An intense source of free electrons has been observed to strongly influence the time history of the electron density in a high-pressure (> 15-Torr) helium afterglow. The electronic recombination coefficient $\alpha$ of molecular helium ions was measured by utilizing this source and was found to be over five times larger than the effective recombination coefficient obtained by equating the net loss rate of free electrons to the recombination loss rate in the usual manner. If $\alpha$ is assumed to be of the form $\alpha ={\alpha }_0+k_{p}p$, then ${\alpha }_0=1.1\mathrm{}\times {10}^{-8\mathrm{}}$ ${\mathrm{cm}}^3$ ${\sec }^{-1\mathrm{}}$ and $k_p=4.1\mathrm{}\times {10}^{-10\mathrm{}}$ ${\mathrm{cm}}^3$ ${\sec }^{-1\mathrm{}}$ ${\mathrm{Torr}}^{-1\mathrm{}}$ over the pressure range from 15 to 56 Torr. A model is presented which indicates that ionizing metastable-metastable collisions are responsible for the source of free electrons.

An analysis is made of the $\lambda$ transition, the phase-separation transition, and the relation between the two, for mixtures of liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. Stability conditions require that $C_x$ (specific heat at constant $x$, where $x$ is the mole fraction ratio $\frac{x_4}{x_3}$ of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ to ${}_{}{}^3{}_{}{}^{}\mathrm{He}$) be less than a certain value, or, equivalently, that ${\left(\frac{\partial {\mu }_4}{\partial x}\right)}_T$ be positive ${\mu }_4$ is the chemical potential of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$). The phase separation occurs when these conditions are violated. The changes in these quantities appear to occur gradually rather than suddenly, as supposed earlier by one of us. The evidence indicates that there is no real critical singularity at the tricritical point. It then seems reasonable to expand thermodynamic functions about each side of the tricritical point separately, and by thermodynamic arguments the relations between the critical exponents $\beta$ (for the coexistence curve) and $\delta$ (for the critical isotherm) can be obtained and compared with observations.

The frequency shift of the backscattered light, stimulated by an intense ruby-laser beam, has been measured in mixtures of 5 atm of S${\mathrm{F}}_6$ and 0-50 atm of He, and also in mixtures of 8 atm of Xe and 0-80 atm of He. For relative He concentrations less than 60%, the frequency is characteristic of stimulated Brillouin scattering. Above 60% He concentration, a rapid decrease in the frequency shift takes place characteristic of stimulated concentration scattering. Good agreement is obtained with the theory and also with recent data on spontaneous concentration scattering in the same gas mixtures.

The turbulent diffusion of a scalar contaminant passively advected by a homogeneous stationary flow is investigated by expanding the velocity and scalar fields in stochastic Wiener-Hermite functionals. The time-evolution integrodifferential equation for the mean scalar concentration and the concentration covariance function are derived in terms of Eulerian one-point multitime velocity correlations and include all orders of the expansions.

By using the Bohm-Pines and Bogoliubov formalisms as well as the random-phase approximation, the investigation of the charged Bose gas is extended into the intermediate densities for which $r_s\lesssim O\left(1\right)\mathrm{}$. The ground state energy is essentially correlation energy, and is therefore negative as expected. The expression for the plasmon spectrum does possess an energy gap; the single-particle excitation spectrum does not. The specific-heat function is examined to first order in the temperature and is shown to approach zero from above as the temperature does the same. Finally, the expression for the pressure is shown to persist in remaining negative for all $r_s\lesssim O\left(1\right)\mathrm{}$ at zero temperature.

An asymptotic evaluation of the specific heat of an ideal Bose gas confined to a thin-film geometry ($\infty \times \infty \times D$) is carried out, under a variety of boundary conditions, without converting summations into integrations. The theoretical results for the Dirichlet boundary conditions (${\psi }_S=0\mathrm{}$) contain all the significant features of the numerical results obtained earlier by Goble and Trainor; in particular, we reproduce the characteristic length $D^{*}$ at which the specific heat of the system is at an absolute maximum. It turns out that $D^{*}$ is directly proportional to the mean interparticle distance $\overline{l}$, with a constant of proportionality $c(\approx 20-30)$. No such characteristic length appears if boundary conditions other than Dirichlet's are employed. The shift, and the rounding off, of the specific-heat maximum are also studied, and the distinguishing influence of the boundary conditions examined.

We investigate the statistical aspects of the cooperative emission of radiation by a system of many atoms. By solving the equation of motion for a suitably defined quasiprobability distribution which represents the density operator of the atoms, we find explicit expressions for the expectation values of products of atomic observables. The system is found to exhibit large quantum fluctuations for the most highly excited initial states of the atoms. For all others it exhibits nearly classical behavior. Previous numerical evaluations of the radiated intensity and its variance are found to be in good agreement with the present results.

Circularly polarized laser radiation propagating in an electron plasma drives the electrons into circular orbits. This orbital motion induces a magnetic field which is either parallel or antiparallel to the laser beam. The generation of this magnetic field is known as the inverse Faraday effect. Because of this magnetic field and the relativistic change of the electron mass, the wave propagation is enhanced for high intensities in the sense that the critical plasma density increases with the laser-beam intensity. For the wavelength $\lambda =1.06\mathrm{}$ μ, corresponding to a neodymium-glass laser, the dependence of the various propagation characteristics on the brightness of the beam is examined in detail. Electron densities varying between ${10}^{20}$ and 6.6 × ${10}^{21}$ particles per ${\mathrm{cm}}^3$ and radiation intensities in the range ${10}^{17}$-${10}^{20}$ W/${\mathrm{cm}}^2$ are considered. Energy losses caused by synchrotron radiation and by electron-ion bremsstrahlung are calculated.

The wave-vector and frequency-dependent orbital susceptibility (${\chi }^{\mathrm{orb}}$) of an interacting electron gas is expressed in terms of suitable vertex functions. This makes the theory parallel to that of the spin susceptibility (${\chi }^{\mathrm{sp}}$) of this system. The equation for the vertex function is solved in the statically screened exchange approximation by a variational method introduced earlier by one of the authors. The static long-wavelength limit of (${\chi }^{\mathrm{orb}}$) is shown to be related to the difference between the $f$- and $p$-wave decomposition of the effective interaction, whereas ${\chi }^{\mathrm{sp}}$ is related to the difference between the corresponding $p$- and $s$-wave parts in the same limit. The classic result that ${\chi }^{\mathrm{orb}}$ is minus one-third of ${\chi }^{\mathrm{sp}}$ for the noninteracting system is modified when the interactions are included. Explicit results are given for a model Yukawa interaction. From these, it follows that, for very short-range interactions, (${\chi }^{\mathrm{sp}}$) reduces to the Stoner-enhanced form while ${\chi }^{\mathrm{orb}}$ is unaffected. The momentum dependence of the interaction is thus more important for the determination of ${\chi }^{\mathrm{orb}}$ than for ${\chi }^{\mathrm{sp}}$. In the unscreened Coulomb limit as well as for small screening, our results reduce to those obtained earlier by Kanazawa and Matsudaira. Several errors in the existing expressions for ${\chi }^{\mathrm{orb}}(\overrightarrow{\mathrm{q}}, q_0)$ are corrected in this work.

As a continuation of a recent paper, using density and current density as coordinates for interacting bosons at absolute zero, this work deals with the perturbation theory. The zerothorder Hamiltonian is the one shown to yield the Bogoliubov energy spectrum. First- or secondorder perturbation calculations have been made of the three-phonon and the four-phonon vertices for the energy corrections of the low-lying excited states. The results in the long-wavelength limit differ, although only slightly, from the quantum hydrodynamic calculations, and indicate that the perturbed excitation energy ${\epsilon }_{\overrightarrow{\mathrm{k}}}$ is an odd-power series in $k$ if the Fourier coefficients of the two-body potential concerned can be approximated by a constant or an evenpower series in $k$. However, whether this remains so in all higher orders of various perturbations is an open question. Two methods were used in the calculation. The first involves functional representations of the coordinates in the ${\rho }_{\overrightarrow{\mathrm{k}}}$ representation recently reported. The second method is new, and employs "occupation-number" representations of the current algebra by introducing creation and annihilation operators for "phonons" from density fluctuations. These latter representations enable us to benefit from the advantages of the canonical field theory.

We have found that the low-temperature collision-time kinetic theories of Khalatnikov and Chernikova and of Disatnik are not in agreement with all of the predictions of superfluid hydrodynamics. In particular, they overestimate, by a factor of about 30, the attenuation of hydrodynamic first sound. In addition, they use a hydrodynamic collision time to describe both the hydrodynamic and collisionless regimes, causing disagreement with many-body calculations valid for the collisionless regime. We have constructed a kinetic theory which is in agreement with superfluid hydrodynamics, and we have analyzed the existing kinetic theories in order to find the origins of the disagreement with hydrodynamics and with the many-body theory. To obtain correct transport coefficients (and therefore correct attenuation of hydrodynamic first sound) it is found necessary to ensure that the system relaxes to local, rather than to static, equilibrium. We calculate the transport coefficients within a collision-time model, and point out that for generality one must employ two hydrodynamic collision times ${\tau }_l$ and ${\tau }_t$ (with ${\tau }_l\ge {\tau }_t$) associated with longitudinal and transverse processes, respectively. From this we show that ${\zeta }_2$ is not necessarily equal to zero. In addition, we discuss difficulties involved in extending the theory to higher frequencies, and present a physical argument which requires the use of a wide-angle collision time to define the (low-frequency) hydrodynamic regime and a small-angle collision time to define the (high-frequency) collisionless regime. This reconciles the disagreement between kinetic theory and many-body calculations upon the collision time which defines the collisionless regime. Various experiments are interpreted on this basis, thereby eliminating certain discrepancies with theory. Measurements in the low-temperature hydrodynamic regime are shown to require relatively large chambers (with linear dimensions ≳ 10 cm).

The afterglow of a 1.3-A 1.5-μsec-duration discharge in helium at 11 Torr was studied in some detail during the times 15 to 35 μsec after the discharge pulse. Spectroscopic measurements were used to obtain the number densities of excited atomic and molecular states, the conductance of the plasma column was determined from simultaneous electric field and current measurements, and a 10-μsec current pulse was used to selectively heat the electrons, thus disturbing some of the afterglow processes. The atomic and molecular ion densities and the electron temperature, obtained from the spectroscopic measurements, were in good agreement with the plasma conductance and field strengths. The inferred recombination rate favors the recent calculations of Mansbach and Keck over the Bates, Kingston, and McWhirter calculations of the collisional radiative-recombination rate. The rate of conversion of atomic into molecular ions was dominated by associative ionization of excited atomic states, and good agreement was obtained by including this process with other known processes.

The afterglow of a 1.3-A 1.5-μsec-duration discharge in helium at 11 Torr was studied during the time 15 to 35 μsec after the discharge pulse. A 10-μsec current pulse was used to selectively heat the electrons, and it was found that the differences in the atomic and molecular intensities subsequent to this heating pulse could be explained by assuming a process of associative ionization of excited atomic helium states resulting in molecular helium ions, ${\mathrm{He}}^n+\mathrm{He}\to {{\mathrm{He}}_2}^{+}+e^{-}$. The rate of this process is determined. It is further shown, by comparison of excited-atomic-state densities with previous measurements at much lower pressures, that there must be a source, rather than a loss, of lower-lying atomic states. A model is proposed in which associative ionization of highly excited atomic states results in vibrationally and rotationally excited molecular ions, which subsequently relax by neutral helium collisions to the ground-state level. Dissociative recombination of these excited molecular ions while in the process of going to the ground-state level then forms a source of additional lower excited atomic states. Extremely rapid vibrational and rotational relaxation rates are required.

The effect of a driving or pump field on the emission and absorption line-shape functions for an atom is discussed. The pump field is assumed to oscillate at a frequency near the resonance frequency for transitions between a single pair of atomic states, and transitions between one of these states and any other state of the atom are analyzed. The pump field is treated classically, and atomic relaxation is treated in general terms. The emission and absorption line-shape function (the latter is defined as the rate of absorption of energy from a weak signal field, applied in addition to the pump field, as a function of the signal-field frequency) are found by evaluating the relevant two-time atomic correlation functions in the Markoff approximation. In the limit of high pump-field intensity, both the absorption and the emission spectra are doubly peaked at frequencies which differ from the usual resonance frequency by $\pm \frac{1}{2} \Omega$, where $\Omega$ is the frequency of the pump-field-induced oscillations in the populations of the two strongly coupled states. The absorption and the emission spectra are represented by essentially the same function in the limit of high pump-field intensity, as they are also in the limit of vanishing pump-field intensity. For intermediate pump-field intensities, however, the two functions are quite different in form, and no simple proportionality exists between them.

The stability of an equilibrium phase is described in thermodynamics in terms of certain convexity properties of the free energy. The phase is said to be unstable with respect to an equilibrium phase transition if the isothermal response of the system to a static external field is infinite. It is also known that associated with several second-order and some first-order transitions there are "soft collective modes" (for instance, in ferroelectric, antiferromagnetic, liquidgas, and structural phase transitions). In this paper we show that in systems where the order parameter can be treated as an ergodic variable, and which possess collective excitations, at least one of the collective modes must go soft when the system undergoes a second-order phase change (or more generally, at the stability limit of the system). Implications to discontinuous firstorder transitions are also briefly discussed. Examples of soft modes associated with phase changes are given.

Inelastic neutron scattering experiments were carried out on large single crystals of the quantum solid bcc ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The crystals were oriented in the [011] zone and had volumes larger than 5 ${\mathrm{cm}}^3$. Both transverse and longitudinal excitations were studied with propagation vectors along the [100], [111], and [011] principal symmetry directions. Dispersion relations along these three symmetry directions are presented and discussed within the context of the results of recent theories for this highly anharmonic solid. The data, which present clear evidence for strong phonon relaxation, are also compared with theoretical linewidth estimates. The elastic constants calculated from these data are $\frac{c_{11}}{\rho }=1.77\mathrm{}\pm 0.32$, $\frac{c_{12}}{\rho }=1.58\mathrm{}\pm 0.35$, and $\frac{c_{44}}{\rho }=1.07\mathrm{}\pm 0.10$ in units of ${10}^5$ ${\mathrm{m}}^2$/${\sec }^2$, in good agreement with the results obtained from ultrasonic and thermodynamic measurements. When the amplitude of the scattering vector $\left|\overrightarrow{\mathrm{Q}}\right|$ approaches $1.6a^{*}=2.44\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$, where $a^{*}$ is the reciprocal-lattice vector of length 1.525 ${\mathrm{\AA }}^{-1\mathrm{}}$, some extra intensity is observed near an energy of 1.4 meV. Evidence that this intensity is indeed real and anomalous, some four times as much as expected from single-phonon scattering, is presented. The physical origin of this extra scattering is not presently known.

Corrections to the impulse approximation for scattering from a many-body system are derived in the form of a series in inverse powers of the momentum transfer $k$. The coefficients in this series are written in terms of the two-body interaction potential and the particle-density matrices. Application is made to the case of high-energy neutron scattering from liquid helium. Evaluation of correction terms corresponding to a single helium-helium collision during the neutron-helium interaction time indicates (a) a shift in the peak of the incoherent-scattering cross section toward lower energy by a constant amount, and (b) an asymmetry of the cross section with respect to neutron energy loss about its peak value. Numerical estimates are given for these two effects for $k=14.3\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$. Evaluation of condensate broadening due to multiple He-He collisions shows that the condensate-scattering contribution has a width proportional to $k^{\frac{1}{2}}$, and is thus distinguishable from the main noncondensate peak whose width is proportional to $k$. Estimates are given for requirements on experimental-resolution functions necessary to preserve this evidence of a distinct condensate contribution.

Stability of superluminous and subluminous waves propagating transverse to the direction of the external uniform magnetic field is investigated in streaming relativistic homogeneous plasmas. In the relativistic regime for $\Omega <\mathrm{ck}$ ($\Omega$ being the electron cyclotron frequency and $k$ the characteristic wave number), the superluminous waves remain stable as in the absence of external magnetic field; however, for the subluminous waves, the magnetic field has a tendency towards destabilization. For $\Omega \gg \mathrm{ck}$, the superlum inous waves are dynamically unstable for all streaming velocities $U$, which are smaller than $U_c$, or for magnetic fields $\Omega$, which are greater than ${\Omega }_c$, but for the waves with frequencies $\omega \ll \Omega$ ($\Omega \gg \mathrm{ck}$), there exists a minimum streaming velocity above which the system is unstable. In the nonrelativistic regime the system is unstable if streaming is much larger than the thermal velocity but otherwise stable. The unstable region is bounded by ${\Omega }_{min}$ and ${\Omega }_{max}$; ${\Omega }_{min}$ being $k{v}_t$ ($v_t$ being the electron thermal velocity) and ${\Omega }_{max}$ being $\mathrm{kU}$.

A modified two-state model has been assumed in order to investigate the temperature dependence of adiabatic volume viscosities ${\eta }_v$,${\eta }_v^{\prime }$, and mole fraction $x_2$ in the antiparallel dipole state in ethanol. The results show that about 90% of ethanol molecules are in the higher free-energy state.

We have calculated absolute values of dc-induced second-harmonic coefficients for helium, neon, argon, and krypton by using the formulation of Armstrong et al. and mechanism proposed previously by us. Calculated values explain the experimental values of Finn and Ward.