Measurements of the yields of $K$ x rays from Cl, Ca, Ti, Ni, and Cu targets and $L$ x rays from Sn and Au targets produced by bombardment with $\alpha$ particles and deuterons of identical velocities have been performed at energies from 2.9 to 20 MeV/amu. The ratios of $K$ x-ray yields for the Cl, Ca, Ti, Ni, and Cu targets all show substantial deviations from the ratios expected on the basis of the theoretically predicted $z^2$ dependence of the Born-approximation and binary-encounter descriptions. The deviations exhibit a "crossover" behavior in which the measured ratios are smaller than expected at low projectile velocities, rise above the expected value at higher velocities, and finally decrease toward the expected value at the highest velocities. The relationship between these deviations and similar deviations in stopping-power measurements has been investigated. Angular distributions of Ti $K$ x rays and Sn $K$ and $L$ x rays were also measured and found to be isotropic to an accuracy of about 2%.

Previously published experimental data on single-electron stripping for over 100 different neutral-neutral and almost 100 ion-neutral collision pairs are compared with Firsov's statistical ionization model. Reasonable agreement is found for a number of reactions, in particular for collisions between some rare-gas atoms. However, marked disagreement exists for many other collisions. From a model assuming a single-step transition of the ionized electron from the bound state into the continum, a scaling law is developed semiempirically which is found able to reduce a large majority of these published data to within a factor of two of a general cross-section curve. Major disagreements with this model occur only in cases which are particularly well described by the Firsov model.

The large-separation asymptotic forms for the retarded van der Waals forces between a neutral polarizable particle and a conducting wall, and between two neutral polarizable particles, are derived from classical electromagnetism under the assumption that the universe contains fluctuating classical electromagnetic radiation with a Lorentz-invariant spectrum (classical electromagnetic zero-point radiation). These forces were first calculated by Casimir and Polder from quantum electrodynamics, and then recalculated by Casimir using ideas of zero-point energy. The present calculation involves purely classical electromagnetic attractions between classical oscillators driven by fluctuating classical radiation.

Calculations of space-charge-controlled diffusion of electrons and positive ions in an isothermal afterglow are presented. In particular, the transition from electron-ion ambipolar diffusion to free diffusion of the electrons and ions is investigated. The results are in qualitative agreement with the experiment of Gerber, Gusinow, and Gerardo insofar as predicting the general features of the transition from electron-ion ambipolar diffusion to free diffusion. In addition, the results substantiate the general behavior implicitly predicted by the more elaborate steady-state calculations of Allis and Rose.

The existence of temperature oscillations associated with surface gravity waves is shown for an incompressible superfluid in the two-fluid model in equilibrium with its compressible vapor. The properties of the oscillations are consistent with some informally reported observations.

The Liouville equation describing the phase-space density in the multidimensional space formed by the Fourier amplitudes of the canonical-conjugate fluctuation fields in a conservative electron plasma is applied to the turbulence problem. The distributive function of the longitudinal velocity and electric field fluctuations in fully developed stationary turbulence is derived as that solution of the Liouville equation which maximizes the entropy of turbulent randomness. The spectral energy density of the electric field which represents a second-order moment of the phase-space density is evaluated by analytical integration for the general case of three-dimensional turbulence. The theory is applicable in the small- and medium-wave-number regions but not in the large-wave-number region where dissipation by Landau damping or collisional interaction is significant.

Torsional crystal measurements of $\eta {\rho }_n$ have been made for pure ${\mathrm{He}}^4$ and for three ${\mathrm{He}}^3$-${\mathrm{He}}^4$ mixtures ($x_3=0.005, 0.047, \mathrm{and} 0.100$) over temperature intervals which included their respective $\lambda$ points. The precision of the measurements for the mixtures was greater than that of any previous $\lambda$-point $\eta {\rho }_n$ measurements. Doubly reduced plots of $\eta {\rho }_n$ versus $T$ showed a slight but definite tendency for such curves to rotate clockwise about the (1, 1) point with increasing $x_3$ up to about 0.05. Values of $\eta$ were derived from the measurements by computing ${\rho }_n$ as a function of $T^{*}$. For each mixture, both $\eta$ and $\frac{d\eta }{\mathrm{dT}}$ were continuous across $T_{\lambda }\left(x_3\right)$. No tendency was manifest for such curves to develop discontinuities as $x_3$ decreased. It was, therefore, inferred that both $\eta$ and $\frac{d\eta }{\mathrm{dT}}$ of pure ${\mathrm{He}}^4$ are continuous across $T_{\lambda }\mathrm{}\left(0\right)\mathrm{}$. A further result obtained here is that, up to $x_3=0.100\mathrm{}$, the $\lambda$ viscosity of the mixture ${\eta }_{\lambda }\left(x_3\right)$ bears a linear relationship to the $\lambda$ temperature of $T_{\lambda }\left(x_3\right)$.

Multiphoton transitions are discussed for the case of a resonant driving field strong enough to produce saturation. The atomic system is described in general terms, and the possibility of inversion asymmetry is allowed. The equations of motion for the density submatrix referring to the pair of resonantly coupled states are found by expanding the full atomic density operator in harmonics of the field frequency, and then systematically reducing the equations of motion which result. The effective $n$-photon coupling parameter and the shift in resonance frequency emerge naturally from this reduction.

An experiment is described in which we study the flow of helium through a 20-μ orifice which connects two helium baths. Closed capacitors are used to measure the helium level. Flow-gravitational-head difference characteristics are traced for various temperatures from 1.15 to 2.26 °K. Subcritical and supercritical flow are clearly observed, and the effect of temperature on the relation between the chemical potential and the level difference is discussed. Abrupt appearance of supercritical flow is observed. With a quartz transducer placed in front of the coupling hole, a decrease and subsequent increase of the flow velocity with quartz voltage is measured.

The modified hydrodynamic equations describing the behavior of a fluid under the influence of an optical electric field are solved. The contributions to stimulated scattering arising from electrostriction, absorptive heating, and the electrocaloric effect are exactly described. Previously unreported terms are given which significantly modify both the Rayleigh and Brillouin scattering. In particular, the experimentally observed stimulated Rayleigh scattering in nonabsorbing media is shown to arise as much from electrostriction as from the electrocaloric effect, while anti-Stokes stimulated Brillouin scattering is predicted in a medium near its critical point. The possibility of observing additional scattering contributions proportional to ${\left(\frac{\partial \epsilon }{\partial T}\right)}_{\rho }$ is also discussed.

The electromagnetic waves propagating transverse to the direction of streaming of the contrastreaming plasmas in the presence of a uniform magnetic field are investigated. For electron plasmas these waves become unstable only for some bounded values of the streaming velocity $U_0$, namely, $U_{min}<U_0<U_{max}$. For relativistic streaming velocities, the electron thermal effects are destabilizing whereas for nonrelativistic streaming these are stabilizing unless $\frac{c^2{k}^2}{{\omega }_{\mathrm{pe}}^2}<\frac{1}{3}$ and $\frac{k^2{V}_{\mathrm{te}}^2}{{\Omega }_e^2}\ll 1$ ($k$ being the characteristic wave number, $V_{\mathrm{te}}$ the electron thermal velocity, ${\Omega }_e$ the electron cyclotron frequency, and ${\omega }_{\mathrm{pe}}$ the electron plasma frequency). The magnetic field however reduces the region of instability no matter what the streaming velocity is. The effect of nonrelativistic-ion streaming is destabilizing while that of the ion temperature is stabilizing. In the presence of a strong magnetic field, the effect of relativistic-ion streaming is also stabilizing.

The mechanism by which periodic nonrandom forces lead to stochastic acceleration of particles is examined. Two examples considered are (i) the Fermi problem of a ball bouncing between a fixed and an oscillating wall, with various wall-oscillation functions, and (ii) cyclotron-resonance heating in a magnetic mirror. Numerical studies show that the phase plane consists of a complicated but regular structure of islands embedded in a stochastic sea. These islands may have the character of either adiabatic barriers or sinks for particles. The islands can be described analytically by expansions about elliptic singular points. A velocity below which no islands exist is observed computationally and is predicted from Floquet theory. Computations also demonstrate that in some cases an adiabatic wall forms an upper limit to particle diffusion in velocity space. A lower bound on this wall is predicted analytically. The Fermi problem is reduced to a Hamiltonian form, and the nonlinear stability and approximate location of the adiabatic wall is predicted from adiabatic invariance theory. Introduction of an external random-force component modifies, but does not destroy, the basic results. For velocities below which no islands exist, it is shown that the random-phase assumption holds, and that the particle motion can be described by a Fokker-Planck equation. The solution to the Fokker-Planck equation is found to agree with the numerical calculations. Above the stochastic transition velocity, strong phase correlations exist, and a Fokker-Planck description is inappropriate.

Using the model of Oseen and de Vries, we show that phase matching of optical third-harmonic generation can be achieved in a cholesteric liquid crystal with the help of the lattice momentum. Many different collinear phase-matching conditions exist. In some cases, the phase-matched third harmonic is generated in the same direction as the fundamental, and in some other cases, it is generated in the opposite direction. In many other cases, phase-matched third-harmonic generation requires the simultaneous presence of fundamental waves propagating in opposite directions. Analogous to electron-electron interaction in a periodic lattice, these processes can be identified as coherent, normal, and umklapp third-harmonic-generation processes. Experiments using a mode-locked Nd laser as the fundamental source verify the existence of most of the predicted phase-matching conditions. Our results agree well with the theoretical predictions.

A detailed theoretical study of cascade ionization of air by rf fields and by laser beams is given. Experimental rate constants for energy loss, ionization, and attachment are used. The Boltzmann equation for the electrons is solved in both classical and quantum form. Provision is made for both single-photon and multiphoton ionization and detachment processes. The latter processes have been incorporated parametrically in our calculations owing to the lack of a quantitative description of multiphoton absorption. Possible anomalies in comparison with available experiments are noted for photons in the 1-2-eV range when the illuminated volume is large.

The self-focusing (SF) of T${\mathrm{E}}_{01}$ and T${\mathrm{M}}_{01}$ ruby-laser pulses in C${\mathrm{S}}_2$ was studied experimentally and theoretically. The T${\mathrm{E}}_{01}$ and T${\mathrm{M}}_{01}$ modes are characterized by strictly transverse circularly electric and magnetic fields, respectively. Rotational symmetry and, in the case of T${\mathrm{E}}_{01}$, absence of longitudinal field components allow computational predictions on the selffocusing which are valid even close to a "catastrophic" focus where scalar approximations become problematic. Comparison between the critical powers of T${\mathrm{E}}_{01}$ and T${\mathrm{M}}_{01}$ yields information on the induced birefringence selectively from the focal zone. The difference in critical powers depends on the convergence of the light beam incident on the nonlinear medium and disappears for parallel incidence. These theoretical predictions are supported by our experimental findings: giant pulses (∼70 nsec, ∼300-kW peak) and mode-locked pulse trains (∼1 nsec, ≥1-MW peak) in the T${\mathrm{E}}_{01}$ mode were obtained from a $Q$-switched ruby laser by an appropriate mode selection. These pulses could be easily converted into T${\mathrm{M}}_{01}$ by rotating the electric field by 90°. Little difference in critical power of the two modes was seen with singlemode pulses; but at 1-nsec duration a distinct difference in threshold developed with increasing convergence. This finding is clear evidence for the influence of longitudinal field components (of T${\mathrm{M}}_{01}$) on nonlinear light propagation—a phenomenon which, to our knowledge, has never been observed before. Interestingly, the experimental results are closest to the theoretical values for electrostriction and not to the ones attributed to the optical Kerr effect. Although a restraint in conclusions is necessary in view of the well-known complications of the SF process, it may tentatively be concluded that electrostriction plays an important role in the focal zone even at pulse durations as short as 1 nsec—which in turn provides an estimate for the size of the focus.

An optical-pumping experiment has been used to measure the cross sections for the exchange of metastability between ${\mathrm{He}}^3$ atoms in the $1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ ground state and the $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ metastable state in the temperature range from 15 to 115 °K. A density-matrix treatment of the ${\mathrm{He}}^3$ system yields a new relationship between observed linewidth and cross section.

The planar triangular lattice gas with repulsive nearest-neighbor and attractive second-nearest-neighbor interactions is solved in the Bethe-Peierls approximation. The maximum temperature of transition between disordered and ordered phases occurs at a density of one-third. All transitions are first order with a discontinuity in the order parameter at the transition. Deficiencies in the approximation are noted and discussed.

The Brandow boson many-body theory is used to calculate the generalized dielectric constant within the random-phase approximation. The generalized dielectric constant obtained this way agrees with the Bogoliubov theory in the high-density limit and thus yields all of the well-known Bogoliubov results. The momentum distribution function for $\overrightarrow{\mathrm{k}}\ne 0$ is also calculated. The treatment is fully number conserving.

The quantum theory of interference effects is given. Three experiments of particular interest are treated: (i) Young-type experiments, (ii) production of beats in photocurrents, and (iii) optical modulation of electron beams. These have been of considerable interest in recent experiments using lasers. We show that they can be accounted for by the same simple quantum-mechanical principle. In the first case, we include the effect of interference in single-photon processes and correlations in multiphoton processes. Here the method of Weisskopf and Wigner is used, and useful distinction between the concept of interference and correlation is proposed. We further emphasize the dynamical aspect of the theory. In the last two cases, we use the standard method of quantum electrodynamics. Here we view the actual experimental setup as being described by a single dynamical process. The description involves the use of nonstationary states as the relevant states to describe the successive excitation. It is shown that all the three phenomena analyzed are closely related.

The hydrodynamical equations for a system of particles interacting with nonadditive forces are obtained. General properties of these forces are discussed and explicit expressions for the contribution of these nonadditive forces to the stress tensor and heat current are given.