The collective motion of liquid nitrogen is studied by computer simulation. Propagating density waves are found to exist for values of $k=\frac{2\pi }{\lambda }=0.2\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$. The orientational motion does not affect the dynamical structure factor for such a small $k$. The orientational correlation function $\Sigma {i,j}^{}〈P_2\left({\overrightarrow{\mathrm{u}}}_i\mathrm{}\right(0\left)\mathrm{}·{\overrightarrow{\mathrm{u}}}_j\mathrm{}\right(t\left)\right)〉$, which can be related to the depolarized light scattering, is calculated. Comparison with the self term ($i=j$) shows that orientational correlations of neighboring molecules are small.

The Leung-Griffiths equation of state has been used to represent the thermodynamic properties of the relatively simple system C${\mathrm{O}}_2$-${\mathrm{C}}_2$${\mathrm{H}}_4$ near the critical line. It has been shown that the model can account for the critical azeotropy exhibited by this mixture. The overall behavior is similar to that reported for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixtures.

Double-scattering contributions to the intensity of Rayleigh-scattered light near the critical point of a binary liquid are calculated for 90° scattering. We consider a family of sample geometries, namely cylinders with arbitrary length-to-radius ratio and cuboids with square cross sections and arbitrary length-to-side ratio. For binary liquids with nearly matched refractive indices, these terms can be sufficiently large that they affect the interpretation of data with respect to the value of the critical exponent $\eta$ and the deviation of the correlation function from Ornstein-Zernike form, yet small enough that higher-order contributions can be neglected. Numerical results are presented for all temperatures above $T_c$ together with analytical results in certain limiting cases. Near the critical point, the double-scattered intensity is comparable with that lost through extinction and these two effects cancel in leading order. Some analytical results are also obtained for the depolarization ratio. For example, if the height of the sample seen by the detector is small, the depolarization ratio is proportional to the differential cross section and to the sample height. The proportionality constant is $\frac{\pi }{4}$. Numerical results are presented for more general cases.

From the angular distribution of the scattered-light intensity for polystyrene in cyclohexane near its critical mixing point, we have measured $\frac{I_{c,0\mathrm{}}}{T}$ ($I_{c,0\mathrm{}}$ being the extrapolated zero-angle scattering intensity), which is directly proportional to the osmotic isothermal compressibility ${\chi }_T$, and the long-range correlation length $\xi$. We find ${\left(\frac{I_{c,0\mathrm{}}}{T}\right)}^{-1\mathrm{}}=B{(\frac{T}{T_{\mathrm{sp}}}-1)}^{1.24\pm 0.01}$ and $\xi =(5.83\mathrm{}\pm 0.20){(\frac{T}{T_{\mathrm{sp}}}-1)}^{-0.62\mathrm{}\pm 0.02}$ Å along the isochore very near the critical concentration, and ${\left(\frac{I_{c,0\mathrm{}}}{T}\right)}^{-1\mathrm{}}=(2.3\mathrm{}\pm 0.1)B{(1-\frac{T}{T_c})}^{1.21\pm 0.02}$ and $\xi =(2.40\mathrm{}\pm 0.12){(1-\frac{T}{T_c})}^{0.65\pm 0.03}$ Å along the concentrated phase and ${\left(\frac{I_{c,0}}{T}\right)}^{-1\mathrm{}}=(5.9\mathrm{}\pm 0.3)B{(1-\frac{T}{T_c})}^{1.25\pm 0.03}$ along the dilute phase of the coexistence curve. In addition, we have determined the value of the critical exponent ($\delta \simeq 4.4$) which describes the concentration dependence of the chemical potential $\mu$ along the critical isotherm.

The third virial coefficient $B_3$ of a gas of hard spheres, of diameter $a$ and mass $m$, has been expanded in powers of $\frac{\lambda }{a}$, where $\lambda$ is the thermal wavelength ${\left(\frac{2\pi }{kT}\right)}^{\frac{1}{2}}$ $(\hslash =m=1)$. $B_3$ can be expressed in terms of integrals on all configurations of the quantum-statistical-mechanical probability density of the configurations of a three-sphere system. This probability density is proportional to a Green's function which must satisfy zero boundary conditions on the manifolds of the six-space which correspond to contact between two spheres. In the high-temperature limit, where $\frac{\lambda }{a}$ is small, the effects of the sphere curvature can be treated as corrections. To a first approximation, we need only the three-dimensional Green's function $h$ which vanishes on the faces of a trihedral, and the two-dimensional Green's function $g$ which vanishes on the edges of a plane wedge. The curvature effects can in turn be expressed as series of integrals involving $h$ and $g$. Using suitable approximate expressions of $h$ and $g$, we find $B_3=\left(\frac{5{\pi }^2{a}^6}{18}\right)[1+(\frac{3\sqrt{2}}{2})\frac{\lambda }{a}+1.708\mathrm{}{\left(\frac{\lambda }{a}\right)}^2+0.63\mathrm{}{\left(\frac{\lambda }{a}\right)}^3\cdots ]$. (The first three terms were already known).

$P-V-T$ data in the critical region of six fluids (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, Xe, ${\mathrm{O}}_2$, C${\mathrm{O}}_2$, and ${\mathrm{H}}_2$O) have been analyzed in terms of two scaled equations of state using the methods of statistical analysis. The results confirm the hypothesis of universality of critical behavior for these gases to within the current experimental accuracy. The results also support the validity of hyperscaling relations between thermodynamic and correlation function exponents for gases. Using the hypothesis of universality we then present critical-region parameters for fourteen fluids in terms of a universal equation of state.

The description of internal ionization during $\alpha$ decay, as developed by Hansen, is reexamined and extended to the calculation of the ejected-electron energy distributions. The results are compared with recent experimental data for the decay of ${}_{}{}^{210}{}_{}{}^{}\mathrm{Po}$.

The six-dimensional integral involved in the eikonal ($e$, H) rearrangement amplitudes is reduced to a two-dimensional form. When the Glauber condition $\overrightarrow{\mathrm{q}}·\hat{z}=0\mathrm{}$ is imposed, there is no post-prior discrepancy in the elastic rearrangement amplitudes. The Ochkur reduction of the rearrangement amplitudes is obtained in a closed form. Application is made to the inclusion of the exchange effect in the Glauber calculation of elastic ($e$, H) scattering at 50 eV.

It is shown that the quantum theory in the Born approximation gives the classical result when scattering of electrons in the presence of a radiation field occurs in a time short with respect to the period of the radiation. It is argued that the result of Bunkin and Fedorov may be used only when the collision frequency of the electrons in a plasma is much smaller than the frequency of the electromagnetic radiation.

Attention is called to phenomena that should serve as sensitive indicators of the field acting upon slow electrons as they traverse the edge of atoms.

The continuum $K$ x-ray spectrum from 200-MeV Kr + Zr has been found to undergo a Doppler shift with an effective Doppler velocity equal to $(0.92\mathrm{}\pm 0.03)v_{\mathrm{ci}}$, where $v_{\mathrm{ci}}$ is equal to the center-of-mass velocity of the intermediate Kr + Zr molecule, corresponding to the incident projectile velocity. If the x rays are indeed generated by quasimolecular processes, the expected Doppler velocity is $0.90v_{\mathrm{ci}}$, taking into account the slowing down of the projectile in the target. The anisotropy of the continuum spectrum in the c.m. system is derived.

Using the formulation of Seely and Harris, the intensity dependence of the collision frequency has been studied numerically for both Coulomb and screened Coulomb potentials. The results are discussed in the context of the laser-induced gas breakdown.

It is found that a general description of excitations in terms of self-energy effects such as relaxation, correlation, and electron-hole interactions, is possible. A formalism is developed to analyze the contributions to each of these effects, and criteria are established which, if met, allow a much simpler description of the excitation processes than with the general formalism. These procedures are tested by calculations on atomic Be and Ne, and the structure of each of the processes contributing is studied.

It is shown how the many-body Green's-function method, previously developed by the authors for treating elastic and inelastic electron scattering of closed-shell systems, can be extended to open-shell systems. The method can now be applied to all open-shell systems where at least one of the members (generally those of highest and lowest multiplicity) of the degenerate multiplet can be adiabatically connected to a single-determinant unperturbed state. The resulting $S$ matrix is the sum over partial-wave $S$-matrix elements for the highest (or lowest) multiplicity state—all of which elements can be calculated by the standard many-body Green's-function techniques, which have been developed for closed-shell systems—weighted with the appropriate transformation matrix elements and Clebsch-Gordon coefficients.

The double-integral expression derived previously for Bryon's unrestricted Glauber approximation has been evaluated numerically to obtain scattering amplitudes for elastic collisions of electrons on hydrogen, as well as $2s$ and $2p$ excitation. The resulting values of cross sections and Ly-$\alpha$ polarization fractions are similar to previous Glauber calculations, but the alignment and orientation of Ly-$\alpha$ radiation as a function of scattering angle is markedly different from the predictions of the Born and conventional Glauber calculations.

Measurements were made of the average energy $W$ per ion pair formed in liquid xenon by internal-conversion electrons from ${}_{}{}^{207}{}_{}{}^{}\mathrm{Bi}$. We observed voltage pulses resulting from electron collection either in liquid xenon or in a gaseous mixture of argon (95%) and methane (5%). The relative pulse heights for the two materials determine the ratio of the $W$ values. Using the known $W$ for the gaseous mixture, we obtained a liquid-xenon $W$ of 15.6 ± 0.3 eV. This value is considerably smaller than the gas-phase values, 21.5 or 21.9 eV. For interpretation, we adapted Platzman's energy-balance equation to liquids, assuming a conduction-band picture. Theoretical values thus calculated agree well with experiment.

We have calculated $K$-shell pickup cross sections using the full first Born approximation developed by Jackson and Schiff for a number of heavy-ion collisions for which experimental data have recently become available. These include protons on argon at a range of velocities and fully stripped ions $Z=1, 6, 7, 8, 9$, on argon at three velocities. The calculations attempted to include the effect of screening by target electrons with a crude effective potential. We conclude that the full first Born charge-exchange cross section gives nonphysical results for the systems examined, thus casting further doubt on the theoretical significance of the good agreement with experiment one obtains for protons on hydrogen.

Viehland and Mason have developed a method of calculating diffusion coefficients of gaseous ions from measured ionic mobilities by means of a generalized Einstein relation. Their method has been tested with our data on longitudinal diffusion coefficients for alkalimetal ions in atomic gases and found to give excellent results over a very wide range of the energy parameter $\frac{E}{N}$. (Here $E$ is the intensity of the electric field in our drift tube mass spectrometer, and $N$ is the number density of the gas molecules in the drift tube.) In this paper we extend the test of the generalized Einstein relation to ${\mathrm{K}}^{+}$ ions in ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, ${\mathrm{H}}_2$, NO, CO, and C${\mathrm{O}}_2$, to ${\mathrm{Na}}^{+}$ ions in C${\mathrm{O}}_2$, and to ${\mathrm{O}}^{-}$ ions in ${\mathrm{O}}_2$. The main objective is to assess the validity of the relation for molecular gases, in which inelastic collisions occur at the higher values of $\frac{E}{N}$. Such collisions are not allowed for in the theory on which the Viehland-Mason method is based. We demonstrate that the generalized Einstein relation gives extremely good results for ${\mathrm{K}}^{+}$ in ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, and CO. In the other cases, the agreement between theory and experiment is not close at very high values of $\frac{E}{N}$, but is much better than has been obtained by the alternative approaches previously available.