The mobility of a large hard-sphere impurity in a Fermi liquid has been calculated by solving the transport equation for the quasiparticles exactly to order $T^2$. Using the Landau parameters known for ${\mathrm{He}}^3$, the correction to the zero-temperature mobility, which was previously found to be proportional to $T^2$, turns out to be somewhat too small. The temperature dependence is in agreement with experiment.

A classical vortex with a movable impurity in its core is used to study the interaction of vortex waves with a trapped ion in rotating He II. The reflection probability is evaluated in the long- and short-wavelength limits. An approximate interpolation formula allows a calculation of the low-temperature mobility of an ion along the vortex axis.

Intensity correlation measurements of lasers oscillating in many transverse modes are found to be very sensitive to slight misalignment of the beams that have to be superimposed on each other for such measurements. This fact is shown to be due to the lack of spatial coherence in such lasers. It is theoretically shown that if the modes oscillate independently of each other, the fluctuation behavior becomes different for different points of the beam profile. This fact is demonstrated experimentally. An analysis of intensity correlation measurements of mode-locked lasers oscillating in many transverse modes is presented. The effects of slight mis-alignments on measurements of contrast ratios in two-photon fluorescence (TPF) patterns and second-harmonic measurements are discussed. In TPF measurements, even minute mis-alignments effectively reduce the contrast ratio from 3:1 to 2:1. Previously published data may be explained in this way.

Measurements of the thermomagnetic torque for a large number of gases indicate that the field and pressure dependences of the torque can be represented by a single curve for most gases. The pressure ($P$) dependence of $H_0$, the field for maximum torque, is given by $H_0=b(P+a)\mathrm{}$, where $b$ and $a$ are constants. The molecular rotational $g$ values for the gases can be estimated from the relation $g_J=1.\mathrm{}27\times {10}^{16}\frac{\sigma \overline{v}}{\mathrm{}\left(\mathrm{QbT}\right)\mathrm{}}$, where $\sigma$ is the molecular cross section, $\overline{v}$ the average molecular velocity, $T$ the absolute temperature, and $Q$ a constant (taken to be $4\pi$). The sign of $g_J$ is given by the torque direction. Values of $g_J$ calculated from the torque are in reasonable agreement with other determinations for all gases except ${\mathrm{Cl}}_2$. Previously undetermined $g_J$ values are estimated for a number of gases. The existence of multiple torque maxima in ${\mathrm{O}}_2$, NO, N${\mathrm{O}}_2$, and HD is discussed.

The present paper includes the influence of collisions in the high-intensity laser theory by Stenholm and Lamb. The history of an atom is divided into field- and collision-dominated intervals. The collisions are treated as instantaneous independent events (impact approximation). The equation of motion for the density matrix of an ensemble of atoms undergoing collisions is derived. The collisions manifest themselves as an integral operator in the equation of motion. As a model, collisions which do not change the populations of the atomic levels are treated. Physical conditions on the kernel matrix of the collision integral are used to construct a simple nontrivial model. To simplify the treatment, the phase and velocity changes are assumed to take place in different collisions. This model is used to solve the problem of a high-intensity laser with collisions. Only the lowest nonvanishing terms in the Fourier expansion of the density matrix elements are used. Typical numerical results are evaluated and shown in the figures. Connections with other papers and generalizations are discussed.

The spectral power distribution of a broadband maser signal that is saturating a two-level system is derived using stationary Gaussian statistics for the electric fields and assuming the bandwidth is large compared to the homogeneous linewidths of the two levels. The results are applied to travelling-wave amplifiers of this type, the cosmic OH and ${\mathrm{H}}_2$O masers, to obtain the saturated maser output intensity and linewidth as a function of amplifier length.

The quasistationary-state formalism for describing all manner of resonant collision processes and the diabatic states of molecules is made unique by defining the hitherto arbitrary quasistationary-state energy uniquely. The unique quasistationary-state energy $E_r$ (together with its wave function) is defined by a pair of eigenvalue equations which require that it remain unshifted by coupling to the continuum. Two alternate and equivalent definitions are also given, and the results are generalized first to the many-resonance case and secondly in the unusual direction of negative energies, where the quasistationary state produces a resonance among the discrete set of Rydberg levels. This last generalization is necessary for the principal present application of the states, i.e., to the diabatic states mediating molecular transitions, since the energy of these diabatic states moves freely between the continuum and the negative-energy region of the Rydberg states.

The one-dimensional spin-½ Ising model is solved exactly with very long-range, equivalent-neighbor ferromagnetic interactions of strength $J_{\mathrm{LR}}$ superimposed on nearest-neighbor anti-ferromagnetic interactions of strength $-J_{\mathrm{sr}}$. For $-\frac{J_{\mathrm{lr}}}{J_{\mathrm{sr}}} >R=3.\mathrm{}1532$... there is a critical point of classical type in zero field. For $2-\frac{J_{\mathrm{lr}}}{J_{\mathrm{sr}}}=R$ the critical exponents take the values $\beta =\frac{1}{4}$, $\gamma =1={\gamma }^{\prime }$, $\delta =5\mathrm{}$, and $0=\alpha \ne {\alpha }^{\prime }=\frac{1}{2}$. For $2<-\frac{J_{\mathrm{lr}}}{J_{\mathrm{sr}}}<R$ the transition in zero field is of first order, and the critical points which occur in finite field are of classical type. For $0<-\frac{J_{\mathrm{lr}}}{J_{\mathrm{sr}}}<2\mathrm{}$ there is no phase transition in zero field, although there are classical critical points in a field.

The memory-function formalism of Zwanzig and Mori is used to study the density-density correlation function $〈\tilde{\rho }\mathrm{}\left(S\right)\mathrm{}{\rho }^{*}〉$ in a single-component fluid. Using the hydrodynamic variables suitable for longitudinal disturbances, $〈\tilde{\rho }\mathrm{}\left(S\right)\mathrm{}{\rho }^{*}〉$ is expressed in terms of the appropriate memory functions. This formally exact relation is then shown to be equivalent to the result obtained by Kadanoff and Martin in terms of a dispersion function. By considering the approximations suitable for the analysis of Brillouin scattering experiments, it is also shown that the formal expression for $〈\tilde{\rho }\mathrm{}\left(S\right)\mathrm{}{\rho }^{*}〉$ can be reduced to results previously derived by Mountain and by Bhatia and Tong on the basis of a macroscopic analysis using the linearized hydrodynamic equations coupled either with relaxing shear and bulk viscosities or with thermodynamic relaxation theory. Present analysis thereby provides a microscopic basis for these hydrodynamic theories, as well as revealing to some extent the nature of approximations involved. Our microscopic analysis also suggests a simple model to take into account the effects of coupling between heat flux and the viscosity stress tensor.

A beam of noninteracting particles, bosons or fermions, is described by the superposition of stochastic wave packets. This description allows in each case (bosons or fermions) the determination of the detection process of the particles. This process is defined by the set of the $p$-order coincidence probability densities, a general formulation of which is given. In the case of a stationary and weak incoherent beam, these coincidence probability densities are studied thoroughly and several results are obtained. The well-known bunching effect for bosons and the "antibunching effect" for fermions are shown to come from the detection of indistinguishable particles. In the boson case, all the well-known results for thermal light are found. In the fermion case, the detection process is, under certain conditions, identical to a renewal process.

In analogy with the work of Kawasaki and Oppenheim on the shear viscosity, the density expansion of the bulk viscosity is obtained for gas systems which interact with attractive forces and repulsive forces. In the case of repulsive forces, the first term in the density expansion of the bulk viscosity is of order ${\rho }^2$. In the case of attractive forces with bound states, the density expansion possesses a term of order $\rho$.

The overlap matrix element ($\overrightarrow{\mathrm{k}}+\overrightarrow{\mathrm{l}},\overrightarrow{\mathrm{h}}\left|\mathrm{l}\right|\overrightarrow{\mathrm{k}},\overrightarrow{\mathrm{l}},\overrightarrow{\mathrm{h}}$) which occurs in the theory of phonon dispersion has been evaluated by a completely explicit procedure involving the convolution approximations for the three-, four-, and five-particle distribution functions. The same result is found here by a simpler method involving only the convolution form for the three-particle distribution function.

The problem of vertex renormalization at nonzero temperatures for a system of bosons interacting via a strong short-ranged repulsive potential and a weak long-ranged attractive potential is examined. It is shown that with the assumption of low temperatures and densities, one obtains expressions for the thermodynamic functions which corroborate the results of an earlier paper.

The inhomogeneity correction to the correlation energy of an electron gas is added to the Thomas-Fermi energy-density functional for atoms. The density is significantly modified only inside a radius of the order $Z^{\frac{-1\mathrm{}}{3}}\times {10}^{-5\mathrm{}}$ Bohr radii. This does not reduce the density gradient sufficiently to make the expansion convergent.

The electric dipole polarizability of ${\mathrm{H}}^{-}$ is calculated by the variational method. The computed values of the polarizability corresponding to the unperturbed wave functions of the form ($e^{-\alpha r_1-\beta r_2}+e^{-\beta r_1-\alpha r_2}$) and $(e^{-\alpha r_1-\beta r_2}+e^{-\beta r_1-\alpha r_2}) (1+\gamma r_{12})$ are 73.6 and 19.5 ${\mathrm{\AA }}^3$, respectively.

Two methods of analyzing speed-of-sound data in gases to obtain the second virial coefficients $B\left(T\right)\mathrm{}$ are compared. The older method, which assumes a form for the temperature dependence of $B$, is shown to correspond to finding an exact solution to an approximate differential equation for $B$, while a method recently proposed by Bruch solves the exact equation, but in an approximate manner. Examination of the errors in each method indicates that the first method is preferable.

Procedures which derive the second virial coefficient of a gas from the acoustic second virial coefficient or the Joule-Thomson coefficient are discussed. Model calculations with realistic helium intermolecular potentials are presented. The validity of a procedure which does not directly face the uniqueness problem is tested.

Results of calculations of angular distributions of photoelectrons from the outer $p$ subshells of Ne, Ar, Kr, and Xe are presented for electron energies between 0 and 2 Ry (27.2 eV).