Two mutual friction numbers are derived for superfluid helium which can describe the onset of turbulence in counterflowing helium. The numbers are $M_n=\frac{A{\rho }_s{\rho }_n{〈{\overrightarrow{\mathrm{V}}}_r〉}^3{d}^2}{{\eta }_n〈{\overrightarrow{\mathrm{V}}}_n〉}$ and $M_s=\frac{A{\rho }_s{\rho }_n{〈{\overrightarrow{\mathrm{V}}}_r〉}^3{d}^2}{{\eta }_n〈{\overrightarrow{\mathrm{V}}}_s〉}$, where $M_n$ predicts the onset of turbulence in the normal fluid and $M_s$ predicts the onset of turbulence in the superfluid. Staas, Taconis, and van Alphen's Reynolds number is found to apply only to flow conditions for which ${\overrightarrow{\mathrm{V}}}_n\simeq {\overrightarrow{\mathrm{V}}}_s$.

When describing the behavior of a multimode laser, it sometimes is convenient to express the cavity field in terms of an evolving wave packet that is reflected by the mirrors. We consider here the general relation between the normal-mode description of the field, where mode amplitudes and frequencies characterize the oscillations, and features of the corresponding wave packet. It is shown that in this problem it is natural to represent a packet as a linear superposition of monochromatic waves, integrating over wave number $k$. To illustrate some of the concepts, an example is treated that relates packet parameters to parameters of a theoretical model for the laser medium.

The drift-tube photodetachment technique was used to measure the absolute photodetachment cross section, and the solar photodetachment rate of ${\mathrm{O}}_3^{-}$. The energy dependence of the cross section $\sigma$ was measured with the use of 18 color filters. By fitting the data with a least-squares program, we found that $\sigma =\left[\alpha \mathrm{}\right(E-3.0\mathrm{})+\beta ]H(E-E_0)$, where $\alpha =(5.6\mathrm{}\pm 1.7)\times {10}^{-19\mathrm{}}$ ${\mathrm{cm}}^2$/eV, $\beta =(8.7\mathrm{}\pm 1.6)\times {10}^{-19\mathrm{}}$ ${\mathrm{cm}}^2$, $E_0=1.99\mathrm{}\pm 0.10$ eV. $E_0$ is the threshold energy and $H$ is the Heaviside step function. The solar photodetachment rate was 0.082±0.015 ${\sec }^{-1\mathrm{}}$. The ${\mathrm{O}}_3^{-}$ ions were identified by mobility.

The basic formalism and mathematical techniques required for a Green's-function theory of transport phenomena are presented, and it is shown that features of divergences that appear in conventional theories of transport can be treated by a much more systematic process, in a relatively natural manner.

The time dependence of the ${\mathrm{Ne}}^{+}$ ion density was measured during the decay period of plasmas produced in neon for reduced gas pressures varying from 0.33 to 7.6 Torr and a gas temperature of 300 °K. The reaction rate constant for the termolecular ion-neutral association reaction ${\mathrm{Ne}}^{+}$ + 2Ne→${\mathrm{Ne}}_2^{+}$ + Ne was found to be $k=(4.4\mathrm{}\pm 0.4)\times {10}^{-32\mathrm{}}$ ${\mathrm{cm}}^6$ ${\sec }^{-1\mathrm{}}$. The value of the mobility of ${\mathrm{Ne}}^{+}$ in neon was confirmed to be $\mu \left({\mathrm{Ne}}^{+}\right)=(4.0\mathrm{}\pm 0.1)$ ${\mathrm{cm}}^2$ ${\sec }^{-1\mathrm{}}$. At gas pressures smaller than about 1.7 Torr the phenomenon of diffusion cooling was observed.

Low-frequency signals on a grid in a cylindrical plasma column excite both ion acoustic and guided electron plasma waves. Experiments are described which show that the latter provide the dominant asymptotic response. Measurements of phase velocities and excitation levels are consistent with theoretical predictions.

Self-diffusion by a particle-vacancy exchange mechanism is investigated in solid hydrogen and deuterium. The calculations are based on our quantum-crystal formalism published previously. The self-diffusion coefficient is calculated as a function of temperature, and the results compared with values inferred from nuclear-magnetic-resonance measurements; agreement of theory and experiment appears to be satisfactory. The effect of pressure on diffusion is also considered.

Recently, several authors have contended that the pair-correlation function for a simple liquid asympototically goes to zero in a way proportional to the two-particle potential. We critically examine the basis of their assertion and find that the conclusion is unfounded. Existing x-ray and neutron-diffraction data on liquids are inconclusive insofar as the asymptotic form of the pair correlation is concerned. We propose an experiment which may shed some light upon the large-$r$ behavior of this important quantity.

Simple features of transverse waves in a Bose system are illustrated from a purely microscopic viewpoint. Taking advantage of an integral equation obtained previously in the microscopic theory of second sound, we examine the transverse-current response function in the weak-coupling and low-temperature limit. The dispersion curve for the transverse waves in this limit is evaluated exactly.

Calculated potentials for the NaHe molecule are used to obtain collision-induced widths and shifts for the sodium $D$ lines together with cross sections for fine-structure transitions and the relaxation of the multipole polarizations of the resonance levels. The atomic collision is treated in an adiabatic approximation in which the colliding atoms form a molecular system which rotates during the collision. We find the resonance lines to be broadened equally and to be approximately 70% wider, and with associated shifts of an order of magnitude smaller, than expected on the basis of van der Waals forces. The dependence of the cross sections for relaxation of the multipole polarizations of the resonance levels on the molecular-coupling conditions and the rotation of the system during collision is discussed and indicates a limitation on the sum rule for these cross sections. Good over-all agreement with the existing experimental data is obtained.

Previous Monte Carlo computations of ground-state properties of solid helium using a correlated trial wave function are extended in several directions. A generalized wave function which includes a simple model for "phonon" correlations is tested; no significant lowering of ground-state energies is obtained. Detailed results for bcc ${\mathrm{He}}^3$ and hcp ${\mathrm{He}}^4$ are tabulated in the low-density region. The extension of the variational computations to considerably higher densities (10 ${\mathrm{cm}}^3$/mole) stresses the need for inclusion of short-range correlations over a wide density range and clearly reveals the inadequacy of the commonly used Lennard-Jones 12-6 potential with the de Boer parameters. Various other recently proposed interaction potentials are investigated in conjunction with known three-body forces. Reasonable agreement with experimental energies, pressures, and compressibilities follows from the use of a potential due to Beck. The relation between the melting properties of helium and two "hard-core" models is discussed and the possibility of Bose-Einstein condensation in the solid is investigated in conjunction with a theorem due to Reatto.

It is shown that measurements of dc currents due to charges passing from a region of high dielectric constant to a region of low dielectric constant contain information on the lifetime for escape over the induced potential barrier associated with the interface. It is also shown that no additional mechanism, other than the induced potential barrier, need be invoked to explain the saturation of the current at high temperatures observed in recent experiments in liquid helium. The analysis can be further generalized to cover more complicated systems.

The interaction of microwaves with a traveling refractive-index change generated by ultra-short laser pulses in liquids which exhibit a strong orientational Kerr effect is analyzed using two different approaches. The index change is treated in the first approach as a polarization source for parametric generation with the microwaves and in the second approach as a fastmoving dielectric mirror reflecting the microwaves. Under certain assumptions a phase-matching condition can be satisfied and the phase-matched direction coincides with the direction the reflected wave propagates. The output waves calculated from the two descriptions are consistent with each other. In this context the large frequency shift that can be realized in the reflected wave can be explained as being supplied by the beating of two laser photons in the liquid. The choice of appropriate experimental parameters is discussed and a simple sketch of possible experimental arrangements is given.

An error in an earlier paper [Phys. Rev. 124, 983 (1961)] is corrected. This error occurred in the derivation of nonlinear transport equations from a generalized Fokker-Planck equation, and took the form of neglecting certain fluctuations. When these are accounted for, the resulting transport equations contain fluctuation-renormalized transport coefficients.

The relativistic correction to the hyperfine-structure splitting of the metastable $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ state of ${\mathrm{He}}^3$, first calculated by Sessler and Foley to be 315 ± 3 ppm, is reevaluated as ${\Delta }_{\mathrm{rel}}=327\mathrm{}\pm 3$ ppm. Using this new value, the theoretical ratio of the hyperfine splitting in the $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ state of ${\mathrm{He}}^3$ to the hyperfine splitting in the $2{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ state of ${\mathrm{He}}^{3+}$ becomes ${\rho }_{\mathrm{th}}=6.221\mathrm{}1911\pm 0.0000187$ The experimental value for the ratio is 6.221 1384±0.000 0012, and the 8±3 ppm discrepancy is presently unexplained.

Self-consistent-field calculations by the expansion method, and the calculation of dimagnetic susceptibility, were carried out for the negative ion ${\mathrm{I}}^{-}$, ($Z=53\mathrm{}$), $5s^{2}5p^6$, ${}_{}{}^1{}_{}{}^{}S$. The results are the most accurate available. Also, we calculated the electronic affinity of atomic iodine, which agrees with the value determined by experiments to two significant figures. In general, this work presents additional information to our previous publications on heavy-atom systems.

The lifetime of the $2p^{3}3s{}_{}{}^5{}_{}{}^{}S$ metastable state of oxygen has been measured using the time-of-flight technique. The velocity distribution of metastable atoms resulting from the dissociation of excited oxygen molecules is sampled and detected at two positions, 1.8 and 6.6 m from the pulsed electron gun used to bombard the ground-state molecules effusing from a source slit. A comparison of the number of metastables within specific velocity intervals at the two detectors determines the number which decay in flight and yields an experimental plot of the number which decay vs time of flight. The lifetime $\tau$ is then obtained from the slope ($=-\frac{1}{\tau }$) of a straight line least-squares fitted to the decay plot. The result is $\tau =185\mathrm{}\pm 10$ μsec.

The separable approximation for the correlation function proposed by Mittleman is critically examined. It is shown that this assumption is generally inconsistent with the properties of the correlation function and that it is unnecessary for reducing the elastic scattering to a pair of coupled Schrödinger equations. The resulting pair of coupled equations is explicitly given and its validity is investigated.

By analyzing all existing frequency data of the oxygen molecule in microwave, submillimeter, and infrared spectroscopy, a new set of values for molecular parameters is obtained. Our values are $B_0=43.100\mathrm{}518$, $B_1=-1.44962\mathrm{}\times {10}^{-4\mathrm{}}$, $B_2=-1.57\mathrm{}\times {10}^{-10\mathrm{}}$, ${\lambda }_0=59.501342\mathrm{}$, ${\lambda }_1=5.847\mathrm{}\times {10}^{-5\mathrm{}}$, ${\mu }_0=-0.252\mathrm{}586$, and ${\mu }_1=-2.464\mathrm{}\times {10}^{-7\mathrm{}}$ in GHz.