We present measurements of differential elastic cross sections for various alkali-alkali pairs, as well as the angular dependence of the probability of electron spin exchange in these collisions. The resolution is sufficient to reveal interference structure in the angular dependence of both quantities. We describe our apparatus, which polarizes one incident beam and analyzes the polarization of the scattered atoms, and discuss the measurement and data-reduction procedures. Results are presented in the range 0.1-0.2 eV for the systems Na-Cs, Na-Rb, Na-K, K-Cs, and K-Rb.

We analyze the data on differential spin-exchange scattering in collisions between alkali atoms which was presented in Paper I by Pritchard, Carter, Chu, and Kleppner. The data on the probability of exchange is analyzed to obtain the relative phase shift produced by the triplet and singlet potentials. A semiclassical impact approximation is developed and used to calculate this phase shift from theoretical calculations of the asymptotic behavior of the potentials. The results are consistent with the data only when the largest calculated value for the van der Waals potential is combined with the smallest calculated value of the difference potential. We have also analyzed the rainbow structure in the spin-summed differential cross section to obtain information about the depth and shape of the minimum in the triplet potentials in various alkali-alkali systems. Finally, we compare the result of our analysis with results from other experiments on alkali-alkali systems.

A theoretical interpretation of recent experiments on ruby-laser-induced breakdown in liquid helium is presented. The dynamics of unbound electrons initially at nonthermal energies in helium proceed until the electrons are finally and stably trapped in a fully thermalized electron bubble. Arguments are presented indicating that intermediate steps in the dynamical process are collisions between the unbound electron and helium atoms, followed by a low-mobility state which may be thermally destroyed, and ending with a thermally stable electron bubble which grows to its equilibrium configuration and thermalizes. Several experimental results are correlated to deduce numerical estimates for the lifetime of the low-mobility state against thermal destruction and against development into a thermally stable electron bubble. An experiment is suggested to unambiguously measure the photoionization threshold energy of an electron bubble.

The spectral properties of trapped filaments of light in many liquids have been studied in detail using, as an excitation source, a ruby laser operating in different regimes. It has been found that the regular periodic structures in the spectra, which are typical of the self-phase modulation process, can be obtained with high reproducibility under excitation with laser pulses of $\approx 5$ psec. These properties have been interpreted using the method of stationary phase, which makes it possible to derive the temporal behavior of the nonlinear refractive index $\delta n$ in the filaments in a fairly simple way. Other conclusions deduced from this method about the structure of the spectra have been confirmed by experiment. By using a functional relation between $\delta n$ and the optical field intensity $A^2$ based on a model given by Starunov the relaxation time ${\tau }_1$ of $\delta n$ and the temporal behavior of the pulse intensity have also been derived. The value of ${\tau }_1$, which is consistently of the order of a few tenths of a picosecond, gives a strong indication that a "molecular rocking" is the main mechanism for trapping with picosecond excitation. The optical pulse derived has a time width of $\approx 2.5$ psec and an asymmetrical shape. The self-consistency of the method employed has been checked by using the derived pulses $\delta n\left(t\right)\mathrm{}$ and $A\left(t\right)\mathrm{}$ to calculate, by computer, the spectral power density of the optical pulse. The spectrum so calculated fits the experimental one fairly well.

Liquid and solid volumes are calculated over the region of the melting anomaly for ${\mathrm{He}}^3$. Both phases are represented by theoretical models, and the volume variations are determined down to absolute zero. There is satisfactory agreement with measurements over the present experimental range. Although the melting-pressure curve is smooth, the solid volume at melting has a sharp cusp at its spin-ordering temperature. This feature should enable one to detect the process of spin ordering in the solid. The solid at melting expands with temperature decrease throughout its spin-ordering range. The volume change on adiabatic solidification of the liquid has also been obtained and should be useful in establishing a melting-pressure temperature scale based on the thermodynamic properties of melting ${\mathrm{He}}^3$ at very low temperature.

The diffusion coefficient for the helium metastable molecule in a 300 °K helium afterglow has been measured. The experimental technique is that of particle counting instead of the usual method of optical absorption. The value obtain d was $D_M{P}_0=361\mathrm{}\pm 34$ ${\mathrm{cm}}^2$ ${\sec }^{-1\mathrm{}}$ Torr.

An investigation of the effects of mass on diffusion in liquids was undertaken and the results are presented herein. The diffusion of gold and silver in liquid mercury was measured over the temperature range -33.0 to 136.0 °C at solute (mole fraction) concentrations ≤ 4×${10}^{-7\mathrm{}}$, where solute-solute interactions are negligible. These systems were chosen for a study of the mass effect in the liquid state because all other properties likely to influence the diffusivity values are essentially identical, and both closely fulfill the requirements of simple liquids. The data, which were obtained using both the well-known capillary-reservoir technique and a new modification of the diaphragm-cell method, can be expressed in the conventional form $D=1.11\mathrm{}\times {10}^{-4\mathrm{}}\times e^{\frac{-1360\mathrm{}}{\mathrm{RT}}}$ and $D=0.96\mathrm{}\times {10}^{-4\mathrm{}}\times e^{\frac{-1309\mathrm{}}{\mathrm{RT}}}$ ${\mathrm{cm}}^2$/sec for the Ag-Hg and Au-Hg systems, respectively. Contrary to the predictions of most current theories of transport properties of liquids, the diffusivities were found to be independent of the mass of the solute. The probable reasons for the lack of a mass dependence are discussed.

A phenomenological theory is used to account for the observed variation of the mobility of electrons in high-density low-temperature helium gas. Thermodynamic relaxation times are introduced to characterize the lifetime of localized and delocalized states. By allowing these relaxation times to be a function of the helium density, we are able to account quantitatively for the density dependence of the electronic mobility and the anomalous electric field dependence of the electron drift velocity, as observed by Levine and Sanders. The computed critical density, where the free energy of the localized configuration is equal to the free energy of the delocalized state, is 9.5 × ${10}^{20}$ atoms/${\mathrm{cm}}^3$.

A study of the thermomagnetic torque (Scott effect) in N${\mathrm{H}}_3$ is reported. The small positive Scott torque is measured as a function of magnetic field for absolute pressures of 0.028, 0.043, 0.048, 0.057, and 0.078 Torr. At maximum torque, the magnetic field $H_0$ for each pressure $P$ is given by $H_0=b(P+a)\mathrm{}$, where $a=-4.4\mathrm{}\times {10}^{-3\mathrm{}}$ Torr and $b=3.18\mathrm{}\times {10}^3$ Oe/Torr.

Electron energy distributions have been obtained for electrically excited ${\mathrm{N}}_2$, CO, C${\mathrm{O}}_2$, and their mixtures by numerically solving the Boltzmann equation for conditions typical of electric discharges. Reported electron cross-section data have been used in the calculation. The calculated distribution functions were found to be markedly non-Maxwellian, having energy variations which reflect the important electron-molecule energy exchange processes. Solution of the electron energy conservation equation using these distribution functions revealed that vibrational and electronic excitation of ${\mathrm{N}}_2$, CO, and C${\mathrm{O}}_2$ dominates electron-molecule energy exchange processes for average electron energy in the 1-3-eV range typical of electric discharges. Electron-molecule vibrational excitation rates were also evaluated for a variety of gas mixtures and discharge conditions. The importance of these results to molecular gas-discharge lasers is discussed.

Using the Vlasov equation we calculate ${\sigma }_{\mathrm{zz}}$ of the conductivity tensor for counterstreaming plasmas in a magnetic field. Using the dispersion relations for ordinary waves, we consider the electromagnetic instability. The spectrum of the instability and its growth rate have been calculated.

The velocity correlation function of an atom in a simple liquid is calculated using a frequency-dependent version of the Stokes-Einstein formula. Stokes's law for the frictional force on a moving sphere is generalized to arbitrary frequency, compressibility, and visco-elasticity, with arbitrary slip of the fluid on the surface of the sphere. This frequency-dependent friction coefficient is then used in a generalized Stokes-Einstein formula, and the velocity correlation function is found by Fourier inversion. By using physically reasonable values for viscoelastic parameters, good agreement is obtained with the velocity correlation function determined by Rahman using computer experiments.

The classical equations of motion of a one-dimensional, finite, anharmonic lattice, with nearest-neighbor interaction of the Lennard-Jones type, are investigated numerically. The results indicate that when the vibrational energy per particle is equal to or greater than 2-3% of the depth of the potential well, one has, in time average, equipartition of the energy among the normal modes, thus giving a hint toward ergodicity of the system at sufficiently high energy. For lower energies one finds recurrent motions if initially only one normal mode is excited in analogy with a famous result due to Fermi, Pasta, and Ulam. In this case the numerical results are consistent both with the existence of a long relaxation time and with a lack of ergodicity for low energies.

An effective total cross section is calculated for elastic scattering of a monoenergetic beam of test particles in a plasma of arbitrary velocity distribution. Closed-form solutions are obtained for the special case of Maxwellian field particles taking into account small-angle scattering. The result are compared with those obtained using the Debye cutoff technique, and it is shown that such an arbitrary cutoff can lead to erroneous results in the effective cross section and can lead to different conclusions with regard to the relative importance of plasma ions and electrons in test-particle scattering.

The method of correlated basis functions (CBF) is examined for the special case of a weakly interacting Bose gas. Using the Hugenholtz-Pines theory, we compute the ground-state energy exactly to fourth order in the interaction strength. The resulting expression is compared term by term with the unperturbed ground-state energy computed in the CBF using a Jastrow function as the correlating factor. We find that the three leading orders are all accounted for by the Jastrow function, while beginning in the fourth order only selected terms are included. The use of a correlated wave function in effect corresponds to summations of sellected diagrams to all orders. In particular, the ring diagrams and the ladder diagrams are most susceptible to these summations. In a separate paper we shall examine effects of perturbation in the CBF.

Continuing the diagrammatic analysis of the method of correlated basis functions (CBF) for the weakly interacting Bose gas, as reported in the preceding paper, we take off from the unperturbed problem, which is solved essentially by a variational method using a Jastrow correlating factor as the trial wave function. We compute low-order corrections to the unperturbed energy, using a set of correlated basis functions. It is found that the simplest second-order correction in the CBF accounts for all discrepancies (between the Hugenholtz-Pines theory and the unperturbed CBF calculation) which arise in the fourth order of the interaction strength $O\left({\lambda }^4\right)$. It is also demonstrated indirectly that the Jastrow function sums rings and ladders at least up to $O\left({\lambda }^5\right)$.

Spontaneous emission from a system of $N$ identical two-level atoms is considered using a master equation recently derived by the author. The master equation describing the time evolution of the phase-space distribution function associated with the reduced density operator of the atomic system is obtained. This master equation, which is of the type of a Fokker-Planck equation, is used to derive the equation of motion for the mean values of various atomic operators characterizing the physical properties of the system. This leads to a hierarchy of equations, which is decoupled by making a suitable approximation. The intensity of the spontaneously emitted radiation is then calculated. Next, the spontaneous emission from geometrically small systems is considered. For this case, the master equation is solved exactly, and an exact expression for the radiation rate is obtained. The exact solution of the master equation is also used to calculate the normally ordered correlation functions for the electric field. Section V deals with the spontaneous emission from a system of harmonic oscillators, the size of the system being small compared to a wavelength. The master equation for this problem is also solved exactly, and it is shown that this system also leads to superradiant emission in some cases, e.g., if all the oscillstors are excited initially to some coherent state $|z_0〉$.

The absence of exact periodicity in the oscillation of the energy expectation value between a coupled linear oscillator and an angular momentum oscillator, even when the oscillators are macroscopic, is shown to be a consequence of the uncertainty principle.

The usual interpretation of the inelastic-coherent-neutron-scattering cross section from phonons in crystal lattices preserves the existence of a one-phonon peak, varying rapidly with neutron energy loss, on top of a smooth multiphonon background, with negligible interference between the two. We point out that previous theoretical analyses arriving at these conclusions are not necessarily applicable to solid helium, since the dimensionless product of neutron momentum transfer and mean atom zero-point displacement is not, in this case, a small parameter. A new expression for the differential cross section is derived, based on a functional variation technique, which allows the dimensionless product to take on an arbitrary value. In the first order of approximation, the one-phonon peak is broadened and shifted from the equilibrium self-consistent phonon spectrum. Estimates are made of the extent to which interference terms distort the observed neutron cross sections in solid helium. The mathematical techniques are also applicable to the model of Feynman et al. for the polaron mobility.

A one-dimensional system of particles in an external periodic potential interacting via two-body hard-core repulsions is considered as a qualitatively valid model of a submonolayer film absorbed on a solid substrate. At particular values of the hard-core diameter, the free energy is found exactly for all coverages in both the classical and the quantum regimes. We conclude that the thermal implications of adsorbed particle localization (i.e., "mobility") proposed by Hill and developed by Dash and co-workers are qualitatively unchanged by including hard-core interactions for both classical films and quantum films obeying Fermi statistics. The effects of dimensionality on Bose systems appear to be too drastic to reach any firm conclusions on the basis of a one-dimensional model.