A recent study of thin ${\mathrm{He}}^4$ films by Chester, Yang, and Stephens using a quartz-microbalance technique has shown frequency anomalies ascribed to the onset of superfluidity. The data imply that superfluid is present at thicknesses less than those at the anomalies. We propose a model involving surface heterogeneities to explain the results. Using the same model, it is possible to resolve several puzzles associated with other studies of onset, including the anomalous attenuation of third sound.

The exchange energy at finite temperature is discussed as a first-order perturbation. Consistent thermodynamical definitions of the average exchange potential are suggested for a Hartree-Fock-Slater calculation. It is shown that the exchange interaction satifies the virial theorem.

Recently obtained data on doubly ionized Rb in the free state indicate that the satellite of the $\mathrm{Rb}\mathrm{}\left(4s\right)\mathrm{}$ resonance in the photoelectron spectra of RbF and RbCl is primarily due to a $4{s }^{2}4{p }^{4}4d {}_{}{}^2{}_{}{}^{}S$ final state rather than a $4{s }^{2}4{p }^{4}5s {}_{}{}^2{}_{}{}^{}S$ one. For the potassium salts, the satellite of the $\mathrm{K}\mathrm{}\left(3s\right)\mathrm{}$ resonance is most likely due to a $3{s }^{2}3{p }^{4}3d {}_{}{}^2{}_{}{}^{}S$ final state. The absence of a satellite for the $\mathrm{Na}\mathrm{}\left(2s\right)\mathrm{}$ resonance for the sodium salt is due to the nonexistence of $2d$ electrons.

An exact local representation of the relativistic Hartree-Fock exchange potential for electrostatic interactions is presented for closed-shell atoms. This single-particle potential depends upon all relativistic single-particle quantum numbers except the magnetic quantum number $m$. This exchange potential should be useful for relativistic atomic Hartree-Fock calculations.

The $K$ x-ray spectrum of Mg produced by 30-MeV oxygen ions is observed to consist of four regions of $K$ x-ray excitations. These regions consist of the $K\alpha$ satellite lines, the $K\beta$ satellite lines, the $K\alpha$ hypersatellite lines, and the $K\beta$ hypersatellite lines. The last region is observed for the first time and corresponds to $1s\to 3p$ transitions in an atom consisting of double $K$-shell vacancies as well as multiple $L$-shell vacancies.

It is shown that viscous flow and equipartition in the large-scale modes are sufficient conditions for $t^{\frac{-n}{2}}$ behavior of the velocity-autocorrelation function. Dissipation via viscosity is critical; other mechanisms give different rates of falloff.

In a recent paper Bugnolo suggested that first-order smoothing theory describing wave propagation in media with random fluctuations of the refractive index should not be used for wave numbers larger than the correlation length. This suggestion is shown to be incorrect.

Total $\gamma$-ray cross sections at 12 $\gamma$ energies (most of them are at new energies) are determined in Cu, W, and Pb and the results are reported. The error in these results is of the order of 1%. An analysis of the data is presented.

The excitation function for metastable molecular nitrogen has been studied over the electron-impact energy range 7-14 eV with an energy resolution of 0.05 eV. No resonances were observed below 11.8 eV in the $A{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ and $a{}_{}{}^1{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ channels. There is a sharp resonance at the threshold of the metastable $E{}_{}{}^3{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ with a peak at 12.00 eV. Smaller structures were seen at 12.14 and 12.25 eV. A series of five resonances were observed at 12.59, 12.80, 13.03, 13.24, and 13.52 eV presumably in one or both of the $A{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ and $a{}_{}{}^1{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ channels. These confirm some of the structures observed in a recent transmission experiment. On the basis of the spacings and relative intensities of these resonances, a possible assignment for them is a temporary state of $N_2^{}{}_{}{}^{-}$ consisting of two Rydberg electrons around a core state $A{}_{}{}^2{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ of $N_2^{}{}_{}{}^{+}$.

A multichannel semiclassical collision theory, based on Feynman's path-integral formulation of quantum mechanics and developed by Pechukas, is discussed. The theory is applied to low-energy, elastic and inelastic, collisions between ${\mathrm{He}}^{+}$ and Ne. The calculation involves the solution of a boundary-value problem, and a numerical method for obtaining this solution is presented. The numerical results and the qualitative interpretation of them are compared with the predictions of other available theories.

The convergence of the Sturmian expansion (i.e., the Weinberg series) for the Coulomb $t$ matrix at negative energies is discussed. It is pointed out that the series for the full three-dimensional $t$ matrix diverges, and that the series for the partial-wave $t$ matrix converges conditionally at best and sometimes diverges because of the long range of the Coulomb potential. The $t$ matrix is rigorously expressed as the limit of a power series at a point on its circle of convergence, with the power series itself at that point being just the Sturmian expansion. The possibility of finding alternative separable expansions with better convergence behavior is discussed, the conclusion being reached that the poor convergence is an inevitable result of the long range of the Coulomb potential.

The cross section ${\sigma }_{\mathrm{MT}}$ for the elastic momentum transfer of electrons with helium atoms at ultralow energies has been deduced from measurements of the microwave absorptivity of a transient cryogenic afterglow plasma. The electrons were selectively heated by an adjustable-microwave electromagnetic field. This cross section can be approximated as a function of the incident electron kinetic energy $u_e$ between 2×${10}^{-4\mathrm{}}$ and ${10}^{-1\mathrm{}}$ eV by ${\sigma }_{\mathrm{MT}}\left({\mathrm{cm}}^2\right)=5.15\mathrm{}\times {10}^{-16\mathrm{}}{[u_e\frac{\left(\mathrm{eV}\right)}{2}\times {10}^{-4\mathrm{}}]}^{-0.02\mathrm{}}$.

Improved apparatus has been developed for measurement of the constant-volume heat capacity $C_V$ of condensed phases at low temperatures. The high-pressure calorimeter is closed by a remotely operated valve at the calorimeter and several problems associated with the usual blocked-capillary technique are thus eliminated. The heat capacity of hcp ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ has been measured from approximately 0.35 K to the temperature of the transition to a mixed phase and for molar volumes $V$ between 20.5 and 21. 0 ${\mathrm{cm}}^3$/mole. The data permit reliable extrapolations to 0 K to determine ${\Theta }_0$, the Debye characteristic temperature at 0 K, and the entropy. $C_V$ can be represented by the same function of $\frac{T}{{\Theta }_0}$ for all molar volumes in the range studied. The data are in good agreement with Ahlers's recent measurements in the limited region of overlap, but the temperature dependence of $C_V$ at low temperatures and densities is different from that deduced by Ahlers by extrapolation from higher temperatures and densities. The values of ${\Theta }_0$ obtained in this work and by Ahlers at higher densities can be represented by ${\Theta }_0=2340\mathrm{}{V}^{-0.8114\mathrm{}}\times e^{-0.09690V}$.

A theory for neutron scattering by a semiclassical system, which is appropriate for liquid neon, is described. The theory is based on a generalized mean-field approximation involving the polarization potential and the screened response function, similarly to what has been done previously for argon and helium. The screened response function is assumed to be a sum of Gaussian functions weighted by the momentum-distribution function. The polarization potential and the width of the Gaussians are determined by the zeroth and third moments of the scattering law. The momentum distribution has the Maxwell—Boltzmann form, but includes quantum corrections to order ${\hslash }^2$. The quantum-mechanical zero-point energy is found to increase the kinetic energy per particle to a value of about 30% greater than the classical equipartition value. Calculations have been done for wave-vector transfers in the range 0.75-5.5 times the wave vector at the principal maximum in the static-structure factor, and the theoretical line shapes have been folded with the resolution function for the experiments of Buyers et al. Comparison of the position of the maximum, full width at half-maximum, and line shapes with the experimental results gives good agreement.

Measurements are presented on the angular distribution of energy flux radiated from a pulsed heater immersed in He II at low temperatures. Two small carbon heaters with different surface structures are located in a relatively large volume of He II maintained at temperatures in the range of 230 mK. Heater pulse widths are varied from 50 to 1000 μsec and heater power densities $W_h$ extend from 0.1 to 20 ${\mathrm{W}/\mathrm{c}\mathrm{m}}^2$. The radiated energy flux is monitored by a number of small carbon detectors which are located at distances of 1 and 2 cm from the heaters and at angles varying from 7° to 89° with respect to the heater normals. In the arrangement used, signals free of wall reflections can be observed. For values of $W_h$ below 0.5 ${\mathrm{W}/\mathrm{c}\mathrm{m}}^2$ the energy flux is found to travel at 235 ± 10 m/sec without any appreciable dispersion; the angular dependence of the flux is characteristic of the diffuse radiation of non-interacting flux of phonons emanating from the heater surface. When $W_h$ exceeds 0.5 ${\mathrm{W}/\mathrm{c}\mathrm{m}}^2$, the angular distribution is changed. Also, at higher heater power densities a second slower component appears in the radiated flux. This component travels at 130 ± 30 m/sec and is most likely associated with the helium excitations near the roton minimum. The results are discussed briefly in terms of model calculations for the effective source of excitations. It is shown that the experimental data are consistent with formation of a layer of relatively hot helium adjacent to the heater; this layer, whose shape and extent depends on the total energy flux produced by the heater, acts as the effective source of excitations radiated into the ambient low-temperature liquid helium.

We investigate the statistical properties of the intensity of radiation emitted by $N$ two-level systems, for which the cooperation number is constant. The $l$-fold moments of the intensity are shown to obey a closed set of equations. For long times, the normalized moments are found to go up to infinity. But, taking into account the experimental limitations, large fluctuations will be seen only for almost completely excited systems.

The heating of plasma electrons in a laser beam by the inverse Bremsstrahlung process is considered from a quantum-mechanical viewpoint. A kinetic equation is derived and the change in kinetic energy of the electrons is calculated. Effective collision frequencies are found for the two cases of weak field and strong field and are compared to the classical results. It is found that the Coulomb logarithm, which appears in the classical expressions for the effective collision frequency, does not appear in the strong-field expression for effective collision frequency of the present work.

Proton excitation was employed to obtain new information on the vacuum-ultraviolet (vuv) emissions from helium gas. Time-dependent studies of the 584-Å resonance line and the vuv continuum (600-950 Å) have been made as a function of pressure. The decay rate for 584-Å resonance photons shows a type of pressure dependence which indicates that the $2^{1}P$ atomic state is destroyed much more rapidly by collisions than by radiation to the $2^{1}S$ metastable state. Most of the vuv continuum decays with two time components (fast and slow). The number of ions and the population of the lowest-ten excited states resulting when an energetic (4-MeV) proton loses a fraction of its energy in helium, and when the secondary electrons completely degrade in energy, have been calculated. The theoretical studies indicate that about 30% of the energy lost by a single proton goes into atomic excitation, where about one-half of these excited states are $2^{1}P$ states. These new results are combined with previous information to propose an energy pathways model for helium. We suggest that the $2^{1}P$ state is primarily destroyed by collisions to the $D$ and $B$ molecular states which are then the source of the fast vuv radiation (640-950 Å) and the precursor of slow radiation, respectively. In our model the metastable $B$ molecular state stores the energy which is utilized in producing additional ionization (Jesse effects) when impurities are added to helium, in contrast with previous interpretations which assumed that the energy is stored in atomic metastable states.