The transition from ambipolar to free diffusion for ${\mathrm{He}}_2^{+}$ in a helium afterglow has been observed with a mass spectrometer. The theory of Allis and Rose predicts the general features of the observed behavior.

We propose and demonstrate a method to directly measure with high accuracy the group velocity of light. We make use of the natural fluctuations of light and determine in a correlation experiment the coincidence of fluctuations of light passing through a sample path and a reference path with known delay. It is shown that this coincidence can be detected by using amplitude interferometers such as a Michelson interferometer, or intensity interferometers. Accuracies of the order of ${10}^{-6\mathrm{}}$ are practically possible. That is orders of magnitude better than previous methods allow. Using a Nd:glass laser as light source and an intensity interferometer for detecting coincidence, we demonstrate our method by measuring the group velocity of light in water within 2 × ${10}^{-4\mathrm{}}$ using a sample length of only 15 cm. The limitations of this new method caused by second-order dispersion are discussed quantitatively; higher-order effects are discussed qualitatively.

It is shown that average atomic kinetic energies in liquid helium can be deduced, as a function of temperature, in an elementary fashion, using existing experimental data and an empirical interatomic potential. The resulting kinetic energies are compared to the results of fitting recent high-energy neutron scattering data with the simple model of Puff and Tenn.

Previous ultrasonic measurements in the binary mixtures aniline cyclohexane and nitrobenzene $n-\mathrm{hexane}$ have been analyzed according to a method recently proposed for Xe. The experimental results are compared with numerical calculations based on a theoretical formulation by Fixman and Kawasaki. At high frequency ($f^{*}>1\mathrm{}$), the behavior of the sound absorption is quite different from that observed in Xe. We find that the low-frequency form of the theory can be used to fit the data in the entire frequency range. In particular, the Kawasaki prediction ${\alpha }_{\lambda }\sim f^0{\epsilon }^0$ when $f^{*}\gg 1$, which seems to be confirmed by the experimental results in Xe, is not verified for the two mixtures examined here. We suggest that this different behavior is a consequence of the different behavior of the specific heats at constant volume.

The time-average intensity of electromagnetic radiation scattered by a 50-kV electron beam from a $Q$-switched laser beam, incident at 90° and polarized with $\overrightarrow{E}$ perpendicular to the electron beam, is measured as a function of angle with respect to the electron beam. The measured values agree with those calculated using a model that corrects for the fact that the scattering electrons pass through the scattering region during the period of observation. This correction is important in the measurement of plasma distribution functions by laser scattering for plasmas with electron temperatures greater than 10 keV.

We describe the dynamics of an open system $\mathcal{S}$ in terms of a nonunitary time evolution operator. The latter is defined to solve the generalized master equation for the density operator of $\mathcal{S}$ as obtained using Zwanzig's projector technique. Multitime correlation functions of observables of $\mathcal{S}$ are expressed in terms of this time evolution operator. Our results generalize well-known fluctuation dissipation (or regression) theorems valid for Markovian motions of open systems. Moreover, they can be used to combine density-operator and Green's-function methods in dealing with open systems. As an example we treat the retarded electron-electron interaction in superconductors.

We introduce a straightforward quantum-electrodynamic approach to the problem of superradiant spontaneous emission from a system of two-level atoms, and also discuss two classical superradiant systems. The same physical concepts underlie our treatment of both the quantum and classical cases. Explicit expressions are found which describe the time evolution and directional character of the radiated power. Our approach applies to an arbitrary number of atoms which are confined to a region with linear dimensions which may be large compared with the mean wavelength of the emitted radiation. The radiative decay half-life of a large many-atom system is found to be much shorter than the natural lifetime of a single atom, but not as short as the half-life of a small atomic system with the same number of atoms. The far-field radiation pattern appropriate to the case of a circular cylinder of emitters which have been excited by a plane-wave pulse is considered in detail. Polar plots are presented of the radiation patterns produced when the atoms are excited by a plane-wave pulse. Exciting pulses traveling in directions both parallel and at an angle of 10° to the axis of the cylinder are considered. A discussion and generalization of Dicke's "coherence-brightening" criterion is given.

A many-body theory is presented here for the Van Hove pair (or density) correlation function, in a quantum fluid obeying Boltzmann statistics, of which the Fourier transform $S(q,\omega )$ determines the differential cross section for inelastic coherent scattering of slow neutrons. The theoretical formalism of two-particle thermodynamic Green's functions is based on Baym and Kadanoff's conserving $T$-matrix approximation, developed for strong short-range (intermolecular) potentials. The only other approximations made are: (i) the smallness of the activity or fugacity $z\ll 1$, which implies Boltzmann statistics for the single-particle states; and (ii) the $T$ matrices are replaced by elastic scattering amplitudes. Our results for $S(q,\omega )$ developed to order $z^2$ are found to consist of Boltzmann averages of Lorentzian distributions in the energy transfer $\hslash \omega$ (except for a three-particle scattering term which is developed in the $\delta$-function limit of the Lorentzians). Our results are general enough to satisfy detailed balancing at all stages and are found to generalize Van Leeuwen and Yip's results for the classical case. The only unknown in our results is the intermolecular scattering amplitude or phase shifts. Our results seem, however, to break down in the hydrodynamic limit $\omega$ and $q\to 0$ since each term in our expansion diverges in this limit.

The time evolution of the optical field produced by a $Q$-switched He:Ne laser has been investigated experimentally, in the neighborhood of the threshold of oscillation. The experiment was based on a measurement of the variation of the photoelectric counting probability with time, following the turn-on of the laser. $Q$ switching was achieved with the help of an external mirror to extinguish the laser, and a Pockels cell to switch out the mirror. The working point of the laser could be held anywhere in the threshold region, by use of a feedback arrangement which controlled the cavity length, and therefore the atomic gain. Results are presented showing the evolution of the mean light intensity, the variance of the light intensity, and the counting probability with time, for several different values of the laser pump parameter. The results are found to be in very good agreement with the calculations of Risken and Vollmer, based on a rotating-wave van der Pol oscillator model of the laser.

Thin-film cold-cathode emitters were used to inject electrons into solid helium, liquid helium under pressure, and gaseous helium at 4.2 and 20 °K. The cross section for the interaction of the injected quasifree electrons with the helium was deduced by use of an appropriate model for the thermalization of the electrons, and sundry other parameters of the quasifree state, such as its lifetime and collision frequency of the electron therein, were deduced. The cross section derived is within a factor of 2 of the value for the elastic scattering cross section for the isolated atom. The description of the scattering and thermalization process is dependent only on the helium atomic density and is independent of phase.

A modified Hall's theory of structural relaxation has been applied to explain the excess ultrasonic absorption in methanol in the temperature range 0-50 °C. Two states, one characterized by higher volume (icelike structure) and the other by lower volume (close-packed structure), are assumed to be available to each molecule of methanol. The assumption made here, regarding the assignment of $\tau$ values for methanol obtained from correlating its acoustical properties to that of water, shows very good agreement between the theoretical and experimental approaches. The value of ${\beta }_{\infty }=53\mathrm{}\times {10}^{-12\mathrm{}}$ ${\mathrm{cm}}^2$/dyn and $\frac{\Delta V}{V}=0.45\mathrm{}$ have been used for the calculation.

In a previous investigation, a general theory for spontaneous emission from a system of $N$ identical atoms or molecules was developed. This theory was based on the master equation recently derived in another paper. In that paper, the master equation relating to spontaneous emission from a system of harmonic oscillators was also derived. In the present investigation, the normally ordered correlation functions for the oscillator system are calculated and these are then used to calculate the radiation-field correlation functions in the far zone. These correlation functions are compared for two different modes of excitation, viz., (i) when each of the oscillators is excited initially to a Fock state, and (ii) when each of the oscillators is excited to some coherent state. It is found that the even-order ($2n$) correlation functions for the second mode of excitation (superradiant excitation) are of order $N^{2n}$ higher than those for the first mode of excitation. It is also shown that the photoelectron counting distribution for the superradiant excitation is Poissonian. Finally, the non-Markoffian effects in the spontaneous emission are studied in detail and their connection with exact results is described.

The scattering of 300-eV electrons from atomic Hg was used to study the validity of some recently published analytical potentials. Comparison with experimental data showed rather poor agreement with a potential derived on a nonrelativistic basis and good agreement with a potential derived on a relativistic basis. The best agreement has been achieved by adding to the scattering potential an exchange contribution due to exchange between the incoming electron and the target electrons. Experiment and theory are found to deviate significantly at the minima in the differential cross section.

The economies resulting from the transfer of the Physical Review from monotype printing to typewriter composition have made it possible to reduce the publication charge of all sections of the Physical Review from $70 per page to $65 per page, effective with the issue of June 1971. (The charge for advance publication of the abstract in Physical Review Abstracts will remain at $15.)

The switch to typewriter composition has also resulted in a reduction in the time lag between date of acceptance and date of publication.

The method of pure electric field level-crossing spectroscopy has been used to measure the tensor polarizability of the $5{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ state of potassium. Our result is ${\alpha }_2=-0.263\mathrm{}\left(40\right)\mathrm{}$ MHz/ ${\mathrm{}(\mathrm{k}\mathrm{V}/\mathrm{c}\mathrm{m})\mathrm{}}^2$. Numerical values of the scalar and tensor polarizabilities of the first, second, and third ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ states of Li, Na, K, Rb, and Cs have been calculated using the Bates-Damgaard technique to evaluate the necessary radial integrals. The polarizabilities show remarkable systematic trends among the various states of the atoms. Our present and previously reported results are compared with previous theoretical and experimental work. The agreement between theoretical and experimental values ranges from fair to excellent.

One intuitively expects that a long-lived decaying state must have many properties like those of true eigenstates, with interesting technical modifications to encompass the complex energy. We examine here the small change in the complex energy due to the application of a weak perturbation.

The five hyperfine transition frequencies of the $S_{\frac{5}{2}}$ ground state of ${\mathrm{Mn}}^{55}$ have been measured in a spin-exchange optical pumping experiment. The optical pumping flasks contained a neon buffer gas, and the measurements were made as a function of buffer-gas pressure. The measurements were carried out at a temperature of 700 °C. The linewidth of the Mn signal was typically 300 Hz. The hyperfine interaction constants were found to be $A=-72420836\mathrm{}\left(15\right)\mathrm{}$ Hz, $B=-19031\mathrm{}\left(17\right)\mathrm{}$ Hz, $C=-0.7\mathrm{}\pm 1.1$ Hz, $\mathrm{}\left|D\right|<0.25\mathrm{}$ Hz, and $\mathrm{}\left|E\right|<0.02\mathrm{}$ Hz. The fractional pressure shift in $A$ was found to be $\left(\frac{1}{A}\right)\left(\frac{\partial A}{\partial P}\right)=(2.6\mathrm{}\pm 0.2)\times {10}^{-8\mathrm{}}$ ${\mathrm{Torr}}^{-1\mathrm{}}$. No pressure dependence of the other interaction constants was observed.

In this paper we present the results of some atomic calculations as affected by the Coulomb correlation. We deal with atoms and ions with and without spin polarization. Thus we are able to compare calculated energy eigenvalues and hyperfine fields of contact with the experimental ionization energies and fields. Our approximation for the mass operator (exchange plus correlation) can thus be compared with the approximations proposed by Slater, Gaspar, Kohn and Sham, and Liberman. A broad evaluation of the results implies that our approximation for exchange and correlation is correct. Furthermore, when neglecting the correlation effects, we noticed that the results become poorer. Thus, this paper favors a single-particle description of many-body systems based on an effective-wave equation with the mass operator instead of the simpler exchange operator of the Hartree-Fock theory.

The angular correlations of photons from positrons annihilating in liquid and solid argon, krypton, and xenon show positronium-bubble formation in the liquid phase but not in the solid. Positronium formation increases with increasing atomic weight while bubble radii decrease with increasing atomic weight.

For many excited $d$- and $f$-electron configurations there exist instabilities in the iterative self-consistent solution of the Hartree-Fock (HF) equations which make it practically impossible to obtain HF solutions using standard methods. These instabilities are associated with the sudden contraction of the $d$- or $f$-electron wave function to smaller radii near the beginning of the corresponding transition or rare-earth series. The instabilities have been overcome by new methods of solving the HF problem which involve the temporary relaxation of the normalization condition and the application of techniques which search directly for that integral of the differential equation having the highest degree of self-consistency. Using these new methods, HF solutions have been obtained for excited $d$- and $f$-electron configurations throughout the transition and rare-earth series of elements, and the results of these calculations have been employed to study the nature of the solutions and of the associated instabilities.