The energy spectra of electrons ejected from 25-keV ${\mathrm{Ar}}^{+}$ + Ar collisions have been measured. By employing the coincidence technique we were able to study specifically those electrons from collisions in which the projectiles were scattered through a known angle, $\theta ={21}^{\circ }\pm 2^{\circ }$, and were ionized to a known final charge $m$. Data were taken in the range of ejected-electron energies from 10 to 250 eV. The data reveal both fast electrons produced by Auger transitions which fill vacancies in the inner ($L$) shell and slow electrons produced by excitation of the outer ($M$) shell. A detailed examination of our spectra supports the conclusion that slow electrons may be ejected after as well as before the Auger event. Furthermore, the ratio of the number of fast Auger electrons to the number of slow electrons observed indicates that most inner-shell vacancies are filled after the ions have separated to a considerable extent.

We have calculated the third- and higher-order (multitime) cumulants of the intensity of single-mode laser light using the rotating-wave van der Pol (RWVP) model. Our results indicate a distinctly nonexponential time dependence of the cumulants slightly below threshold and an oscillatory time dependence somewhat above threshold. One can interpret this oscillatory behavior as showing that the larger fluctuations above the mean decay more rapidly than those below the mean. Measurements of the third-order intensity cumulants above threshold would be desirable to check for this behavior and to provide a more rigorous test of the RWVP model than the second-order intensity correlation.

Kinetic equations for the phase—space-time correlation functions contain memory functions that involve projection operators. It is shown that these memory functions can be represented by integral equations involving only real-time correlation functions, thereby eliminating the projection operators completely in the kinetic description of correlation functions. The weak-coupling and density expansions of the memory functions have been obtained through these integral equations.

Measurements of the molar specific heat $c_{P,x}$ of liquid ${\mathrm{He}}^3$/${\mathrm{He}}^4$ mixtures at saturated vapor pressure near the junction of the $\lambda$ and phase-separation curves reported in an earlier paper have been used to calculate values of ${\left(\frac{\partial s}{\partial T}\right)}_{P,x}=\frac{c_{P,x}}{T}$, ${\left(\frac{\partial \phi }{\partial T}\right)}_{P,x}=-{\left(\frac{\partial s}{\partial x}\right)}_{P,T}$, $s$, and $\phi -{\phi }_0$ at saturated vapor pressure throughout the junction region. Here $\phi$ is the difference ${\mu }_3-{\mu }_4$ between molar chemical potentials, $x$ is the mole fraction of ${\mathrm{He}}^3$ present, and the subscript 0 denotes the value of a quantity at the junction. Comparisons of ${\left(\frac{\partial s}{\partial T}\right)}_{P,x}$ and ${\left(\frac{\partial \phi }{\partial T}\right)}_{P,x}$ with their respective upper bounds at the $\lambda$ curve ${\left(\frac{\mathrm{ds}}{\mathrm{dT}}\right)}_{P,\lambda }+{\left(\frac{d\phi }{\mathrm{dT}}\right)}_{P,\lambda }{\left(\frac{\mathrm{dx}}{\mathrm{dT}}\right)}_{P,\lambda }$ and ${\left(\frac{d\phi }{\mathrm{dT}}\right)}_{P,\lambda }$ suggest but do not require that ${\left(\frac{\partial s}{\partial T}\right)}_{P,\phi }=\frac{c_{P,\phi }}{T}$ diverge all along the $\lambda$ curve, as our results indicate that it does at the junction. Our results are consistent with the following asymptotic behaviors at the junction: ${\left(\frac{\partial s}{\partial T}\right)}_{P,x,0\mathrm{}}-{\left(\frac{\partial s}{\partial T}\right)}_{P,x}\sim {(T-T_0)}^1$ at $x=x_0$ for $T>\mathrm{}{T}_0$; $|\phi -{\phi }_0|\sim {|x-x_0|}^2$ at $T=T_0$ for $x\lessgtr x_0$; ${\left(\frac{\partial s}{\partial T}\right)}_{P,\phi }\sim {|T-T_0|}^{\frac{-1\mathrm{}}{2}}$ at $\phi ={\phi }_0$ for $T\lessgtr T_0$.

In the continuing effort to establish contacts between the method of correlated basis functions (CBF) and the diagrammatic perturbation theory, we carry out parallel calculations of the excitation spectrum of a weakly interacting Bose gas. The Hugenholtz—Pines (HP) theory is first used to obtain the exact liquid-structure function and the energy spectrum, each to three orders in the strength parameter $\lambda$ that characterizes the interaction between a pair of particles in the system. Next we construct sets of CBF using three different correlating factors, and in each case calculate the excitation energy of the system. The results are compared to those obtained from the HP theory. Complete agreement is found to all orders considered. In conjunction with a paper to follow, the analysis demonstrates the flexibility of the CBF method and the relative ease of application in comparison to other methods.

The excitation spectrum of a charged Bose gas in the high-density limit is calculated to two orders in the expansion parameter $r_s^{\frac{3}{4}}$ by the method of correlated basis functions (CBF). To $O\left(r_s^{\frac{3}{4}}\right)$, the result differs from that obtained variationally, but agrees with that obtained by Ma and Woo via diagrammatic perturbation theory. The choice of the basis functions is, however, not unique. By choosing an alternate set of CBF which employs the ground-state eigenfunction as a correlating factor, we find it possible to extract from the excitation spectrum an expression for the liquid-structure function, also to two orders in $r_s^{\frac{3}{4}}$, which represents a new result. This new facet of CBF helps to demonstrate the flexibility of the method and the ease with which it can be applied to calculating properties of many-particle systems, model as well as realistic.

In this paper a new fully renormalized kinetic theory for self-diffusion is described. The theory is developed in terms of time-dependent correlation functions, and the main effort is in deriving general microscopic expressions for the memory function associated with the phase-space fluctuation function. These general expressions are valid for all frequencies and wave numbers and are rearranged in a way such that approximations can be made at a microscopic level in a straightforward manner. The main idea in the rearrangement is the expression of the memory function in terms of an effective two-body problem where the dynamics are described by the two-particle Liouville operator and an effective source representing the effect of the other $N-2$ particles in the system on the colliding pair. An exact microscopic expression for the two-particle source is derived. It is shown that even the simplest approximation in this scheme leads to the nontrivial Boltzmann-Enskog approximation for the memory function.

The momentum-translation approximation is valid for electromagnetic transitions in bound systems caused by external radiation of photon energy much less than the transition energy. Its utility is explored here for two types of problems that violate that restriction. One application is to resonant bound-bound multiphoton transitions of low multiphoton order, and results are compared to recent perturbative calculations. The other application is to both the transition rate and the spectrum of two-photon spontaneous emission from the metastable $2S$ state in hydrogen. Predicted transition rates are too low, but the spectrum agrees well with the known results. All momentum-translation results follow from simple closed-form analytical expressions.

In a previous paper a general formalism was developed for treating the time-dependent correlation functions that arise in the theory of self-diffusion. In this paper this formalism is used in conjunction with the approximation where the two-particle source is approximated by a sum of one-particle sources. This approximation follows from physical arguments and from an analysis of the exact equation for the two-particle source. The resulting expression for the memory function is similar to that found previously by Pomeau and is related to the ring terms studied by Kawasaki and Oppenheim. It is further shown that this correction to the Boltzmann-Enskog memory function can be written in terms of a product of phase-space correlation functions. This theory, to the extent that the hydrodynamical projection onto these correlation functions is dominant, provides a microscopic basis for the various mode-mode coupling theories. The associated long-time behavior of the velocity-autocorrelation function is shown to go as $t^{\frac{-3\mathrm{}}{2}}$ and the coefficient agrees with that found by Dorfman and Cohen for low densities. For higher densities there are differences. It is further demonstrated how one can remove the wave-number cutoffs used in other theories, and the velocity-autocorrelation function is calculated, in a particular approximation, over the complete range of times with no adjustable parameters.

We present semitheoretical estimates for the liquid structure function $S_k\mathrm{}\left(x\right)\mathrm{}$ of ${\mathrm{He}}^3$-${\mathrm{He}}^4$ solutions at low-${\mathrm{He}}^3$ concentrations $x$. Our calculation makes use of a perturbation theory in the representation of correlated basis functions, a variational procedure for intermediate- and high-momentum transfers, experimental data on the concentration dependence of the velocity of sound, and an interpolation between $k\approx 0.6$ and 1.2 ${\mathrm{\AA }}^{-1\mathrm{}}$. For a 6% solution, the entire $S_k\mathrm{}\left(0.06\right)\mathrm{}$ curve is obtained. Experimental measurements, presumably by x-ray scattering, are not yet available.

Estimates are given for the zero-momentum condensate fraction of ground-state ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ described by a Jastrow wave function at the solidification density of the fluid (2%) and at the melting density of the solid (∼1%). Indications are given that these estimates may be sensitively dependent on the form of the pair function utilized.

High-resolution measurements of the pressure coefficient ${\left(\frac{\partial P}{\partial T}\right)}_{\rho }$ of ${\mathrm{He}}^4$ are reported in both the one-phase and two-phase regions close to the critical point. The data consist of 29 isochores covering the density range $-0.2<\Delta \rho <0.2\mathrm{}$ and the temperature range $-0.020<t<\mathrm{}0.032\mathrm{}$, where $\Delta \rho =\frac{(\rho -{\rho }_c)}{{\rho }_c}$ and $t=\frac{(T-T_c)}{T_c}$. The intersections of the isochores with the coexistence curve locate 28 points on the coexistence curve. These points fit the equation $\left|\Delta \rho \right|=(1.395\mathrm{}\pm 0.020)t^{\beta }$, with $\beta =0.3554\mathrm{}\pm 0.0028$ and ${\rho }_c=69.580\mathrm{}\pm 0.020$ ${\mathrm{m}\mathrm{g}/\mathrm{c}\mathrm{m}}^3$. Parameters are reported for the best fit of the data to the "linear model" of Schofield, Litster, and Ho, in which the critical exponents have the values $\alpha =0.115\mathrm{}\pm 0.006$ and $\gamma =1.1743\mathrm{}\pm 0.0005$, and to a more accurate parametric model in which $\alpha =0.067\mathrm{}\pm 0.006$ and $\gamma =1.2223\mathrm{}\pm 0.0017$. The more accurate model does not have the symmetry required by the scaling hypothesis.

The Landau theory of Fermi liquids is used to calculate the frequency power spectrum of density fluctuations in liquid ${\mathrm{He}}^3$. Light-scattering intensities from "zero" sound, first sound, and quasiparticle-hole pairs are computed in detail. Finite-temperature x-ray structure factors are compared with experimental values and agreement is obtained within the considerable scatter of the experimental points. Light-scattering experiments are feasible and would provide detailed confirmation of Landau theory.

Optimization of the short-range correlation function in the Jastrow-Nosanow-Koehler form of trial ground-state wave function for quantum crystals, by functional minimization of the ground-state energy, is proved to result automatically in phonon frequencies which are fully consistent: frequencies defined from the one-phonon excitation energy and from the Gaussian portion of the ground-state wave function are identical.

Laser oscillation of atomic oxygen at 8446 Å occurs in four closely spaced lines with peculiar intensity ratios, all detuned from the atomic center frequencies of the three fine-structure transitions. These anomalies are caused by the selective reabsorption of resonance radiation from the lower laser level by ground-state oxygen atoms. The selectivity results from the fact that the velocity distribution of the laser levels is considerably wider than that of the ground state, because of the dissociative mode of production of excited oxygen atoms. Possible extension of this mechanism to the atomic-hydrogen system is discussed. New atomic-oxygen laser lines at 2.89, 4.56, 5.97, 6.86, and 10.40 $\mu$ are also reported and assigned.

The atomic-oxygen laser oscillates at four closely spaced frequencies on the gain profile of the 8446-Å fine-structure transitions. A set of experiments is reported which studies the competition among these four lines by suppressing one of them. The results are explained on the basis of the interaction of laser lines oscillating on Doppler-broadened transitions sharing a common lower level.

First-order Stark shifts and level-crossing fields have been calculated for states $n=2,3,4\mathrm{}$ and $Z=1,2,3,4\mathrm{}$, for applied electric fields from 0 up to a few kV/cm, using the solutions of the Dirac—Coulomb Hamiltonian. Comparison with the earlier work of Lüders and the experiments of Steubing, Junge, and Gunther has been made.

A Monte Carlo technique has been developed for evaluating the partition function of a hardisk system which should be generalizable to other many-body integrals. Evaluating the partition function directly, and hence the free energy per particle, instead of simulating the system allows much smaller systems to be used as realistic samples of an infinite system since a canonical ensemble of such systems is actually sampled. This eliminates the metastable-state problem that tends to lock simulated systems in one phase or another. The free energy has been evaluated for a 16-particle system with periodic boundary conditions for $0\le \rho \le 0.9$ with $\rho =\frac{\mathrm{density}}{\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{e}-\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{k}\mathrm{e}\mathrm{d}}$ density. The free energy is below that of a free-volume calculation which assumes crystallization for $\rho \le 0.79$ and equal to it for higher densities. At $\rho =0.8\mathrm{}$ the free-volume equation can be extrapolated to $N=\infty$ and gives $\frac{A\left(0.8\right)\mathrm{}}{\mathrm{NkT}}=4.01\mathrm{}\pm 0.04$, which compares well with the 3.96 ± 0.01 which Ree and Hoover obtained by integrating the pressure curve. The pressure in the phase-change region can also be extrapolated to give $\frac{P{V}_0}{\mathrm{NkT}}=7.6\mathrm{}$, which compares well with the Alder-Wainwright result of 7.72. The phase-change region, the only part which cannot be easily extrapolated, is $1.25\le \frac{V}{V_0}\le 1.28$ for 16 particles, which is about the correct density but only about 60% of the width of theirs ($1.266\le \frac{V}{V_0}\le 1.312$) for 870 particles because of a combination of $\frac{1}{N}$ effects and smoothing in fitting to the $\frac{A}{\mathrm{NkT}}$ data.

The experimental value of the polarizability anisotropy of a fluid is found to be an increasingly smaller fraction of the computer-calculated dipole-induced dipole anisotropy as the density is increased. This leads to the conclusion that the distortion of the polarizability of an individual atom from spherical symmetry produces an anisotropy which opposes and finally dominates the dipolar density anisotropy in determining the intensity of the depolarized light scattering.

Measurements of the intensity of luminescence produced by weak $\alpha$-particle sources in He II are presented for $0.3<T<\mathrm{}4.2\mathrm{}$ °K, for different chamber sizes, and with an electric field applied in the region of the $\alpha$-particle source. With zero field the intensity exhibits a complex behavior, remaining approximately constant between $T_{\lambda }$ and 1.2 °K, then dropping to a minimum near 0.6 °K, and rising again at lower temperatures. The application of an electric field (up to 13 000 V/cm) in the source region reduces the intensity above 0.8 °K but increases it at lower temperatures. The transient behavior of the luminescence upon application of a pulsed field is described and discussed. The qualitative features of the temperature dependence of the luminescence are accounted for in terms of radiation from metastable systems, the diffusion coefficient of which rises exponentially ($\sim e^{\frac{\Delta }{\mathrm{kT}}}$) as the temperature drops. Approximate values of the diffusion coefficient are presented. The electric-field-induced amplification of the luminescence below 0.8 °K is attributed to metastable interactions with charged vorticity.