The surface pressure exerted by a monomolecular layer of pentadecanoic acid spread on a pH-2 distilled-water substrate has been measured as a function of temperature and surface density in the vicinity of the gas-liquid critical point for this two-dimensional system. From these measurements, the shape of the gas-liquid coexistence curve and the isothermal compressibility along both sides of the coexistence curve and above the critical temperature are deduced. In agreement with the findings of Hawkins and Benedek obtained on pure distilled water, we find that a true phase transition exists between the liquid and gaseous states of the film and that the behavior of the film in the vicinity of its critical point can be characterized by power-law behavior with mean-field exponents. We do not, however, find it possible to interpret all of our data in terms of a simple mean-field phase transition.

When a plasma is extremely dense or hot, the electrons lose their efficiency for stopping heavy charged particles. The main process for their slowing down then is the small-angle ion-ion scattering, where the bare Coulomb cross section becomes infinite as ${\theta }^{-4\mathrm{}}$. The purpose of this paper is to evaluate the collective screening effects which make the ion Coulomb cross section finite. The calculations are performed in the random-phase approximation and show that the Coulomb cross section is essentially cut off for energy transfers smaller than $\hslash {\omega }_p$, where ${\omega }_p$ is the plasma frequency of the ions.

The transport properties of molten alkali halides have been calculated in molecular dynamics "experiments" based on rigid-ion pair potentials of the Huggins-Mayer form with parameters proposed by Tosi and Fumi. The coefficients of shear viscosity and electrical conductivity are obtained by computing the response of the system to a small applied field of the appropriate type, and the extension of the method to the calculation of current-current correlation functions of acoustic and optic character is also considered. Comparison with experimental data shows that the electrical conductivities are very well reproduced, but systematic discrepancies are found for diffusion coefficients and viscosities.

Muonic x-ray spectra have been measured for target sequences including graphite, diamond, their boron-nitride counterparts, three organic compounds, ice and water, eight oxides of metals, alkali halides in aqueous solution and alkali chlorides in anhydrous crystalline form, and calcium and titanium hydrides. Comparisons are made of Lyman-series intensity patterns, and relative muon capture probabilities in the constituent elements of compounds are compared with the "$Z$-law" relation. The Lyman intensities of the C and N in the low-$Z$ targets are found to exhibit two kinds of pattern, one with relatively weak higher-series members characterizing the diamond and graphite structures, and one with stronger higher-series members characterizing the other (hydrogen-containing) compounds. There is some evidence that the latter intensity behavior applies to the aqueous ions as well. For the oxide sequence, increasing covalency appears to correlate with increasing muon capturing ability of the metal element and with increasing intensity of the higher Lyman members for both the metal element and the oxygen. Effective relative muon-capture cross sections have been obtained for aqueous alkali and halide ions.

Correlation functions at two times and three space points are considered as an extension of recent investigations of time-independent triplet correlation functions. The formal kinetic theory for these functions is shown to be the same as that for the usual two-point functions. The results are expressed in terms of the solution to the formal one-particle kinetic equation, a two-particle functional that is the kernel for the collision operator in the one-particle equation, and various equilibrium static correlation functions. In particular, the three-point density correlation function is considered and related to the pressure derivative of the dynamic structure factor as a means to indicate indirect experimental accessibility to the triplet functions. A simple but relatively accurate kinetic model for the dynamic structure factor is used to illustrate the behavior of the pressure derivative.

The equilibrium and dynamical structure factors of a nitrogenlike system near its triple point are computed by a molecular-dynamics simulation using an "atom-atom" potential. Both structure factors are shown to be almost identical to the structure factors of a system of spherical molecules when the intramolecular contributions have been subtracted and the rotational degrees of freedom taken into account in a trivial way. Thus only very little information on the anisotropic part of the intermolecular interaction can be gained from these two quantities. For the dynamical structure factor, a strong and unexpected disagreement between our computation and the experiment of Carneiro and McTague at small wave numbers probably indicates that the experimental results should be corrected for double-scattering contributions.

The evolution of a homogeneous dilute gas is treated as a Markov process in the complete set of $K$ coarsegrained velocity states of all $N$ particles. From the Siegert master equation for the process a Fokker-Planck equation is derived which describes, in the limit $N\to \infty$, the fluctuations in the occupation numbers $n_i\mathrm{}\left(t\right)\mathrm{}$, whose average behavior is governed by the (appropriately discretized) Boltzmann equation: The continuum limit $K\to \infty$ corresponds to fluctuations in the usual molecular distribution function $f(\overrightarrow{\mathrm{r}}\overrightarrow{\mathrm{v}};t)$. On similar reasoning, a Fokker-Planck equation is obtained for the fluctuation process near equilibrium, where the average is governed by the linearized Boltzmann equation. The theory of linear irreversible processes, which offers a statistical description of fluctuations on a thermodynamical basis, is applied to the linearized Boltzmann equation—treated as a linear phenomenological equation—following the development given recently by Fox and Uhlenbeck: The resulting stochastic equation is seen to be equivalent to the Fokker-Planck equation obtained from the master equation, yielding a multidimensional Ornstein-Uhlenbeck process which describes the fluctuations in molecular phase space.

The drift velocity of electrons in mixtures containing a molecular gas in a rare-gas diluent has been calculated as a function of $\frac{E}{N}$ (ratio of the electric field to neutral number density) and of molecular-gas concentration using a numerical solution of the Boltzmann transport equation. The results agree well with available experimental data where gas purity was strictly controlled. In argon, it is shown that very small amounts of a molecular additive can drastically alter the behavior of the electron drift velocity. The curves exhibit a local maximum with respect to $\frac{E}{N}$ and an absolute maximum with respect to molecular concentration. A useful formula for the mobility has been derived, which explains the peculiar behavior of the electron drift velocity in these gas mixtures.

An extension of the interaction theory of a Langmuir probe with a plasma to the case of an electron-emitting probe surface is used in a simplified model of the cathode region of high-pressure refractory cathode arcs. The interaction determines the matching condition at the plasma-cathode interface. Such an interaction is physically reasonable when the cathode drop is small compared with the plasma ionization potential. The model, formulated to be only qualitative, is solved analytically and its behavior analyzed. The model's ability to display a wide range of arc currents over which the cathode drop is nearly constant at a few volts is demonstrated in a numerical example.

The energy loss of a fast ion to a degenerate electron-ion plasma via the excitation of ion waves is calculated by the dielectric-function formalism. This collective contribution is at most a few percent of the energy loss arising from ion-ion collisions for plasmas in the laser fusion domain but can be a significant fraction of the total energy loss to ions in higher-density plasmas encountered in astrophysical situations.

Measurements of the temperature dependence of the hyperfine density shifts of ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$, ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$, and ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$ in He, Ne, Ar, and ${\mathrm{N}}_2$ buffer gases have been extended to low temperatures (- 125 to 25 °C). The results confirm and extend the nonlinear temperature dependence. Low-order polynomial fits of the density shifts vs $T\left(°\mathrm{C}\right)$ have been calculated for each alkali metal and buffer gas.

The literature contains three definitions of superradiant lifetime, standing in the ratio 1:2:4. The first may be defined by ${\tau }^{\mathrm{RE}}=\frac{T_1}{N\mu }$, where $\mu$ is the geometrical factor of Rehler and Eberly. The second appears naturally in Dicke's equation $\dot{\phi }={\left({\tau }^{\mathrm{D}}\right)}^{-1\mathrm{}}sin\phi$. The third may be defined, following Arecchi and Courtens, by $I=\frac{\hslash {\omega }_0}{{\tau }^{\mathrm{AC}}}$ for a maximally superradiant sample. For large Fresnel number, $\mu =\left(\frac{3}{8\pi }\right)\frac{{\lambda }^2}{A}$; the numerical coefficient has been calculated incorrectly by some authors, so that the resulting formulas for superradiant lifetime do not match the definitions. The many superradiant lifetimes in current use are identified with the above three.

The quantum-mechanical impulse approximation (IA) has been successfully applied to vibrational and rotational excitation in atom-diatomic-molecule collisions. An additional closure approximation used previously to calculate total vibrational transition probabilities is discussed. A comparison with exact IA calculations shows that the closure approximation overestimates large vibrational transitions. This discrepancy is due to the fact that the vibrational transitions are accompanied by large rotational excitations.

The Born approximation, including the internuclear interaction, is used to compute cross sections for the transfer of one electron from a multielectron atom to an incident proton. When the full internuclear interaction is included, the results lie far above high-energy experinental $K$-shell data for $p$+Ar. However, when only enough internuclear interaction is used so that the total projectile-target interaction goes to zero asymptotically in accord with plane-wave functions actually used, fair agreement at high energies is obtained. The latter form of the Born approximation is compared to data on $K$-shell capture from helium as well as argon, in addition to the simpler approximation of Oppenheimer and of Brinkman and Kramers (OBK), where no internuclear interaction is included. The OBK results typically lie a factor of 2 to 8 above the data, while our Born results are within a factor of 2 of most of the existing high-velocity $K$-shell data, i.e., with an accuracy comparable to more sophisticated calculations.

Absolute cross sections for the single ionization of ${\mathrm{Tl}}^{+}$ ions by electron impact have been measured as a function of electron energy from below threshold to approximately 2000 eV. It was found that the cross section increased from a zero value at and below threshold to a maximum value of about 1.7 × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ at an incident electron energy of approximately 100 eV. Measurements were made in a crossed-beam facility operating in the pulsed-beam mode. Numerous consistency checks were performed to evaluate possible sources of experimental error.

The semiclassical theory for the spontaneous radiative association coefficient is reviewed. The example of ${\mathrm{H}}_2^{+}$ formation during a proton collision with a hydrogen atom is considered in both the Kramers and Ter Haar and the Bates versions of the semiclassical theory. These two semiclassical predictions are identical for $T>\mathrm{}50\mathrm{}°\mathrm{K}$. Below this temperature range they differ and show the small-$T$ limiting behavior expected from asymptotic considerations. The quantum theoretical rate coefficient for the same process is also evaluated. For $500\le T\le 32000°\mathrm{K}$, the quantum and semiclassical rates are in quantitative agreement. The quantum rate and the Bates version of the semiclassical rate show identical temperature dependence as $T$ becomes small, $O\left(T^0\right)$, but their magnitudes differ for $T\le 500°\mathrm{K}$. The quantum rate always exceeds the Bates semiclassical rate in this temperature range, with the maximum difference being nearly an order of magnitude. This enhancement of the rate of molecule formation due to quantum effects is anticipated to be important in the context of the interstellar media.

The excitation cross sections $Q({}_{}{}^3{}_{}{}^{}P-3s{}_{}{}^3{}_{}{}^{}S_{}^o{}_{}{}^{})$ and $Q({}_{}{}^3{}_{}{}^{}P-3s{}_{}{}^5{}_{}{}^{}S_{}^o{}_{}{}^{})$ are calculated using a close-coupling formalism, which includes exchange effects. A cascade-adjusted cross section for $Q({}_{}{}^3{}_{}{}^{}P-3s{}_{}{}^3{}_{}{}^{}S_{}^o{}_{}{}^{})$ is obtained which agrees with the experimental cross section of Stone and Zipf within estimated error uncertainties. Finally, some discussion is given concerning the effects of poorly positioned ${\mathrm{O}}^{-}$ autodetaching states, which are introduced by an inadequate close-coupling expansion.

We have measured projectile and target x-ray cross sections for F + Ar and F + Kr collisions using fluorine beams of charge states 7 +, 8 +, and 9+ with energies from 20 to 76 MeV. Pronounced enhancements for the Ar $K$ and Kr $L$ vacancy cross sections using ${\mathrm{F}}^{9+}$ ions compared to those for the 7+ projectile can be explained by charge exchange as described by an empirically scaled Brinkman-Kramers theory. The Ar $L$, Kr $K$ and Kr $M$ cross sections are found to exhibit features expected for Coulomb ionization. The projectile $K$ x-ray production for the 9+ ion is accounted for by charge exchange processes. Predictions of the first Born approximation for direct single-step excitation to bound states by the target nucleus overestimate the observed cross sections for ${\mathrm{F}}^{7+}$ and ${\mathrm{F}}^{8+}$.