Molecular dynamics experiments made on a system of 864 particles interacting through a Lennard-Jones potential for various high-density states are used to study the self-correlation in classical fluids. The self-diffusion constant is computed and interpreted in terms of a hardsphere model. The memory-function formalism is used to give a simple phenomenological fit for the computed velocity autocorrelation function and for the self-intermediate-scattering function. A detailed comparison is made with the various existing theories for the latter quantity.

The quantum theory of laser behavior developed in the first paper of this series is extended to include finite atomic and cavity temperatures and to include the effects of atomic detuning from the cavity eigenfrequency. The dependence of the photon statistics and the laser line-width on temperature and detuning is given.

A quantum theory of an optical maser was developed in the first paper of this series, in which the active medium is made up of static two-level atoms excited in their upper level while the damping atoms are taken in their lower level. The theory was extended in the fourth paper by generalizing to finite atomic and cavity temperatures, and the frequency pulling and pushing relations were also derived. In the present paper we extend the work of the previous papers by allowing the lasing atoms to have thermal motion. Recoil of the atoms due to photon emission or absorption is also considered, and its effect on the laser threshold and operating frequency is given. The influence of the atomic motion on the photon statistics, frequency shift, and line shape of the laser radiation is shown explicitly.

The general expression for the transport coefficients at finite frequency is given by the spectral function of the autocorrelation of the flux corresponding to the transport phenomenon considered. Because the explicit analytical solution of such a correlation function involves the whole many-body problem for strongly coupled systems, appeal must be made to a model in order to derive the explicit frequency dependence of the transport functions. In the first part of this paper, we calculate these functions analytically [i.e., the diffusion $D\left(\omega \right)$, the viscosities ${\eta }_S\left(\omega \right)$ and ${\eta }_B\left(\omega \right)$, and the thermal conducti̧vity $\kappa \left(\omega \right)$] from the generalized Berne-Boon-Rice model. The frequency dependence of these transport functions becomes significant at high frequencies, i.e., when $\omega$ approaches ${\omega }_c\sim {\tau }_c^{-1\mathrm{}}$, where ${\tau }_c$ is the collision time, and should be essentially responsible for the departure from classical hydrodynamics. This is shown in Sec. II of this paper, where we present a calculation of the spectral distribution of the light scattered from thermal fluctuations in simple fluids. When the transport functions are introduced in the hydrodynamic equations to replace the usual constant transport coefficients, the spectrum of the scattered light is modified significantly, to second order in $\Gamma k^2$, where $\Gamma$ is essentially a linear function of the transport functions. The second-order spectrum obtained here is in agreement with previous results, but it is shown that the main effect arises from the frequency dependence of the transport functions, which was ignored in previous work. These effects induce a small but significant negative dispersion in the first-sound velocity. This prediction is in qualitative agreement with the recent light scattering experiments by Fleury and Boon on liquid argon, which were initially interpreted as a possible experimental observation of the frequency dependence of the transport functions in simple liquids.

In this paper we report the first experimental observation of the excitation of the spiking resonance in a semiconductor laser by the quantum fluctuations intrinsic to the lasing process. Such excitation and the resulting anomalous peaks in the microwave noise spectrum of the laser intensity were initially predicted by McCumber and later calculated in detail for semiconductor lasers by Haug. In the present observations made with continuously operating GaAs junction lasers, this anomalous peak has been observed at currents $I$ from less than 1% to nearly 100% above threshold $I_{\mathrm{th}}$. The frequency of the peak varied with current as ${(\frac{I}{I_{\mathrm{th}}}-1)}^{\frac{1}{2}}$, in agreement with previous analytical results. However, the resonant frequency was observed to be independent of temperature between 80 and 150 °K, in apparent contradiction with the recent calculations of Haug.

It is proven that a system of nuclei and electrons, confined by walls in the shape of an infinite slab or a rectangular rod of infinite length, cannot have maximum long-range crystalline order. The proof is based on the Bogoliubov inequality.

When the thermal expansion coefficient ($\alpha$) is retained in the linearized hydrodynamic equations of the two-fluid model of superfluid liquid helium, pressure and temperature waves are not independent. Thus a periodically varying temperature source produces not only temperature waves in liquid helium, but also two pressure waves $p_1^{\prime }$ and $p_2^{\prime }$, which propagate at the velocity of first and second sound, respectively. Similarly, a vibrating diaphragm produces not only pressure waves but also two temperature waves $T_1^{\prime }$ and $T_2^{\prime }$, which also propagate at the velocity of first and second sound, respectively. Lifshitz has shown that the amplitudes of these cross modes should be proportional to $\alpha$. An investigation of this coupling has been made by observing and studying the two pressure waves $p_1^{\prime }$ and $p_2^{\prime }$ produced by a heater and the temperature wave $T_2^{\prime }$ produced by a capacitor microphone. The temperature dependence of the amplitude of these waves has been studied using both pulse and standing-wave techniques in the temperature range from 1.2 K to the $\lambda$ point. Good agreement with theory has resulted only for the $p_1^{\prime }$ mode.

Applying the formalism of action-angle variables in quantum statistics to an exactly solvable model Hamiltonian, explicit expressions have been calculated relating the superfluid tunneling current and the corresponding phase coupling between two helium baths connected by an orifice. The relevance of the calculation to a recent experiment has been pointed out.

The one-detector photoelectron counting statistics of a harmonic signal mixed with thermal light was considered in paper I. In the present paper, we consider the extension to the counting statistics with several detectors. An expression for the factorial moment generating function of the number of counts is obtained in terms of the eigenvalues of an associated matrix integral equation. This expression is used to evaluate the factorial cumulants of the number of counts.

The impact-parameter dependence of $L$-shell vacancies in the collision of 30-MeV I ions with Te atoms has been remeasured with improved accuracy.

The relativistic calculation of radiative widths for $K$ shell and $L$ subshells, as reported by Scofield, are in agreement (within 0.1%) with our independent calculations. Theoretical total $K$-shell widths (x ray + Auger) are presented as a function of the atomic number. Using the experimental widths of $K{\alpha }_1$ and $K{\alpha }_2$ and our theoretical results, calculated $L_2$- and $L_3$-subshell fluorescence yields are presented versus atomic number.

In a recent paper Payne reports on experiments verifying the existence of the "heat-exchange torques" predicted by Penney and Overhauser. His results were obtained by measuring the heat-induced changes in the logarithmic decrement of a cylindrical torsion pendulum immersed in He II and seem to be in good agreement with the measurements of the torque on heated cylinders in rotating superfluid helium reported earlier by the present author. Payne claims however, that these earlier measurements are open to serious question because of a torque-producing mechanism which he calculates will be effective if the test cylinder is heated nonuniformly. In this note we show that the physical model chosen for Payne's calculation is unrealizable, and further, that the mathematics is carried through incorrectly. When properly analyzed, the mechanism he proposes yields zero net torque for all distributions of the heat input and could not, therefore, have been a complicating factor in the earlier experiments.

The product of the Stark width and the oscillator strength for the resonance lines of neutral argon and neon has been measured from a comparison of the Stark-broadened emission profiles of these lines with those of Lyman $\alpha$ and Lyman $\beta$, all lines saturating at the blackbody level. The Stark-broadening (damping) constant for each of the lines is found from this product using known values of their respective oscillator strengths. The lines investigated and their Stark widths for an electron density of ${10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$ are ArI1048 Å, (4.6±0.7)×${10}^{-4\mathrm{}}$ Å; ArI1067 Å, (5.1±0.7)×${10}^{-4\mathrm{}}$ Å; Ne I 736 Å, (1.2±0.5)×${10}^{-4\mathrm{}}$ Å; Ne I744 Å, (1.3±1.0)×${10}^{-4\mathrm{}}$ Å. Further, comparison of the experimental Stark profiles of the Lyman line indicates that their current theoretical line shapes agree with each other to better than ∼ ± 10%. The radiation source employed was an electromagnetically driven $T$ tube filled with the appropriate gas mixtures of argon-hydrogen and neon-hydrogen. Electron densities and temperatures were determined from the measured half-widths of H $\beta$ and the relative intensities of selected visible lines, respectively.

The magnetic dipole and electric quadrupole hyperfine constants have been calculated for the ${}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$ states of scandium and copper and the ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ states of gallium and bromine atoms. Both restricted and unrestricted numerical relativistic Hartree-Fock calculations have been carried out; the relativistic core-polarization contribution to the hyperfine constants is studied in comparison with the nonrelativistic results.

A search for x rays from the capture of kaons in helium has disclosed neither $K$- nor $L$- series radiation; the upper limit of the x-ray yield is in the range 7-10%. This contradicts results of an earlier measurement, but is in better agreement with related data on kaon-helium scattering. In the same experimental arrangement, the yields of pionic and muonic x rays in helium were also measured. We find anomalously low yields, accompanied by intensity distributions of the $K$-series members in disagreement with the conventional cascade picture of a predominantly circular set of orbits. Monte Carlo cascade calculations could not duplicate the observed results unless weak Stark mixing, in the form of "sliding transitions" ($n,l\to n,l\pm 1$), was added. Agreement with observation was achieved in muonic, pionic, and kaonic atoms with a single value for the parameter describing the strength of the Stark mixing. Yields and energies of kaonic x rays in other light elements, Li, Be, and C, were also measured. Yields of x rays from muonic and pionic capture in these elements were remeasured also, and cascade calculations like those for helium repeated. In these elements the addition of Stark mixing is not needed to achieve agreement with experiment. In the pionic atoms $2p$-state absorption rates, and in kaonic atoms $3d$-state absorption rates for He, Li, Be, and C can be derived from the experimental data and compared with theoretical values, with good agreement. In addition to the identifiable kaonic transition lines also observed by Wiegand and Mack, additional lines not ascribable to kaonic atoms were found in all three elements. After careful consideration of possible origins of these lines, we ascribe the two lithium lines to $M\alpha$ and $M\beta$, and the Be line to $M\alpha$ transitions in $\Sigma$-hyperonic atoms. Such atoms are formed if ${\Sigma }^{-}$ hyperons from kaon capture (whose abundance is about 15%) are slowed down and stopped in the target. The observed yields and energies are consistent with this interpretation, and with no other we have been able to invent. A line in C, however, cannot be ascribed either to kaonic or $\Sigma$ atoms, and appears to be a pionic $L\alpha$. Why such a line appears only in C is not understood.

The atomic $g_j$ factor for the ${}_{}{}^2{}_{}{}^{}D_{\frac{5}{2},\frac{3}{2}}^{}{}_{}{}^{}$, ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2},\frac{1}{2}}^{}{}_{}{}^{}$, and ${}_{}{}^4{}_{}{}^{}S_{\frac{3}{2}}^{}{}_{}{}^{}$ levels of $p^3$ configurations of Ni and Oii have been calculated with precise Hartree-Fock wave functions. These values are compared with available experimental results. The observed discrepancies are seen to be too large to be attributable to the use of Hartree-Fock wave functions.

Bands of $W{}_{}{}^3{}_{}{}^{}\Delta _{\mu }^{}{}_{}{}^{}\leftarrow X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$, a new system of molecular nitrogen, have been identified in absorption from their locations as predicted by the spectroscopic constants obtained in infrared emission. Three bands have been observed and measured, the (5, 0), (6, 0), and (7, 0). A Deslandres table with Franck-Condon factors is presented, which indicates that the system will occur most readily below 2500 Å. The relevant potential energy curves for the system are given with the observed transitions displayed.

In the reduced-density-matrix variational method, a trial density matrix ${\Gamma }_t^{\mathrm{}\left(2\right)\mathrm{}}$ is varied subject to physical realizability conditions in order to calculate the ground-state energy $E_0=\frac{1}{2}N min \mathrm{Tr}{H}^{\mathrm{}\left(2\right)\mathrm{}}{\Gamma }_t^{\mathrm{}\left(2\right)\mathrm{}}$. Here we expand ${\Gamma }_t^{\mathrm{}\left(2\right)\mathrm{}}$ in a finite basis of Hartree-Fock geminals and apply a number of equalities to reduce the parameter space of ${\Gamma }_t^{\mathrm{}\left(2\right)\mathrm{}}$. The method is completely general, but application is made only to the ${\mathrm{C}}^{++}$ ion, where a six-geminal expansion coupled with positivity of ${\Gamma }_t^{\mathrm{}\left(2\right)\mathrm{}}$ recovers the Hartree-Fock result.

A formal operator definition of indistinguishability of identical particles alternative to permutation invariance of configuration probabilities is presented. The exchange-symmetry properties of many-particle wave functions are shown to follow simply and directly from the new definition.