The density fluctuation in a Bose gas interacting via a strong short-range repulsive potential and a weak long-range attractive potential is studied by the methods of quantum-field theory. The density-density correlation function is generated by taking the functional derivative of the single-particle matrix Green's function $G_1\mathrm{}(1,2)\mathrm{}$ with respect to an auxiliary scalar field. For $G_1\mathrm{}(1,2)\mathrm{}$, we use the Hartree approximation for the attractive potential and the Hartree-Fock approximation for the short-range repulsive potential. We show that the density fluctuation spectrum is identical to the Beliaev approximation for the single-particle excitation spectrum.

Transition probabilities for O I lines emitted in the vacuum ultraviolet were measured using a wall-stabilized arc discharge operating in a mixture of argon and oxygen. The lines were emitted from a column of plasma which was observed end-on and which was characterized by a nearly uniform temperature. Optically thin conditions were achieved by reducing the relative concentration of oxygen atoms in the discharge to levels of less than one part per million. Absolute values for the O I transition probabilities were obtained by determining the oxygen-atom density and plasma length through a measurement of the absolute intensity of the O I $\lambda =7773.4\mathrm{}$ Å line, whose transition probability is known. The following values were measured for lines in the resonance transition array: $A({}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}-{}_{}{}^1{}_{}{}^{}D_2^{\mathrm{o}}{}_{}{}^{},\lambda =1152\mathrm{}\mathrm{\AA })=5.5\mathrm{}\times {10}^8$ ${\sec }^{-1\mathrm{}}$; $A({}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-{}_{}{}^1{}_{}{}^{}P_1^{\mathrm{o}}{}_{}{}^{},\lambda =1218\mathrm{}\mathrm{\AA })=1.8\mathrm{}\times {10}^8$ ${\sec }^{-1\mathrm{}}$; $A({}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}S_1^{\mathrm{o}}{}_{}{}^{},\lambda =1306\mathrm{}\mathrm{\AA })=0.66\mathrm{}\times {10}^8$ ${\sec }^{-1\mathrm{}}$; $A({}_{}{}^3{}_{}{}^{}P_{2,1,0}^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}S_1^{\mathrm{o}}{}_{}{}^{},\lambda =1303.5\mathrm{}\mathrm{\AA })=5.9\mathrm{}\times {10}^8$ ${\sec }^{-1\mathrm{}}$. These values are in excellent agreement with recent lifetime measurements. Existing discrepancies in the literature concerning a previous arc determination of the O I vacuum ultraviolet oscillator strengths by Boldt and Labuhn are discussed. The present method is considered to be an improvement over the method used by Boldt and Labuhn which relied, first of all, upon extrapolation techniques to reach the linear part of the curve of growth and, secondly, upon a complex calculation of the oxygen-atom number density using basic conservation equations.

The electric field gradient at Li in LiH has been computed with a 200 configuration-interaction function including single and double excitations from the Hartree-Fock function of Cade and Huo. This value, in conjunction with the experimental LiH $\mathrm{eqQ}$ value, leads to a suggested value of $Q\left({\mathrm{Li}}^7\right)=-(3.66\mathrm{}\pm 0.03)\times {10}^{-26\mathrm{}}$ ${\mathrm{cm}}^2$. This value is substantially different from that obtained using previously calculated field gradients derived from less complete wave functions.

In contrast to a rather common statement, we show that at a liquid-liquid critical point there are very large density fluctuations. A general property of the correlation functions of local dynamical variables is proposed on the basis of the behavior of various thermodynamic derivatives near a critical point in binary mixtures. Our analysis applies to the general case. Possible isolated points such as an azeotropic critical point are not considered.

The relation $S^{\mathrm{}\left(0\right)\mathrm{}}\mathrm{}\left(k\right)=\frac{\hslash k}{2m{c}_0}$ as $k\to 0$ is derived for Fermi liquids in the strong-coupling limit. $S^{\mathrm{}\left(0\right)\mathrm{}}\mathrm{}\left(k\right)\mathrm{}$ is the contribution to the static structure factor $S\left(k\right)\mathrm{}$ from the zero-sound excitation with velocity $c_0$. Together with simple sum-rule arguments, we present some upper and lower bounds on $S\left(k\right)\mathrm{}$.

It has recently been shown by Jaynes and collaborators that semiclassical radiation theory contains a description of spontaneous emission of radiation and of radiative level shifts. The present paper gives a gauge-invariant derivation of the radiant energy production rate, using only Maxwell's equations and the usual definitions of electric current and charge density for a many-particle material system described by Schrödinger's equation. A complementary derivation, using the time-dependent Schrödinger equation, verifies the instantaneous conservation of energy and probability during the radiation process. The semiclassical rate of spontaneous emission differs from the usual formula (Einstein's $A$ coefficient) because it depends on the occupancy of both initial and final states of the material system. The implications of this with regard to thermal equilibrium and Planck's law are examined. If a new hypothesis is introduced, postulating the decomposition of the equilibrium radiation into incoherent components, each interacting with a specific pair of energy levels of the material system, then Planck's law is shown to hold for the total intensity of radiation. If this hypothesis is not introduced, the equilibrium conditions for different transitions are incompatible, and the semiclassical radiation theory is incapable of describing thermal equilibrium.

The Ginzburg-Pitaevskii phenomenological theory has been extended to include the effects of vortex lines. The model calculations are compared with some of our recent experimental results on the He II-He I transition in the presence of a heat current.

Correlation effects in the quantum crystals ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ are studied in detail. The single-particle wave function is obtained in the harmonic effective-field approximation; the parameters of the harmonic-oscillator potential are determined self-consistently from the two-body correlation function and the bare interatomic potential. We determine the two-body correlation function by solving numerically an equation derived by decoupling the three-body correlation function into a product of two-body correlation functions. This equation is similar to one derived on the basis of the $T$-matrix approximation, but yields the correct behavior of the correlation function as the distance between the particles tends to zero. The ground-state energy, pressure, and compressibility are computed over a wide range of molar volume for ${\mathrm{He}}^3$ in the bcc and hcp structures, and for hcp ${\mathrm{He}}^4$. In bcc ${\mathrm{He}}^3$ we employ two different interatomic potentials, the Lennard-Jones 6-12 potential generally used in calculations of this type and also the Yntema-Schneider potential. We find a ground-state energy about 1½°K too low with the former and about 5°K too high with the latter, demonstrating that the choice of potential is of considerable importance for detailed comparison of theory and experiment. We also examine the effect of three-body correlations on the equation for the two-body correlation function; the result suggests that the effect is to force the two particles toward one another, which also seems physically reasonable, as the atoms surrounding a particular pair of particles should tend to push them together. We incorporate this effect into the two-particle equation by including a potential linear in the interparticle distance; for a given molar volume, its magnitude is chosen by imposing a constraint on the average interparticle distance. The calculated correlation functions for neighboring particles have peaks at about the corresponding lattice distance, and the numerical results for energy, pressure, and compressibility are in reasonable agreement with experiment. Our approach is compared with other recent theories of quantum crystals.

The impulse approximation is used to describe the inelastic cross section for high-energy neutron scattering from superfluid helium in terms of a ground-state momentum distribution of the helium atoms as given by existing variational calculations. The predicted shape of the cross section is compared with recent experimental data and with a previous theory which approximated the noncondensate contribution to the dynamic structure factor by a single-Gaussian function. In contrast to conclusions obtained using the single-Gaussian approximation, our predicted inelastic cross section omitting a condensate contribution provides an acceptable fit to the experimental data. This fit is worsened by introducing a contribution from a condensate fraction in the amount consistent with the variational calculations, namely 11%. If the condensate fraction is arbitrarily reduced from this value, it is found that a much smaller value, with an upper limit of about 3%, is consistent with the available experimental data. It appears that unique assignments of condensate-fraction contributions to inelastic neutron scattering, for the range of neutron energies presently available, will require an improved theory of final-state effects on the shape of the condensate contribution.

It has already been reported that a laser subject to an axial magnetic field and having end mirrors which exhibit relatively high $x-y$-type loss anisotropy can be described by two theoretical methods. The first method uses self-consistent-field equations with distributed losses, whereas the second one is based on a resonance condition for a complete round-trip pass. The following study of a Zeeman laser with different $x-y$-type loss anisotropy at each mirror shows that the localization of the losses and the nonreciprocal character of the Farady rotation require a different formulation for each initial system. The rotation of the plane of polarization is different at each end of the laser, but it is shown that there always exists for central tuning a real or virtual average polarization vector which obeys Lamb's theory. The equivalence of the two methods is discussed.

The mobility and density of states as functions of the energy are computed from the mobility and free energy reported previously by Neustadter and Coopersmith. The results are shown to be equivalent to the recently published calculations by Eggarter and Cohen based on a semi-phenomenological model. Some difficulties with both theories are noted and commented upon.

We discuss the cooperative decay of initial atomic excitation for a pencil-shaped active volume filled with two-level atoms. As long as the length of the sample is much smaller than a certain maximal cooperation length, the atom-field interaction producing the superradiant pulse can be treated in terms of the simplest possible laser model (single mode). The basic laser master equation turns out to be exactly solvable if specified for the superradiance limit which is characterized by two conditions: (i) The photons escape from the low-$Q$ cavity so fast that they cannot feed themselves back into atomic excitation to any appreciable amount (this no-feedback condition is equivalent to the above-mentioned requirement for the length of the sample). (ii) The incoherent atomic decay due to natural relaxation is so slow that the individual atomic dipoles do not dephase before engaging themselves cooperatively in the interaction with the electromagnetic field. The present paper presents the derivation and general discussion of the equations describing the statistical properties of atoms and field in a superradiant pulse. Analytical and numerical solutions will be presented in a subsequent paper.

The classical theory for mass defects in crystals is inapplicable to quantum crystals, where zero-point motion leads to a force-constant renormalization on the introduction of mass defects. We develop a variational theory for handling such problems which simplifies the renormalization so that the problem reduces to that of a single frequency-dependent mass defect, to be calculated in a self-consistent fashion. Various anomalies observed in the properties of quantum crystals are discussed in light of the present theory. The theory may also be used to calculate in a simple fashion the properties of extended defects in classical crystals.

Pressure effects in gas lasers are studied within the framework of a theory that treats the center-of-mass motion of the active and perturber atoms quantum mechanically. Such a theory considers the perturber-induced energy-level variations and the velocity changes of the active atom caused by collisions on an equal basis. The calculation is carried out assuming that the active atom undergoes many binary collisons before it decays. As such, this paper represents a generalization of our previous work, which was valid only if the active atom underwent, on the average, at most one collision in its lifetime. The transition from the "one-collision" to the "many-collision" domain is achieved by use of a pseudoclassical collision model. This model enables one to incoporate the results of a rigorous quantum-mechanical treatment of the one-collision problem into a standard classical procedure for handling many (binary) collisions. The result is a quantum-mechanical theory of collision effects valid in the many-(binary-)collision pressure region. Using this theory, expressions for the laser intensity profile are derived employing a collision model which, although quite elementary, should prove to be reasonably accurate for lasers operating slightly above threshold at pressures where both the collision-broadened linewidth and cavity detuning are much smaller than the Doppler width associated with the laser transition. A comparison of theory and experiment is made, and the significance of their relatively good agreement is discussed.

Using two different extended basis sets of Slater-type orbitals, we have carried out a study of the correlation energy and hyperfine structure of the ${}_{}{}^4{}_{}{}^{}S$ ground state of the nitrogen atom. Symmetry-adapted pair correlations were evaluated with respect to a multiconfiguration reference state, the first-order wave function. It was found that each symmetry-adapted pair correlation energy could be rather accurately (to about 3%) approximated as a sum of effects due to symmetry-determined classes of configurations. Using the larger of the two basis sets, the effects of 1633 configurations, constructed from 19 530 distinct Slater determinants, were considered. With this basis set the correlation energy obtained was 0.181 75 hartree, compared to the estimated correlation energy 0.186 hartree. It was found that pair correlations had large canceling effects on the hyperfine structure, the net result of which was a spin density 77% of experiment, and only slightly larger than the first-order spin density, which includes core polarization effects. Several points in common are found in a comparison with the many-body perturbation theory results of Dutta, Matsubara, Pu, and Das. The most useful and interesting result of the present work is a clear picture of the different effects which contribute to the correlation energy and hyperfine structure of ${}_{}{}^4{}_{}{}^{}S$ N.

The correlation function of an electron gas is evaluated at short distances by using the solutions of the Schrödinger equation for two electrons. The correlation function of a classical electron gas is evaluated explicitly to $O\left(r^3\right)$, where $r$ is the separation of the two electrons. The value of the correlation function at $r=0\mathrm{}$ is evaluated numerically as a function of a dimensionless parameter $\delta =\frac{2\lambda }{a_0}$, where $\lambda ={\mathrm{}\left(\mathrm{kT}\right)\mathrm{}}^{\frac{-1\mathrm{}}{2}}$ and $a_0$ is the Bohr radius. Quantum-mechanically degenerate cases are also considered.

The ground-state energy of a many-boson system in the uniform limit is obtained in the Bijl-Dingle-Jastrow function space by minimizing the expectation value of the Hamiltonian operator with respect to the correlation function. The procedure is found to be equivalent, through third order, to the indirect variational approach in which the radial distribution function is varied without constraints.

The possibility of accelerating particles with a focused laser is considered. The particle is accelerated transversely by the electric field and redirected to the forward direction within a single half-cycle by the magnetic field of the radiation. The equations of motion of the particle are solved and discussed. Special attention is given to an intuitive understanding of the constraint imposed by the geometry of the focal region. Optimum conditions are examined.

Calculations of cohesive energy, pressure, and compressibility have been made for liquid Na at 393°K. They are based on the Ashcroft form for the pseudopotential and the self-consistent dielectric function recently given by Singwi et al., which have been found to give good agreement with the measured phonon dispersion relations in crystalline Na, and a liquid strucutre derived from a recent molecular-dynamics calculation by Rahman. The theory is formulated in terms of a volume-dependent pair potential and additional volume-dependent terms. A model which considers only volume-independent pairwise interactions gives incorrect results for the cohesive energy and pressure. It also gives a different result for the compressibility from the full theory, owing to the neglect of certain three- and four-particle interactions which are considered in the full theory; this result is, however, in reasonable agreement with experiment. The full theory gives good agreement for the cohesive energy, pressure, and compressibility if and only if an adjustment is made to the Hartree energy, similar to that made in a previous calculation for the crystal.

Optical spectroscopic techniques were used to observe light from a room-temperature flowing-helium afterglow at a pressure of 1 Torr. A nonthermal electron distribution was found in the afterglow. This distribution could be represented to first order by two independent equilibrium distribution functions. Characteristic temperatures of ${10}^3$ and of ${10}^4$ K were measured from intensities of atomic helium transitions using the Saha equation. The density of the low-temperature group of electrons was one order of magnitude greater than the density of the high-temperature group. A model was developed to explain the mechanisms by which ionization is maintained in the afterglow region of the plasma. Energy-exchange mechanisms included in the model are three-body electron-ion recombination, ionization of excited-state helium atoms, and an exchange of electrons between the two equilibrium distributions. The relationship to the model of electron diffusion and relaxation is described. A quantitative comparison between theoretical and experimental values for the steady-state population of atomic helium states through a complete range of the principal quantum number is now possible. An expression for the decay of the electron density in the afterglow was derived giving results in agreement with experiment.