The behavior of negative ions in superfluid helium at high electric fields has been investigated. It is concluded that at sufficiently high fields the negative-ion complex is not an electron trapped on a circular, singly quantized vortex ring. The size of the complex is measured and found to be about 35 μm. The ion complex is observed to break up at very high fields.

A theory of a ring laser subject to a uniform, axial dc magnetic field is given in extension of the two-mirror standing-wave treatment by Sargent, Lamb, and Fork. The active medium consists of thermally moving atoms that have two electronic levels with arbitrary angular momenta. The electric field is treated classically for two circular polarizations of opposite sense in a cavity with any degree of cavity anisotropy. Losses due to backscattering are also included. In addition, the results of a generalized treatment are given which includes arbitrarily oriented magnetic field, a general state of electric field polarization, varying isotopic abundance, and hyperfine structure. The self-consistency requirement is used to obtain amplitude- and frequency-determining equations for multimode operation as functions of laser parameters. A general calculational technique, the "perturbation tree," is introduced in the calculation of the third-order component of the population matrix, greatly simplifying the algebra involved by allowing it to be abstracted in tabular form.

Expressions derived from a rotational Fokker-Planck equation based on a Langevin model are employed to calculate the nuclear magnetic relaxation rates in spherical molecules which result from intramolecular dipole-dipole interactions, spin-rotational interactions, and quadrupole interactions. The results for the Langevin model are compared with results calculated by use of a rotational-diffusion equation, results calculated by use of the $J$-diffusion model, and experimental results for liquid C${\mathrm{Cl}}_4$ and liquid Cl${\mathrm{O}}_3$F. The relation between the correlation time for dipole-dipole and quadrupole interactions and the correlation time for spin-rotational interactions calculated from the Langevin model agrees better with the experimental results than does the relation calculated from the rotational-diffusion equation, but not quite as well as does the relation calculated from the $J$-diffusion model.

Polarized positive muons are stopped in solutions in magnetic fields transverse to their polarization. Positrons from the asymmetric decay are detected as the muons precess, allowing measurement of the magnitude and direction (phase) of the apparent initial polarization $P_{\mathrm{res}}$. Variations of $P_{\mathrm{res}}$ with reagent concentration are compared with theoretical predictions. Measurement of both magnitude and phase of $P_{\mathrm{res}}$ allows sensitive tests of the mechanism of "fast" ${\mu }^{+}$ depolarization. Evidence is found for both epithermal "hot-atom" reactions and chemical reactions of muonium involving formation of rapidly reacting radicals. Chemical rate constants are extracted and compared with rates for analogous reactions of atomic hydrogen.

By expanding the atomic density matrix in powers of the light intensity, it is possible to derive simple formulas for the light shifts and optical broadening of magnetic-resonance lines in optical pumping experiments. Thus, we have obtained for the first time approximate analytic formulas for the light shifts in Zeeman multiplets with spins greater than 1/2. The predicted light shifts for a high-spin atom are similar to those for a spin-1/2 atom, and shifts due to real and virtual transitions can be identified. However, in contrast to the situation with a spin-1/2 atom, the light shifts for a high-spin atom depend on the magnitude of the rf field, and the shifts for the longitudinal and transverse components of orientation and alignment are not necessarily the same.

A variational method is used to obtain solutions to Schrödinger's equation for a particle in a static screened Coulomb potential. Energy eigenvalues are obtained for the lowest 45 states. The analytic wave functions generated by this method are used to obtain the probabilities for spontaneous emission in the dipole approximation as a function of screening length, for transitions between the six lowest states.

A free-path model is set forth for the phenomenon discovered by Scott whereby a gas exerts a torque on a heated cylinder when the gas is subjected to a magnetic field parallel to the cylinder axis. The model is particularly applicable to the phenomenon of torque resonance found by Smith and Scott when they modulated the magnetic field. The free-path model is not intended to compete with Chapman-Enskog-type theory in providing a precise description of the Scott effect, but is intended rather as an aid to physical intuition. Within the limits of its purpose, the model appears to be quite successful. Namely, it provides an intuitive picture of why there is a torque and it enables one to understand how the resonances come about. Moreover, it gives the same formula for torque resonance as do the systematic treatments. The model has an interesting sidelight: In its simple form the model yields Lorentzian-type resonances with molecular speed as a parameter. When the speed is averaged over a typical distribution, the Lorentzian resonances are converted into functions of similar shape involving the incomplete $\Gamma$ function. These latter functions seem to be natural generalizations of the Lorentzian.

A class of quasiclassical adiabatic approximations is described that enables upper bounds to be determined for the partition function of a system and, hence, lower bounds for its Helmholtz function. Based upon a neglect of the lack of commutativity of selected observables with others, these adiabatic approximations become exact in classical statistical mechanics. The effects of carrying out sequences of such adiabatic approximations and of relaxing intrinsic exchange-symmetry restrictions is to produce additional upper-bound expressions for the partition function. The lower-bound property of the adiabatically approximated Helmholtz function provides an alternative proof of the inequality that relates the lowest-energy eigenvalue of a system and that given by the Born-Oppenheimer approximation, as well as improvements of it.

The Dicke theory of coherent spontaneous emission is generalized by means of group-theoretical methods. Effects of superradiation and the structure of coherent responses of an equilibrium medium to pulsed excitation are considered. A method of calculating cooperative effects in second-order perturbation theory is developed. The role of collective properties of a system of radiators in experiments with high power exciting radiation is discussed. Some "anomalous" features of stimulated Raman scattering are accounted for.

The effect of the earth's gravity on light scattering from a simple fluid near its critical point is investigated. It is found that, in general, gravity influences the angular distribution of the scattered irradiance in three ways. First, the forward scattering at the critical point does not diverge. Second, the irradiance in any but the forward direction is not greatest at the critical temperature, but slightly above it. Third, Ornstein-Zernike-Debye plots of the inverse irradiance versus the square of the wave number are concave downward at small scattering angles. This last feature is usually attributed to a nonvanishing of the critical exponent $\eta$ and thus indicates that the experimental evidence for this conjecture is misleading. Computations are peformed using an approximate equation of state to exhibit these deviations from the traditional Ornstein-Zernike theory.

The time-displaced self-correlation function for a one-dimensional hard-core fluid with independent stochastic forces acting on each core is solved exactly and concisely. At long time, the distribution has a spread given by $\delta x\left(t\right)={\left[\frac{R\left(t\right)\mathrm{}}{n}\right]}^{\frac{1}{2}}$, where $R\left(t\right)\mathrm{}$ is the absolute dispersion in position of a noninteracting particle and $n$ the free-volume reduced density. The diffusional behavior without stochastic background, and non-Fickian diffusion of Levitt with Brownian background, are reproduced.

When the approximation of overlapping momenta, in calculating the phonon and roton contributions to the thermodynamic properties of liquid helium II, is removed and the resulting expression for the specific heat of the system is fitted to experimental data at low temperatures, seemingly improved values of the phonon dispersion coefficient $\gamma$ are obtained. At saturated vapor pressure, $\gamma$ turns out to be — 5.6 × ${10}^{37}$ cgs units, which is in excellent agreement with the value resulting from x-ray-scattering measurements. Comparison with neutron-scattering data suggests that $\gamma$ may be strongly temperature dependent.

A general first-order formula is derived for the Fresnel-drag effect in a uniformly moving medium with a plane surface. The two classical equations due to Lorentz and Laub are shown to be special cases corresponding to different experimental arrangements. The recent experiment of Bilger and Zavodny on Fresnel drag in a ring laser is discussed.

The lifetime of the ${}_{}{}^5{}_{}{}^{}S_{}^{\circ }{}_{}{}^{}$ state of atomic oxygen has been measured as $\tau =170\mathrm{}\pm 25$ μsec.

Metastable $K$-x-ray emitters produced in foil excitation of chlorine beams between 23 and 55 MeV have been observed and their production probabilities surveyed over this energy range. Using coincidence techniques, we find that the emitters belong primarily to the helium- and lithiumlike components in the post-foil beam. A search for x-ray emission from systems with more than three electrons has been made and is discussed. The major emitting states have been identified as the $\left(1s2p\right){}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ and $\left(1s2s2p\right){}_{}{}^4{}_{}{}^{}P_{\frac{5}{2}}^{}{}_{}{}^{}$ states in helium- and lithiumlike chlorine whose radiative decay is magnetic quadrupole. Using both coincidence techniques and a doppler-tuned x-ray spectrometer, we have measured the lifetimes and binding energies of these states. The lifetime of the $2{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ state is in good agreement with theory, while the binding energies show the importance of relativistic contributions in the theory. A long-lived component of the excited beam is identified as coming from the $1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\leftarrow 2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ decay. A lifetime of 280 ± 25 nsec has been measured for this state, shorter than the theoretical $M1\mathrm{}$ lifetime of 381 nsec.

The interpretation of straggling experiments in thin absorbers is examined. It is made plausible that the Landau-type solutions of the transport equation are invalid for very thin absorbers. Another solution of the problem is presented. It is shown that the customarily assumed form of the atomic-structure correction for the straggling parameter is incorrect. Finally, various effects influencing the relation between energy lost by the charged particles and the ionization observed in the absorber material are enumerated.

The quenching of the $\nu =0\mathrm{} C{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ metastable state of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ by a static electric field has been measured using the time-of-flight technique. Neutral ground-state molecules effusing from a source slit are immediately excited to the $C{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ metastable state by a pulse of antiparallel magnetically focused electrons. After passing through a uniform electric field region 0.5 m long, the velocity distribution of this thermal beam of metastable molecules is then preferentially detected at the end of the time-of-flight region, 1.825 m from the electron gun. The number of $C{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ molecules arriving at the detector in specific velocity intervals with the electric field off is compared to the number with the field on, to determine the quenching rate ($=k{E}^2$). The result for the quenching constant $k$ is the same for both para- and ortho-${\mathrm{H}}_2$, as well as for ${\mathrm{D}}_2$, and with $E$ in kV/cm is $k=8.6\mathrm{}\pm 0.3$.

The electric and magnetic fields of a point charge moving with constant velocity outside and parallel to a conducting wall of finite conductivity are studied within classical electrodynamics for a nonrelativistic particle and a good conductor. Results are obtained through first order in the particle velocity for a wall with permeability $\mu =1\mathrm{}$, dielectric constant $\epsilon =1\mathrm{}$, and resistivity $\eta$. Calculations show the following: (i) There is no skin-depth behavior for the fields $\overrightarrow{E}$ or $\overrightarrow{B}$ or for the currents $\overrightarrow{\mathrm{J}}$ inside the conductor. (ii) The fields $\overrightarrow{B}$ and $\overrightarrow{E}$ fall off with distance as $r^{-2\mathrm{}}$ and $r^{-3\mathrm{}}$, respectively, inside the conductor. (iii) The magnetic field $\overrightarrow{B}$ and the current density $\overrightarrow{\mathrm{J}}$ inside the conductor are independent of the resistivity $\eta$, although the electric field $\overrightarrow{E}$ inside the conductor is suppressed by a factor of $\eta$. (iv) In the limit of many point charges moving so as to form a steady current outside the conductor, the magnetic field $\overrightarrow{B}$ penetrates the conductor as though it were not present while the electric field $\overrightarrow{E}$ and current density $\overrightarrow{\mathrm{J}}$ vanish inside the conductor. The results obtained here are quite different from those of the familiar calculations involving radiation fields where the penetration depth and the size of the fields inside the conductor are governed by the resistivity. The new results run contrary to the expectations of some physicists and contradict some earlier work in the literature. The calculations arose in connection with the Aharonov-Bohm effect where electrons moving with approximately constant velocity pass very close to a conducting solenoid.

We have measured the lifetime of the ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ metastable state of Mg and obtained a value of 2.2 ± 0.2 msec. The level was excited with a dye laser tuned to the intercombination line ($3s3p{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\leftrightarrow 3s^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$). In addition to the ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ state, the ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ levels were populated by mixing collisions owing to the presence of an inert buffer gas. The populations of all three metastable levels were monitored as a function of time by observing the absorption of Mg resonance radiation (${}_{}{}^3{}_{}{}^{}P_{0,1,2}^{}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$) out of each level. The mixing time was short compared to the ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ lifetime, so that the populations of the three metastable levels were in thermal equilibrium with each other. This produced an apparent lengthening of the ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ lifetime, which would introduce a large systematic error if the degree of mixing were not known. Cenventionally, one observes the fluorescence from the excited levels to obtain their lifetimes. Because the lifetimes of the ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ states are too long, fluorescence from these states cannot be observed, and the observation of fluorescence from the ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ state alone provides insufficient information to determine its lifetime.