We have applied the stabilization method of calculating resonance energies to the elastic scattering from a one-dimensional model potential containing a barrier. For sufficiently large basis sets, the stabilization method yields good approximations to the inner part of the exact scattering wave functions at energies equal to the eigenvalues of the truncated matrix of the Hamiltonian in both the resonant and nonresonant energy regions. We have calculated good approximations to the exact phase shifts from the square-integrable wave functions produced by the stabilization method. We have derived a simple model to explain the behavior of the eigenvalues as a function of the size of the basis. The degree of stability of the eigenvalues approximating the resonance energy is proportional to the width of the resonance. Both the energy and the width of the resonance can be calculated from the change in the stable eigenvalue as the size of the basis increases.

We show how to interpret the Ford-Wheeler semiclassical expression for the scattering amplitude as a integral, over both positive and negative impact parameters, of a quantity depending on the action. This formulation clarifies the relationship between the action and the phase of the semiclassical expression for the scattering amplitude. Using this formulation, we show that interference processes in both one- and two-channel elastic scattering are analogous to those occurring in the two-slit diffraction of light.

Cross-section ratios have been determined for the collisional transfer of electronic energy from the resonance levels of K to those of Rb. The results obtained were $\frac{Q(\mathrm{K}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\to \mathrm{Rb}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{})}{Q(\mathrm{K}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\to \mathrm{Rb}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{})}=1.1\mathrm{}\pm 0.2$ $\frac{Q(\mathrm{K}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\to \mathrm{Rb}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{})}{Q(\mathrm{K}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\to \mathrm{Rb}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{})}=2.2\mathrm{}\pm 0.2$ $\frac{Q(\mathrm{K}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\to \mathrm{Rb}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{})}{Q(\mathrm{K}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\to \mathrm{Rb}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{})}=1.0\mathrm{}\pm 0.2$ $\frac{Q(\mathrm{K}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\to \mathrm{Rb}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{})}{Q(\mathrm{K}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\to \mathrm{Rb}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{})}=2.2\mathrm{}\pm 0.6$ where the errors quoted are purely statistical. Possibilities of systematic errors are discussed. Combined with the absolute cross sections of Ornstein and Zare, these ratios give a complete set of cross-section values, namely, $Q(\mathrm{K}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\to \mathrm{Rb}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{})=2.3\mathrm{}\pm 0.6$ $Q(\mathrm{K}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\to \mathrm{Rb}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{})=5.3\mathrm{}\pm 0.8$ $Q(\mathrm{K}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\to \mathrm{Rb}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{})=2.5\mathrm{}\pm 0.5$ and $Q(\mathrm{K}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\to \mathrm{Rb}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{})=5.5\mathrm{}\pm 1.2$

The Born cross sections for several important discrete excitations of ${\mathrm{Li}}^{+}$ from its ground state have been calculated with correlated wave functions. By extrapolation, cross sections for higher excitations have also been determined. Subtraction of the sum ${\sigma }_{\mathrm{ex}}$ of these excitation cross sections from the total inelastic-scattering cross section ${\sigma }_{\mathrm{tot}}$ obtained through a sum rule for the Bethe cross sections yields a reliable "counting" ionization cross section ${\sigma }_i$. The cross sections thus obtained are ${\sigma }_{\mathrm{tot}}={\left(\frac{z}{\beta }\right)}^2\left(0.536\right\{\ln \left[\frac{{\beta }^2}{(1-{\beta }^2)}\right]-{\beta }^2\}+5.216\mathrm{}\pm 0.002)\times {10}^{-20\mathrm{}}$ ${\sigma }_{\mathrm{ex}}={\left(\frac{z}{\beta }\right)}^2\left(0.265\right\{\ln \left[\frac{{\beta }^2}{(1-{\beta }^2)}\right]-{\beta }^2\}+2.295\mathrm{}\pm 0.002)\times {10}^{-20\mathrm{}}$ and ${\sigma }_i={\left(\frac{z}{\beta }\right)}^2\left(0.271\right\{\ln \left[\frac{{\beta }^2}{(1-{\beta }^2)}\right]-{\beta }^2\}+2.921\mathrm{}\pm 0.004)\times {10}^{-20\mathrm{}}$ where $\mathrm{ze}$ is the charge of the incident particle and $\beta$ is its velocity divided by that of light. The ionization cross section is in excellent agreement with experimental data in the asymptotic region (incident electron energy ≳ 5 keV).

Using Nutt's expression for the two-particle off-shell Coulomb $T$ matrix, and neglecting multiple-scattering terms in Faddeev's expansion for the transition matrix, an expression for the charge-exchange amplitude in proton-hydrogen scattering is derived. The results of numerical calculations are compared with the corresponding results of Brinkman and Kramers, of Jackson and Schiff, and of Drisko. An analytical expression for the total cross section at high energies is obtained from our formalism. In the high-energy limit, our results approach the Brinkman-Kramers formula.

An atomic line profile is theoretically calculated for various relative densities at two temperatures (666 and 800°K) under an adiabatic assumption, with a Lennard-Jones potential, and is compared with the experimental profile of the shorter-wavelength component of the resonance lines of cesium perturbed by xenon. The calculation predicts an appearance of one red satellite and two violet satellites as experimentally observed. Further, the result shows that the agreement between the pressure behavior of the theoretical line shape and that of the observed one is only qualitative, because the calculated satellite intensities are too weak. This disagreement is attributed to an inadequacy of the Lennard-Jones potential for calculating line-shapes under the present approximations.

Characteristic quantum features in atomic collisions are analyzed in the eikonal approximations. Numerical illustrations are given for the (${\mathrm{He}}^{+}$, He) system, using a set of model potentials which provide a reasonable description of the interaction between the ground states of ${\mathrm{He}}^{+}$ and He in the quasiadiabatic (diabatic) limit.

The Fredholm expansion of the determinant whose phase gives the elastic-scattering phase shift is "summed" by use of numerical quadrature, reducing the calculation of the phase shift to evaluation of a single finite-dimensional determinant. The method is essentially exact and is applicable, without modification, to nonlocal potentials. Results for the low-energy static and static-exchange scattering of electrons from hydrogen atoms are presented as a simple illustration of the method.

The problem of electromagnetic fluctuations in a cavity is treated in some generality using the fluctuation-dissipation theorem. The general line shape of the energy spectrum is derived. This reduces to a Lorentzian when ${\epsilon }^{\prime \prime }\left(\omega \right)$, the imaginary part of the dielectric constant, is small and varies slowly with frequency. Deviations from the Stefan-Boltzmann law are calculated in detail for a cubical cavity.

The elastic scattering of two particles is interpreted as the formation and decay of an unstable particle. The collision cross section and the reciprocal of the scattering delay time are used to determine rates of production and destruction in a gas of interacting stable particles. By equating the two rates, a general expression for the equilibrium number density of unstable particles is obtained. This is tested for two specific types of scattering, and it is found that in resonance scattering the expression, in the limit as $\Gamma \to 0$ (stable particles), reduces to that predicted by the equations of chemical and nuclear statistical equilibrium. Dividing a real gas into an ideal stable particle gas and an ideal unstable particle gas, an equation of state for the latter is inferred from the form of the second virial coefficient. The physical and chemical "reality" of unstable particle gases is examined. It is shown that their existence implies small corrections to the equations of chemical and nuclear statistical equilibrium, as they apply to stable particle abundances.

An exact study is made of the surface thermodynamic properties and grand canonical distribution functions for a one-dimensional gas of classical particles with nearest-neighbor interactions bounded by hard walls. The density profile is expressed in terms of the bulk pair correlation function. We also analyze the interface near a potential step.

Mass-identified measurements of the time dependence of the density of krypton ions in decaying plasmas are reported. The measurements show that the conversion of atomic into molecular krypton ions occurs by the three-body reaction ${\mathrm{Kr}}^{+}$ + 2 Kr→${\mathrm{Kr}}_2^{+}$ + Kr with a conversion rate of 2.3×${10}^{-31\mathrm{}}$ ${\mathrm{cm}}^6$ ${\sec }^{-1\mathrm{}}$ at a gas temperature of 300°K. The measured value of the mobility of atomic krypton ions in krypton is in agreement with the previously published values.

The effect of trapped particles on the drift-cyclotron instability in a multipole machine has been considered. Dispersion equations have been obtained for this instability in a nonuniform collisionless plasma using a simplified approach which takes into consideration the magnetic field strength and curvature variation along field lines. The results show the existence of a branch of oscillations with frequency $\left|\omega \right|\sim {\Omega }_0-k{\overline{v}}_g-{\overline{\omega }}_b$, where ${\Omega }_0$, ${\overline{v}}_g$, and ${\overline{\omega }}_b$ are the average gyrofrequency, the drift velocity due to magnetic field gradient, and the ion "bounce" frequency, respectively, with $k$ being the wave vector transverse to the magnetic field. This may explain the discrepancy between the experimentally observed frequency and the theoretical value obtained previously. This branch of the oscillation also shows a larger growth rate.

The time evolution of the classical shock-tube configuration or density discontinuity is studied, using the first two terms of a formal series solution to general initial-value problems. The occurrence of the shock and expansion wave for a gas with a repulsive $\delta$-function interaction between particles is shown explicitly, using an analytic formula for the time and spatial evolution of the density discontinuity.

The phenomenological theory of a Fermi liquid is generalized to nonequilibrium conditions. Landau's theory is reformulated to include fluctuations of the distribution function and quasiparticle energy. The method of fluctuation in kinetic equations is used to establish the collision integral of the quasiparticle Boltzmann equation. This collision integral is expressed in terms of the parameters of Landau's theory, and includes dynamic screening effects. The results are compared with recent theories of transport in Fermi liquids.

A linearized form of the Gross-Pitayevski (GP) equation is used to calculate the rate at which quasiparticles are created by a small sphere moving through a superfluid at a velocity greater than ${\left(\frac{{\omega }_k}{k}\right)}_{min}$, the Landau roton critical velocity. Because the excitations described by the linearized GP equation can be given a hydrodynamic interpretation, the qualitative features of the model porposed here for the roton critical velocity are analogous to the many critical-velocity phenomena of classical physics. The quantitative results of the model indicate that energy dissipation sets in so rapidly that, once the creation of quasiparticles is allowed kinematically, it should be impossible experimentally to force a negative-ion complex to move observably faster than the roton critical velocity. An investigation of the meaning of the linearized GP equation is also given.

A mathematical treatment of time correlations in a one-dimensional system of hard rods has been given by Lebowitz, Percus, and Sykes. In this paper, the problem is reexamined from a simple viewpoint which seems to render the physics of the system more transparent, and some of the peculiarities of the system are discussed.

Hartree-Fock theory is used in conjunction with the quantum Ursell expansion to obtain the grand potential $f(\beta , g, \Omega )$ and the momentum distribution $〈n\left(k\right)\mathrm{}〉$ for a Fermi fluid. It is shown that the perturbation expansion of the quasiparticle Ursell functions thus obtained yields a formal expansion of the grand potential which is easily related to the theory of de Dominicis. After the summation of certain ladder diagrams in the perturbation expansion, $f(\beta , g, \Omega )$ and $〈n\left(k\right)\mathrm{}〉$ take on forms identical to those obtained in the $\Lambda$-transformed theory derived by Mohling, RamaRao, and Shea. It is therefore possible to identify the Hartree-Fock single-particle energy with the quasiparticle energy of those authors' work.

The annihilation of positrons in argon as a function of argon density at densities from 10 to 65 amagats has been investigated at room temperature. The direct annihilation rate, the reciprocal of shoulder width, and the quenching rate of $o$-positronium are found to be linearly dependent on argon density in the density range investigated within the range of the experimental error. The value of $Z_{\mathrm{eff}}$ of the direct annihilation rate is found to be 26.2 for an argon density up to 50 amagats.

A reanalysis of the data reported in a previous paper has produced significant changes regarding the accuracy of electron densities measured from the widths of Stark-broadened neutral helium lines. This analysis indicates that, within the experimental errors of ∼×15%, electron densities measured from the broadening of the neutral helium lines, $\lambda 5016$ Åand $\lambda 3889$ Å, agree with those determined from hydrogen ${\mathrm{H}}_{\beta }$. In addition to the previous measurements, shifts of $\lambda 3889$ Å are presented and a tentative identification of the forbidden line ($2{}_{}{}^1{}_{}{}^{}S-3\mathrm{}{}_{}{}^1{}_{}{}^{}D$, $\lambda 5042$ Å) is made.