is responsible for the excitation of both the infrared-active modes (010) and (001).

The tunable spin-flip Raman laser has been proposed as a potentially useful instrument for high-resolution spectroscopic and heterodyne applications in the infrared. On the basis of the published experimental data, however, the effective linewidth of this laser may be too broad for such applications, and attempts to reduce it could destroy the continuous tunability.

The fragmentation of several diatomic iodine compounds as a consequence of ${\beta }^{-}$ decay was investigated. Information about the velocity spectra of the ${\mathrm{Xe}}^{131}$ fragments was obtained by analyzing the profiles of their $\gamma$ lines using the nuclear resonance fluorescence technique. Experimental cross sections for resonance fluorescence obtained with gaseous ${\mathrm{I}}^{131}$ sources are in satisfactory agreement with predictions using a simple model for the fragmentation process.

A discussion of relativistic bremsstrahlung cross sections is given for incident-electron kinetic energies in the range 5 keV-1 MeV, based on an exact numerical calculation using screened potentials. Comparisons are made with previous authors' results, extending the discussion of a preliminary note. Exact point-Coulomb and Born-approximation results are contrasted. The present results show that the Born approximation significantly underestimates the bremsstrahlung cross sections in the energy region considered. Screening effects are somewhat larger than expected, and when large are not well described by a form factor.

We have measured the $2S_{\frac{1}{2}}-2P_{\frac{3}{2}}$ energy separation ($\Delta E-S$) in the $n=2\mathrm{}$ state of atomic hydrogen by an atomic-beam radio-frequency method. We used a beam of metastable atoms in the single hyperfine state ${\beta }_A(F,m_F=0,0)$. The electric dipole transitions ${\beta }_A-b(F,m_F=1,+1)$ and ${\beta }_A-d(F,m_F=1,-1)$ were observed at fixed frequencies by sweeping the Zeeman magnetic field parallel to the beam axis. Measurements of the frequencies of the rf field used to drive the transition and the magnetic fields at the line centers of the resonance curves, along with the theory of Zeeman splitting were used to determine the zero-field splitting ($\Delta E-S$). Our final value of ($\Delta E-S$) is 9911.250 ± 0.063 MHz, where the quoted uncertainty is one average deviation from the mean. Using the revised experimental value of the Lamb shift, $S_H=1057.90\mathrm{}\pm 0.10$ MHz, we obtain $\Delta E=10\mathrm{} 969.15+0.12$ MHz. The corresponding value for ${\alpha }^{-1\mathrm{}}$ is 137.0356 ± 0.0007.

Millimeter and submillimeter wave rotational transitions have been measured for different isotopic species of arsine and stibine from which accurate values of the rotational constants, including centrifugal stretching constants, nuclear quadruple and nuclear magnetic coupling constants, were obtained. Results (in Mc/sec) are for ${}_{}{}^{75}{}_{}{}^{}\mathrm{As}$${\mathrm{H}}_3$, $B_0=112\mathrm{} 470.59\pm 0.03$, $D_J=2.925\mathrm{}\pm 0.003$, $D_{\mathrm{JK}}=-3.718\mathrm{}\pm 0.004$, $eqQ=-162.63\mathrm{}\pm 0.03$, $C_N=0.106\mathrm{}\pm 0.003$, $C_K=0.028\mathrm{}\pm 0.014$; for ${}_{}{}^{75}{}_{}{}^{}\mathrm{As}$${\mathrm{D}}_3$, $B_0=57\mathrm{} 477.60\pm 0.02$, $D_J=0.741\mathrm{}\pm 0.002$, $D_{\mathrm{JK}}=-0.928\mathrm{}\pm 0.003$, $eqQ=-164.75\mathrm{}\pm 0.03$, $C_N=0.051\mathrm{}\pm 0.003$, $C_K=0.069\mathrm{}\pm 0.015$; for ${}_{}{}^{121}{}_{}{}^{}\mathrm{Sb}$${\mathrm{H}}_3$, $B_0=88\mathrm{} 038.99\pm 0.03$, $D_J=1.884\mathrm{}\pm 0.004$, $D_{\mathrm{JK}}=-2.394\mathrm{}\pm 0.015$, $eqQ=460.31\mathrm{}\pm 0.10$, $C_N=0.245\mathrm{}\pm 0.006$, $C_K=0.247\mathrm{}\pm 0.030$; for ${}_{}{}^{123}{}_{}{}^{}\mathrm{Sb}$${\mathrm{H}}_3$, $B_0=88\mathrm{} 022.51\pm 0.03$, $D_J=1.884\mathrm{}\pm 0.004$, $D_{\mathrm{JK}}=-2.365\mathrm{}\pm 0.015$, $eqQ=586.65\mathrm{}\pm 0.11$, $C_N=0.130\mathrm{}\pm 0.005$, $C_K=0.165\mathrm{}\pm 0.030$; for ${}_{}{}^{121}{}_{}{}^{}\mathrm{Sb}$${\mathrm{D}}_3$, $B_0=44\mathrm{} 694.92\pm 0.03$, $D_J=0.473\mathrm{}\pm 0.004$, $D_{\mathrm{JK}}=-0.598\mathrm{}\pm 0.009$, $eqQ=465.32\mathrm{}\pm 0.10$, $C_N=0.127\mathrm{}\pm 0.006$, $C_K=0.162\mathrm{}\pm 0.030$; for ${}_{}{}^{123}{}_{}{}^{}\mathrm{Sb}$${\mathrm{D}}_3$, $B_0=44\mathrm{} 678.81\pm 0.03$, $D_J=0.476\mathrm{}\pm 0.004$, $D_{\mathrm{JK}}=-0.589\mathrm{}\pm 0.010$, $eqQ=593.06\mathrm{}\pm 0.11$, $C_N=0.063\mathrm{}\pm 0.005$, $C_K=0.044\mathrm{}\pm 0.030$.

The superposition-of-configurations method has been used to calculate, a single pair at a time, the pair correlation energies for Ne, ${\mathrm{Ne}}^{+}$, ${\mathrm{F}}^{-}$, and F. The approach is essentially a symmetry-adapted variation of Nesbet's formulation of the Bethe-Goldstone scheme for the atomic correlation problem, and the aim of this research was to test the usefulness of the method for predicting such physically observable quantities as ionization potentials and electron affinities. The calculations predict an ionization potential for neon of 21.52 eV, compared with a 21.56-eV experimental value, and a fluorine electron affinity of 3.47 eV, for which the experimental value is 3.45 eV.

Ground-state energy eigenvalues for an electron in a stationary finite electric-dipole field are calculated by a novel variational approach. The physical model is taken to be a perturbed hydrogen atom. Accurate energy eigenvalues are obtained for a large range of dipole moments. The simple variational functions used compare favorably with more nearly exact eigenfunctions obtained in complex calculations.

A Zeeman-quenching atomic-beam method has been utilized for the determination of the fine- and hyperfine-structure energies and auto-ionization lifetimes of the metastable $\mathrm{}\left(1s2s2p\right)\mathrm{}{}_{}{}^4{}_{}{}^{}P_J^{}{}_{}{}^{}$ states of ${\mathrm{Li}}^6$ and ${\mathrm{Li}}^7$. Both the fine-structure intervals and the lifetimes of the $J=\frac{3}{2}$ and $J=\frac{1}{2}$ states are found to be in disagreement with existing theoretical calculations. The quenching of metastable lithium atoms in a nonuniform magnetic field can be satisfactorily described with the aid of the "adiabatic criterion." The present results also permit a quantitative evaluation of a proposal for producing polarized lithium nuclei.

Employing analytic Hartree-Fock wave functions, model calculations have been performed on the structure and lifetimes of the slowly auto-ionizing states arising from $(1s, 2s, 2p){}_{}{}^4{}_{}{}^{}P$ in ${\mathrm{He}}^{-}$ and Li. The effect of mixing with the associated ${}_{}{}^2{}_{}{}^{}P\text{'}\mathrm{s}$ is considered and the phenomenon of differential metastability discussed. A framework is provided to interpret experimental observations.

A general treatment is given for the interaction of two propagating modes when they are non-linearly coupled by a large-amplitude driving wave. The equations describing the space-time development of the mode amplitudes have a certain symmetry due to the constraints of small-signal energy conservation. The wave solutions, given the vector coupling relations (${\omega }_d={\omega }_a\pm {\omega }_b,k_d=k_a\pm k_b$), are of four possible types, depending on the signs of the energy densities and group velocities of the individual modes. The periodicity imposed by the driving wave is used to construct a spatial-temporal harmonic dispersion diagram in which these interactions are displayed. The results are then shown to be generalizations of the wave-wave couplings of linear theory.

We study the Thomas-Fermi-Dirac statistical model of the atom in the energy-functional formulation. We obtain minima of the total energy for five analytic-screening-function-density combinations. Total energies, average radii, and rms radii vary from model to model quite markedly, and depart quite substantially from "data" based upon Hartree-Fock or Hartree-Fock-Slater calculations. For the model based upon the analytic screening function due to Green, Sellin, and Zachor and for a closely related "regularized" model, the dependence of the component energies upon the electron number $N$, the model parameters, and certain integral constants is represented analytically. Minimization of the total energy with respect to the potential parameters leads to simple algebraic equations. The results again are poor. However, by making reasonable semiempirical modifications in the component terms, we find we can achieve stability with binding energies and potential parameters which are close to the data obtained from Hartree-Fock (HF) or Hartree-Fock-Slater (HFS) studies.

Absolute transition probabilities in the visible and near-infrared spectra of FI, ClI, ClII, and BrI have been measured using a gas-driven shock tube. Thermodynamic conditions in the source were overdetermined by line intensity, pressure, and electron-density data. $A$ values were obtained by spectroscopic techniques which reduced errors due to residual uncertainties in the source conditions. Measured transition probabilities are compared with theoretical calculations and with other experimental values.

A group-theoretical analysis of the states of first-row atoms and their internal electrostatic interactions is developed. The Hamiltonian is found to be completely expressible as a linear combination of operators that are diagonal in $U\left(3\right)\mathrm{}$, operators diagonal in $O\left(4\right)\mathrm{}$, and operators diagonal in both. This makes possible a simple and uniform treatment of the energy levels of first-row atoms. We use it here to analyze configuration mixing between the $2s^{2}2p^x$ and $2p^{x+2\mathrm{}}$ configurations, and determine the contribution of configurations of $O\left(4\right)\mathrm{}$ and $U\left(3\right)\mathrm{}$ symmetry in several types of mixed-configuration wave functions.

The problem of the threshold and growth of parametric oscillation in a lossy optical cavity is treated quantum theoretically. It is shown that during the growth of oscillation each of the generated modes is statistically as chaotic as those observed previously in the lossless case, and is so chaotic that the additional uncertainty introduced by the loss processes has no further effect on the single-mode photon distributions. However, there is considerable cross correlation between the idler and signal modes. The cross correlation in the numbers of idler and signal quanta is essentially complete for large numbers, but is shown to be reduced when the numbers are smaller, because of noise due to loss. Correlations in phase are also investigated and it is shown that, under certain statistical conditions necessary for phase to be a relevant concept, the phase correlation is also essentially complete.