The interaction between an ultrasonic field and one or a few quantized vortex lines in He II was investigated using the audible cavitation threshold as a means of detection. Experiments involved both rotating ultrasonic buckets and two shafts, each with a paddle attached, rotatable in the same or opposite sense near an ultrasonic field. Histograms of cavitation threshold measurements were not Gaussian, but appeared to be bimodal. The high threshold mode was most frequent in the quiescent state, but the lower mode was most frequent with rotation. The threshold values were found to fluctuate with time both with and without rotation. Slight and gradual reductions of audible threshold were observed in the rotating bucket sometimes, beginning at speeds less than that predicted by the Arkhipov-Vinen formula. Reductions at speeds higher than the Arkhipov-Vinen value were not directly proportional to the total number of vortices believed to be present in the bucket. Two shafts with paddles rotating in opposite senses caused larger reductions in threshold than a single shaft and paddle; but this was not the case when the shafts rotated in the same sense.

In a quantum-mechanical problem with a slowly varying Hamiltonian, such as appears in a semiclassical treatment of inelastic atomic collisions, it is common to restrict attention to a small number of states among which transitions are anticipated. This procedure is justified by an extension of the conventional adiabatic theorem to nearly degenerate states. The correct mixing within the restricted basis is determined by a time-dependent variational principle. The contribution of states outside the basis vanishes as the time scale for variation of the Hamiltonian becomes large. A further generalization deals with pseudoeigenfunctions, such as appear in the theory of the Stark effect.

The magnitude of the atom-wall collision frequency shift in the hydrogen maser has been reduced tenfold by confining the hydrogen atoms in a Teflon-coated cylindrical vessel that is 5 ft long and 5 ft in diam. The wall shift of this large maser was measured to be - (2.3±0.8) × ${10}^{-3\mathrm{}}$ Hz at 27°C. Oscillation is achieved by a prestimulation method in which radiant atoms that have been prestimulated in the high rf field of one microwave cavity maintain a maser oscillation in a second cavity. A signal is extracted from the low-level cavity, amplified to a suitable value, and coupled into the high-level cavity to maintain the rf field there. A detailed theory of a multiple-region maser system is presented.

A description of the parametric amplifier and frequency converter is presented without introducing the classical (i.e., parametric) approximation for the pumping field. Constants of the motion are found which reduce the solution of the Schrödinger equation to the diagonalization of a matrix. This diagonalization is accomplished numerically, and the eigenvalues and eigen-functions of a system with fixed energy are calculated. The time-dependent behavior of the mean number of photons in the amplified or frequency up-converted field is presented. The time evolution of the probability distributions is illustrated. The technique is extended to the problem of coherent spontaneous emission from a system of $N$ two-level atoms interacting with the radiation field where both the atomic system and the radiation field are quantized.

A theory of collective motions in classical liquids, which is valid at short wavelengths and high frequencies, is presented. This theory is based on a self-consistent-field method, which can be viewed as a generalization of the random-phase approximation. The existence of collective effects is considered at the outset by introducing a self-consistent "polarization" potential that provides the restoring force and a "screened" response function. The density response function is expressed in terms of these two functions. The local field corrections enter the polarization potential via the static structure factor of the liquid. Various approximations for the polarization potential and the screened response function, and their relation to the first few moments of the spectral function of the density response, are examined. These approximations are tested by explicit numerical calculations of the spectral function of the longitudinal current correlations for liquid argon. It is found that an over-all good agreement with the data is obtained for the case in which the screened response function is equal to the response function for the self-motion of atoms and the polarization potential is determined through the zeroth-moment sum rule. There are no adjustable parameters in the theory.

The relation between the mean-square fluctuations of magneto-static and dynamic pressures is derived for a turbulent fluid of ideal conductivity in an exterior magnetic field.

We derive quantum-mechanical kinetic equations for the matter density $\rho$ and radiation density matrix $R$, which describe optical pumping phenomena. The resultant kinetic equations are a set of coupled nonlinear equations for $\rho$ and $R$. With appropriate linearizations, we can obtain the present theories of optical pumping. The nonlinear equations describe multiple scattering and line narrowing due to imprisonment of resonant radiation. We show that the coupled equations for $\rho$ and $R$ are equivalent to coupled equations for $\rho$ and a generalized polarization matrix II, whose matrix elements are the second moments of $R$. The polarization matrix II constitutes a complete description of linear phenomena in the same manner as present theories describe optical pumping phenomena by using the matter density matrix $\rho$ alone. As a consequence of our nonphenomenological treatment of radiation, we can provide a completely microscopic treatment of the externally modulated light-beam experiment of Bell and Bloom. We show that the atom absorbs the modulation envelope directly from the external thermal light beam in the same way that the atom absorbs transverse polarization directly from the light beam in optical pumping experiments.

We describe a calculation of the optical absorption spectrum of a simple liquid on the Frenkel exciton model. Moments of the imaginary part of the dielectric constant are expressed in terms of integrals involving the pair correlation function by use of the Kirkwood superposition approximation. We present numerical predictions for three of these moments in the case of liquid helium, using the experimental pair correlation function. The calculation assumes that the atoms are stationary during the absorption process. We show why a more rigorous treatment would not lead to significantly different results, compare this work with previous studies, and discuss the significance of the work and the further studies it suggests.

The work of an earlier paper on the ground-state properties of a system of bosons interacting via a strong short-ranged repulsive potential and a weak long-ranged attractive potential is extended to nonzero temperatures. The technique of temperature-dependent Green's functions is employed. It is shown that with the same restrictions on the two-body potential as imposed in the case of the ground state, it is possible to calculate in a consistent fashion the leading low-temperature contributions to the various thermodynamic functions. The results provide support for Landau's point of view for treating the system at low temperatures as a collection of noninteracting quasiparticles. The isotherms of the system at the low temperatures considered indicate a first-order transition between a phase with a condensate and one without a condensate, and also the possibility, at higher temperatures, of three phases.

A calculation of the optical-absorption cross section of electronic bubbles in liquid helium is presented as a function of energy and pressure for various assumed values of the zero-pressure well depth $V_0\mathrm{}\left(0\right)\mathrm{}$. It is shown that a simple interpretation of the Northby-Zipfel-Sanders experiments on "photoejection" can be based on a value of $V_0\mathrm{}\left(0\right)\mathrm{}$ of 0.95 eV, varying with pressure (i.e., density) according to either the optical or the Wigner-Seitz approximation. We suggest an interpretation in which the electron is not necessarily released from the bubble, and predict that these experiments performed at 12 $\mu$ (zero pressure) to 25 $\mu$ (15 atm) would show a ${10}^2$-larger effect.

The properties of a dilute solution of mass-3 bosons in liquid ${\mathrm{He}}^4$ at low temperatures are computed via a variational procedure. A set of coupled integrodifferential equations is solved, yielding expressions for the ground-state energy per particle, the binding energy of ${\mathrm{He}}^3$ in ${\mathrm{He}}^4$, the (3, 3), (4, 3), and (4, 4) distribution functions, and the long-wavelength limit of the effective interaction between ${\mathrm{He}}^3$ quasiparticles in ${\mathrm{He}}^4$. Numerical results are obtained and compared with experiment.

Recent attempts to calculate relativistic bremsstrahlung cross sections in the intermediate energy region are discussed, using results from an independent exact numerical calculation. The numerical work of Brysk, Zerby, and Penny gives quite good results for the bremsstrahlung cross section, differential only in photon energy, but significantly underestimates and over-estimates the cross section, differential in photon energy and angle, in small-photon-angle regions and in large-photon-angle regions, respectively. The approximate analytical results of Elwert and Haug are quite good for low atomic number $Z$, but we can already see deviations for $Z=13\mathrm{}$. For $Z=79\mathrm{}$, their theory underestimates the cross section by large factors.

Experimental profiles, theoretical Stark-broadened line profiles, and the asymptotic wing approximation of hydrogen Balmer lines ${\mathrm{H}}_6$-${\mathrm{H}}_{12}$ are compared at an electron density 1.2×${10}^{13}$ ${\mathrm{cm}}^{-3\mathrm{}}$ and at a temperature of 1850°K. Theoretical line profiles are calculated using the impact approximation for electrons and quasistatic approximation for ions. The half-widths and $\frac{1}{10}$ widths agree to within mutual tolerances, and over-all qualitative agreement is excellent.

Cross sections for production and destruction of fast ${\mathrm{He}}^0$ atoms in triplet states have been measured for 10- to 30-keV ${\mathrm{He}}^{+}$ ions incident on gas targets of Kr, ${\mathrm{N}}_2$, and Ne. Values of the fractions of neutral ${\mathrm{He}}^0$ atoms in the triplet metastable state emerging from thin targets of Kr, ${\mathrm{N}}_2$, and Ne are 0.12±0.005, 0.06±0.03, and 0.03±0.02, respectively, for incident ${\mathrm{He}}^{+}$ energies of 30 keV.

The need for an accurate description of the electronic structure of the important laseractive ion ${\mathrm{Nd}}^{3+}$ stimulated this work. We calculated self-consistent-field wave functions by the analytical-expansion method for the ground state of the laser-active ion ${\mathrm{Nd}}^{3+}\mathrm{}(Z=60\mathrm{})\mathrm{}$, $4f^3$, ${}_{}{}^4{}_{}{}^{}I$. The results represent the most accurate wave functions for ${\mathrm{Nd}}^{3+}$ published. All the exponents of the basis functions in the analytical expansion were exhaustively optimized. The virial theorem was satisfied to seven significant figures. Values of $〈{\mathcal{r}}^n〉$ for the $4f$ orbital are included.

An improved form of semiclassical radiation theory is developed which includes the effect of the atom's radiation field back on the atom. This formalism is applied to the problem of a single "two-level atom" interacting with a monochromatic field. The resulting equations are solved without resorting to time-dependent perturbation theory, and are found to predict the behavior of the system over times long compared with the lifetime for spontaneous transitions. Not only stimulated emission and absorption, but also spontaneous emission with the proper Einstein $A$ coefficient, and a frequency shift which agrees at least semiquantitatively with the Lamb shift are described. In addition, several nonlinear effects involving the interference between spontaneous and stimulated radiation are described, and new experiments which might detect such effects are suggested.

Generalized variational expressions are presented for calculating rigorous lower bounds to the true expectation value $〈\Psi \mathrm{}\left|F\right|\mathrm{}\Psi 〉$ of a positive semidefinite operator $F$. These extended formulas, which involve an additional variational function, always lead to an improvement over the results previously obtained. The improvement is illustrated numerically with an application to various properties of the helium-atom ground state.

A simple theory of high-energy neutron scattering from liquid ${\mathrm{He}}^4$ is developed. The inelastic scattering cross section for this process is related, for sufficiently high momentum transfer, to two parameters characterizing the ${\mathrm{He}}^4$ momentum distribution. These two parameters are the average kinetic energy per particle and the fraction of particles in the zero-momentum condensate. Comparison of the theory with recent experimental data indicates that the condensate fraction $\frac{{\rho }_0}{\rho }$ is approximately 0.06 at $T=1.27\mathrm{}°$K.

A unified theory of spin-lattice relaxation in solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is developed by starting from the complete Hamiltonian of the system. The "three-bath model" for the system is presented, and rate equations are derived for relaxation among the baths. A new mechanism for relaxation of exchange energy, viz., the modulation of dipole-dipole interaction by diffusion and by exchange itself, is identified and its relation to other processes derived. By inclusion of this mechanism and the simultaneous consideration of the three baths, the rate equations can be cast in the form that was written down phenomenologically in earlier work by considering the three baths in series. It is shown, however, that if the new mechanism is included in the customary sense in the phenomenological equations, it is not possible to explain the experimental results. A critique of the existing theory of relaxation due to off-diagnoal elements of the exchange operator is given, and an alternative theory presented. Finally, we give an interpretation of the experimental results on the basis of the theory.