Hall's modified theory of structural relaxation is applied to explain the pressure dependence of excess absorption in water, methanol, and ethanol in the pressure range 1-5000 kg/${\mathrm{cm}}^2$. An excellent agreement has been found between the theoretically calculated structural absorption and experimentally observed excess absorption for these three associated liquids. The values of structural compressibility ${\beta }_{\mathcal{r}}$, structural relaxation time $\tau$, and the free-energy difference $\Delta F$ between the two states assumed nearly coincide with their corresponding values in the range 1-2000 kg/${\mathrm{cm}}^2$ predicted in previous papers, and beyond this ($p>\mathrm{}2000\mathrm{}$ kg/${\mathrm{cm}}^2$) the values are the same as would be expected by extrapolation of earlier curves up to 5000 kg/${\mathrm{cm}}^2$. This gives strong support to the two-state model and the assumptions made therein to explain absorption results in water, methanol, and ethanol.

Considerable difficulty has been evidenced recently in determining and understanding the excitations in liquid helium and their interactions. Small-angle scattering of nuclear gamma rays is suggested for studying the excitations, which should complement the investigations using inelastic neutron scattering. The theory is presented and experimental problems are discussed. The differential cross section for small-angle scattering of nuclear gamma rays for single excitations is related to the x-ray liquid structure factor. The shift in energy of the nuclear gamma rays is expressed in terms of a Doppler shift which is shown to be comparable to the velocities used in nuclear resonance fluorescence. Scattering angles, linewidths, countrates, and resolution are evaluated.

A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position $\overrightarrow{\mathrm{R}}$ and moving with classical velocity $\overrightarrow{\mathrm{v}}$ It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The QMTE represents a somewhat different formulation of the problem than that considered in earlier works. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

The perturbation theory of liquids developed recently by Weeks, Chandler, and Andersen (WCA) is examined in detail: Each assumption introduced by these authors is tested by comparison with "exact" computer results. It is shown that the basic assumptions of WCA are justified. An improved expression for the radial distribution function of the hard-sphere gas enables us to correct for some further inconsistent assumptions of the WCA theory. We then succeed in giving simple analytical expressions for the thermodynamic functions of the Lennard-Jones fluid shown to be quite good at high density. We show that the remainder of the perturbation series, which converges slowly at lower density, can be evaluated with the help of the Percus-Yevick equation. We therefore possess a unified theory of liquids which is especially simple at high density. Finally we reexpress the original WCA theory in an analytical form.

Measurements of the density $\rho$ versus pressure $P$ along isotherms for six ${\mathrm{He}}^3$-${\mathrm{He}}^4$ solutions ($X_3=0.960, 0.886, 0.800, 0.600, 0.400, \mathrm{and} 0.200$) near their liquid-vapor critical point are presented. For a given mole fraction $X_3$, it was found that the boiling and dew curves in the $\rho -P$ plane could be represented by a relation similar to that for the coexistence curve of a pure fluid. Here the point at the extremity of the two-phase region, which we call the symmetry point with the parameters $P_s$, ${\rho }_s$, and $T_s$, takes the place of the critical point for a pure fluid. The dew curve is given by $({\rho }_s-\rho ) \propto {(P_s-P)}^{{\beta }^{\prime }}$ with ${\beta }^{\prime }=0.375\mathrm{}\pm 0.02$, independent of $X_3$. The determination of the line of critical points in the $P-T$ plane from the dew and boiling curves at various mole fractions is described. The pressure, density, and temperature for the critical and the symmetry points are presented and discussed. From the dew and boiling curves, the true coexistence curves were constructed in the $\rho -P$ plane at constant $T$ and in the $\rho -T$ plane at constant $P$ and could be described approximately by $({\rho }_L-{\rho }_G)\propto {(P_c-P)}^{\beta }T$ and $({\rho }_L-{\rho }_G)\propto {(T-T_c)}^{\beta }P$ with an average value for the various isotherms and isobars considered of ${\beta }_T=0.42\mathrm{}\pm 0.06$ and ${\beta }_P=0.39\mathrm{}\pm 0.05$. Here ${\rho }_L$ and ${\rho }_G$ are the densities along the coexistence curve on the liquid and the gas side, respectively. The measurements of the compressibility $k_{T,X}$ along the critical isochore in the one-phase region seem to exclude a "strong" divergence with ($T-T_c$), but do not extend close enough to $T_c$ to either support or disprove the "weak" divergence as predicted by Griffiths and Wheeler. These measurements are compared with those of the normalized compressibility ${\left(\frac{\rho }{{\rho }_s}\right)}^2{k}_{T,X}$ along the dew and boiling curves. Comparisons are also made with the behavior of the compressibility for a pure fluid along the coexistence curve and above $T_c$. A brief addendum to the analysis for $k_T$ in pure ${\mathrm{He}}^3$ is presented.

Pressure and density measurements along the boiling and dew curves for ${\mathrm{He}}^3$-${\mathrm{He}}^4$ mixtures for several temperatures above 2 K are presented. From these data, the excess chemical potentials and the excess Gibbs energy are calculated.

According to the quantum theory of the optical-pumping cycle, one can describe the effect of a nonresonant light beam on the different Zeeman sublevels of an atomic ground state by an effective Hamiltonian ${\mathcal{H}}_e$ which depends on the polarization and spectral profile of the incident light. In order to check the structure of ${\mathcal{H}}_e$, we have performed a detailed experimental study of the ground-state energy sublevels of various kinds of atoms perturbed by different types of nonresonant light beams. Attention is paid to the modification of the Zeeman structure due to ${\mathcal{H}}_e$. We have been able to obtain experimentally in the ground state of ${}_{}{}^{199}{}_{}{}^{}\mathrm{Hg}$, ${}_{}{}^{201}{}_{}{}^{}\mathrm{Hg}$, and ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$, Zeeman light shifts that are larger than the width of the levels due to the thermal relaxation. The removal of the Zeeman degeneracy in zero external field, due to a nonresonant light irradiation, is observed by different optical-pumping techniques; the full Zeeman diagram of the perturbed atoms is also determined when a static field ${\overrightarrow{\mathrm{H}}}_0$ is added. We have checked that the effect of ${\mathcal{H}}_e$ can be described in terms of fictitious static electric or magnetic fields. These fictitious fields can be used to act selectively on a given atomic level.

The theoretical vortex-core radii of Pollock are shown to be in gross disagreement with recent experimental results of Glaberson and Steingart.

The memory function associated with the phase-space density correlation function has previously been calculated in the low-density limit by Mazenko. In this paper a simple, classical method of arriving at his primary result is pointed out. The application to self-correlations is also noted.

Recent line-shape experiments on the absorption series of cesium pressurized by various concentration ratios of argon and helium provide an opportunity to study the additivity of perturber interactions. Calculations which assume additivity and which assume additive adiabatic collisions agree well with the reported data. The results suggest that a systematic study of such experiments using accurate digitized data can furnish criteria for the valid applications of the additivity approximation.

A time-of-flight technique has been used to investigate the lifetime $\tau$ of the long-lived ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ states of neon, argon, and krypton. The results are, for neon, $\tau \left({}_{}{}^3{}_{}{}^{}P\right)>\mathrm{}0.8\mathrm{}$ sec; for argon, $\tau \left({}_{}{}^3{}_{}{}^{}P\right)>\mathrm{}1.3\mathrm{}$ sec; and for krypton, $\tau \left({}_{}{}^3{}_{}{}^{}P\right)>\mathrm{}1.0\mathrm{}$ sec. The present measurements are limited by residual-gas or beam-beam scattering and by the length of the time-of-flight region being short compared to a decay length.

A perturbation treatment of the variable-phase method for scattering is presented. The zeroth-order phase shift is given by the solution of a first-order nonlinear differential equation. The perturbation corrections are given as the solutions of first-order nonhomogeneous but linear differential equations. A variational procedure for the optimization of the zerothorder approximation is formulated. The results of a test calculation for the $s$-wave scattering from an attractive exponential potential are included.

The probability for Coster-Kronig transfer of vacancies from the $L_2$ to the $L_3$ subshell of Pb is measured by observing the $K$ x-ray spectrum in coincidence with $L\alpha$ x rays in the electron-capture decay of ${\mathrm{Bi}}^{207}$. The intensity of the $K{\alpha }_2$ component of the coincident spectrum is a measure of the $L_2-L_{3}X$ Coster-Kronig transition probability. A value of 0.156 ± 0.010 is obtained for $f_{23}$.

The natural orbitals (NO) obtained from ${}_{}{}^1{}_{}{}^{}S$ Be atom ground-state wave functions which incorporate various amounts of the correlation energy are Fourier transformed to momentum space in order to obtain radial momentum distributions $J_0\mathrm{}\left(p\right)\mathrm{}$. Momentum distributions calculated from several analytical restricted Hartree-Fock (RHF) wave functions are also presented. Correlated and RHF Compton profile values $J\left(q\right)\mathrm{}$ are found to be in better agreement than the corresponding $I_0\mathrm{}\left(p\right)\mathrm{}$ values. In the "valence shell" portion of the $I_0\mathrm{}\left(p\right)\mathrm{}$ distribution, relative differences as large as 25% are observed between correlated and RHF values, whereas in the "core" portion of $I_0\mathrm{}\left(p\right)\mathrm{}$ the correlated and RHF values are in relatively good agreement. The virial theorem is used to explain the differences observed between correlated and RHF $I_0\mathrm{}\left(p\right)\mathrm{}$ distributions. Basis set effects are found to be negligible in comparison with correlation effects. The present calculations indicate that much of the discrepancy between correlated and RHF $I_0\mathrm{}\left(p\right)\mathrm{}$ values, at least for the ${}_{}{}^1{}_{}{}^{}S$ Be ground state, is due to the $2s-2p$ "near-degeneracy" effect. They also demonstrate that the node found when examining the long-range behavior of the RHF $1s$ orbital in position space is of a spurious nature.

The theory of the line shape in coherent electric quadrupole absorption and emission processes involving $N$ interacting molecules is developed, both quantum mechanically and with the use of a classical model. The theory is applied to small clusters and to linear chains of molecules. As in the dipole case, the effects of the interaction include in general a splitting of each molecular transition line into a number of components, a shift of each component from the molecular transition frequency, and a broadening or narrowing of each component relative to the width of the molecular line.

Double perturbation theory has been applied to the calculation of the total and hyperfine interaction energies of ground-state lithium. The effective one-electron potential used contains only the Coulomb terms which arise from the $1s$- and $2s$-electrons, multiplied by a factor of $\frac{2}{3}$ for correct asymptotic screening. The first-order perturbed wave functions in correlation and the hyperfine interaction are obtained by a numerical finite-difference solution of their respective two- and one-particle inhomogeneous differential equations. Convergence of both expansions is rapid, giving a total energy of -7.4793 ± 0.0038 a.u. and a spin density at the nucleus of $(2.850\mathrm{}\pm 0.076)a_0^{-3\mathrm{}}$, in good agreement with their accurate counterparts: -7.47807 a.u. and $2.9096a_0^{-3\mathrm{}}$.

The polarization of quench-induced ${\mathrm{L}}_{\alpha }$ radiation is calculated for a metastable hydrogen atom entering an electric field with entry conditions intermediate between adiabatic and impulsive. We find that for most common experimental geometries the adiabatic value for the polarization may be used with less than 10% error.