Formation of an intense beam of hydrogen atoms in the metastable $2s$ state is not only of basic interest, but is also useful for polarized-ion sources of the Lamb-shift type. The nearly resonant reaction ${\mathrm{H}}^{+}+\mathrm{Cs}\to \mathrm{H}\mathrm{}\left(2s\right)+{\mathrm{Cs}}^2$ is often used for this purpose. The fraction $f$ of metastable atoms relative to the number of neutral atoms in all $n=2\mathrm{}$ states formed in the collision of a proton in a thin Cs-vapor target is reported here for the energy range 0.4-3.0 keV. An apparent maximum of $f=0.43\mathrm{}\pm 0.03$ at 0.5 keV is found. For energies above 0.75 keV, $f=0.25\mathrm{}\pm 0.01$, which would be expected if the $n=2\mathrm{}$ states of H are statistically populated. Previously reported values for ${\sigma }_{+m}$, the cross section for electron pickup in the metastable $2s$ state of hydrogen for ${\mathrm{H}}^{+}$ + Cs collisions, differ by two orders of magnitude for a given energy. It can be assumed that essentially all electron pickup is into the $n=2\mathrm{}$ states at low energy. Thus measured values of $f$ can be multiplied by reported values of ${\sigma }_{+0\mathrm{}}$, the cross section for electron pickup into any neutral state of the H atom, to find values for ${\sigma }_{+m}$. As this method is independent of calibration or normalization of the photon measurements, these values for ${\sigma }_{+m}$ are more reliable than those previously reported. Our results for ${\sigma }_{+m}$ are between 4.3×${10}^{-15\mathrm{}}$ and 1.5×${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ in the energy range 0.5-3.0 keV.

The long-time behavior of a two-dimensional crystal of identical atoms is studied numerically with particular reference to the equipartition of energy among its normal modes. The system is found to have a stochastic behavior when the energy per degree of freedom is sufficiently great. This stochastic limit is found to be well below the corresponding one-dimensional value.

This paer is concerned with the spontaneous-emision rate of two two-level atoms which have different resonance frequencies and whose spatial separation is much smaller than the corresponding mean resonance wavelength. The total radiation rate of such an atom pair is calculated completely quantum mechanically as a function of time. Explicit results are given for various values of the frequeny difference and the following initial states of the atomic system: (a) both atoms in the excited state, (b) one taom in the excited state the other in the ground state, (c) a symmetric combination of those states, (d) an antisymmetric combination of those states, and product states where each atom is in an equal superposition of its ground and excited states, for which the expectation values of the dipole moments are nonzero and may be considered to be osicillating (e) in phase, (f) in opposite phae, and (g) in random phase. Oscillations are found to appear in the radiation rate in all cases when the frequency difference becomes larger than a certain critical value, viz., the mean half-width of the atomic resonance lines. The oscillations are especially pronounced for the initial atomic states (c), (d), (e), and (f), which exhibit superradiance and radiation trapping. For example, for atoms in the antisymmetric state (d), for which the radiation from two identical atoms is zero (completely self-trapped), a pair of nonidentical atoms begins radiating and even oscillates into the superradiant region at times.

The effect of persistent correlations on self-diffusion in a dilute gas, and on Brownian motion, is discussed. It is found in both cases that the second-order diffusion constant is infinite. The distribution function for displacements is calculated, and is found to be more sharply peaked than the usual Gaussian, although the difference is quite small.

The Compton cooling of a photon gas is studied using the Compton-Fokker-Planck equation. Numerical solutions of the Fokker-Planck equation are presented which illustrate the possibility of forming a temporary excess of low-energy photons. The conditions under which it would be possible to observe this excess of low-energy photons are derived. The possibility of using stimulated Compton scattering to generate coherent x rays is also discussed.

The onset temperature $T_0\mathrm{}\left(P\right)\mathrm{}$ for superfluidity of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ has been measured in $d=0.1\mathrm{}-, 0.2-, 0.4-, \mathrm{and} 0.6-\mu m$ wide channels at pressures between saturated vapor pressure and the melting curve. The onset was detected by observing the vanishing of second sound in resonators equipped with superleak transducers. In the channels used the onset temperature $T_0\mathrm{}\left(P\right)\mathrm{}$ was depressed below the bulk transition temperature $T_{\lambda }\mathrm{}\left(P\right)\mathrm{}$ by $2\times {10}^{-5\mathrm{}}\le {\epsilon }_0\le 2\times {10}^{-4\mathrm{}}$. Here ${\epsilon }_0=1-\frac{T_0\mathrm{}\left(P\right)\mathrm{}}{T_{\lambda }\mathrm{}\left(P\right)\mathrm{}}$. For constant $d$, we find that ${\epsilon }_0$ is independent of pressure to within our resolution of ±2%. From the data the exponent ${\lambda }^{\prime }$ and the coefficient $d^{*}$ for the equation ${\epsilon }_0={\left(\frac{d}{d^{*}}\right)}^{-{\lambda }^{\prime }}$, and the exponent and coefficient for the correlation length, $\xi ={\xi }^{*}{\epsilon }^{-{\nu }^{\prime }}$, have been calculated. We show that ${\lambda }^{\prime }$ and $d^{*}$, as well as ${\nu }^{\prime }$ and ${\xi }^{*}$, and the quantity $\frac{\xi {\rho }_s}{T}=(0.16\mathrm{}\pm 0.01)\times {10}^{-8\mathrm{}}$ are independent of pressure, within our resolution of ±2%. The lack of a pressure dependence of the critical exponents is in agreement with universality arguments. For the absolute values we find $\xi =(1.2\mathrm{}\pm 0.1)\times {10}^{-8\mathrm{}}{\epsilon }^{-0.65\mathrm{}\pm 0.02}$, ${\epsilon }_0={\left[\frac{d}{(5.7\mathrm{}\pm 0.6)\times {10}^{-8\mathrm{}}}\right]}^{-1.54\mathrm{}\pm 0.05}$, and $\frac{\xi {\rho }_s}{T}=(0.16\mathrm{}\pm 0.01)\times {10}^{-8\mathrm{}}$.

Electrons trapped on the surface of liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ by the image potential can escape into the gas by thermal ionization. We have calculated the rate of ionization on the assumption that the electrons are strongly coupled to each other and weakly coupled to the liquid and gas. The first electrons to leave the surface extract their ionization energy from the kinetic energy of the electrons that remain behind. This adiabatic cooling effect rapidly lowers the electron temperature to a small fraction of the temperature of the surrounding gas and liquid. Above about 1.2 K gas-atom collisions determine the ionization rate and below 1 K it is determined by ripplon scattering. It is only for temperatures below 1 K that the lifetime measurement can be used to determine the surface-state binding energy.

The dependence of the self-generated magnetic fields associated with a laser-produced plasma on position, time, incident laser power, and nitrogen background pressure has been investigated. The presence of the ambient background is found to influence the generation of the fields during the laser irradiation of the plasma. This influence continues long after laser shutoff and causes the fields to reverse their direction.

The superfluid helium film flow rate and the film profile (thickness versus height) on polished stainless steel have been measured in the same series of experiments down to 0.03 K. The concentration of ${\mathrm{He}}^3$ was varied from that of nominally "pure" ${\mathrm{He}}^4$ (∼ 0.2 ppm) to 0.44% ${\mathrm{He}}^3$. The film profile was measured below 0.7 K by observing isothermal flow oscillations. Apart from a small hysteresis effect, it agrees with the simple Frenkel-Schiff theory using the van der Waals potential calculated from the Lifshitz equation. In agreement with theory the profile is not changed by small concentrations of ${\mathrm{He}}^3$ (up to a few hundred ppm) which, however, significantly decrease the superfluid flow rate below 1 K. The effect of the ${\mathrm{He}}^3$ on the flow rate is most striking below 0.5 K, where surface-tension measurements have shown that the ${\mathrm{He}}^3$ is partially adsorbed on the surface of the ${\mathrm{He}}^4$, lowering the surface tension. In this region the flow rate is observed to be approximately proportional to the square root of the surface tension, as predicted by Arkhipov. With a larger amount of ${\mathrm{He}}^3$ (0.44%) the flow rate below 0.1 K increases quite rapidly with decreasing temperature. The increase is apparently connected with the beginning of Fermi degeneracy in the ${\mathrm{He}}^3$ dissolved in the film. Some observations of the flow rate for very small level differences are also reported.

In a previous paper, I have presented a general theory of the optical pumping of atoms by a polarized multimode-laser beam, in the presence of a magnetic field. Equations of motion, valid at arbitrary laser intensities for the density matrix of the atomic system, have been obtained. In this paper, these equations are exactly solved for a linearly $\sigma$-polarized laser and levels having small angular momenta. More precisely, I consider the laser transitions $J_b=1\mathrm{}\to J_a=0\mathrm{}$, $J_b=1\mathrm{}\to J_a=1\mathrm{}$, and $J_b=1\mathrm{}\to J_a=2\mathrm{}$. Two particular results are emphasized: (i) For $J=1\mathrm{}-J=0\mathrm{}$ and $J=1\mathrm{}-J=1\mathrm{}$ transitions and for the $J=2\mathrm{}$ level of a $J=1\mathrm{}-J=2\mathrm{}$ transition, the laser-induced Hanle effects keep a Lorentzian shape, independent of the laser intensity. For the $J=1\mathrm{}-J=1\mathrm{}$ transition, it is shown that the depolarizing relaxation processes play a leading part in the coupling induced by the laser between the transverse alignments of the two levels. On the other hand, the power broadenings of the Hanle effects are shown to be similar. For the $J=1\mathrm{}$ level of a $J=1\mathrm{}-J=2\mathrm{}$ transition, the Hanle-effect shape presents a departure from the Lorentzian one, owing to a coupling with the laser-induced hexadecapole moment in the $J=2\mathrm{}$ level. (ii) The populations of the levels exhibit a "zero-field saturation resonance" which is due to the coupling with the Zeeman coherences. These resonances, which reproduce the Hanle effects of the transition, can be observed on the $\pi$-polarized fluorescence from the levels. In general, these resonances appear as a saturation effect, i.e., they reduce the laser-induced fluorescence of the levels in zero magnetic field. However, for the $J_b=1\mathrm{}\to J_a=2\mathrm{}$ transition, the $J_a=2\mathrm{}\to J_f=2\mathrm{} \pi$ fluorescence presents an anomalous behavior; the saturation resonance increases the zero-field laser-induced fluorescence. The theoretical study shows the prominent part played by the value of the $J_b=1\mathrm{}$ level lifetime in the interpretation of this anomaly. Other results, such as the laser-induced depolarization of the fluorescence, are also obtained. All the theoretical predictions have been experimentally checked and will be presented in forthcoming papers.

In this paper we derive master equations for two or more systems coupled to each other, perhaps strongly, by using a generalization of the usual projection-operator technique to include time-dependent projection operators. The coupled systems may be either similar or dissimilar and classical or quantum mechanical. Whereas the customary approaches to coupled systems are best able to treat situations in which some of the systems are "baths" with a specified density operator or phase-space probability density, our approach allows us to treat situations where it is necessary or convenient to treat the coupled systems on an equal footing. In our scheme the "relevant" part of the full density operator is considered to be the uncorrelated part of the full density operator and is a symmetric functional of the reduced density operators of each of the coupled subsystems. The "irrelevant" part of the density operator is then the part describing correlations between the coupled systems. Our formalism is particularly useful where systems are coupled to one another predominantly in a self-consistent fashion. First, we develop exact master equations for two coupled systems, taking as our prototype the dynamical problem of quantum optics, where a spatially extended collection of two-level atoms interact with a multimode optical field. We then generalize our results to $N$ coupled systems, taking as our prototype the kinetics of a classical nonideal gas interacting through two-body forces, and derive exact master equations for the system. We then consider as examples several approximate theories resulting from our exact equations. In the case of the imperfect gas we investigate the low-density limit and show how Bogoliubov's form of the Boltzmann equation emerges from our formalism, as well as corrections due to Klimontovich. We consider as special cases of our exact quantum-optical equations the equations in the first Born approximation, with and without memory, and show how several existing quantum-optical master equations are contained in our general results. As a second example in quantum optics, we consider the case where the predominant behavior of the system is described by the self-consistent-field or coupled Bloch and Maxwell equations and derive a first-order perturbation description for deviations from self-consistent-field behavior.

The system of nonergodic hard parallel squares (HPS) appears to be the first nontrivial model for noncentral molecular interactions which seems to bypass the hydrodynamic stage in reaching a final non-Maxwellian velocity distribution. Nevertheless, HPS exhibit the molecular correlations not unlike those exhibited by more conventional ergodic systems. Here we present the initial and the final velocity distributions of Carlier and Frisch and compare the final numerical velocity distribution to an analytic expression obtained as the final stationary distribution from a Boltzmann equation for this system. We find agreement to within 5% for the computed and the calculated results. The Einstein diffusion coefficient and other transport coefficients are calculated for HPS and compared to the results for hard discs. We find that the final velocity distribution depends strongly on the initial distribution. We show that if initially a Maxwellian velocity distribution were selected, the distribution will remain Maxwellian.

The information-theoretic formulation of statistical mechanics is applied to an ideal gas transporting energy without transporting mass. It is shown that the thermal state variables fracture into distinct populations, thus exhibiting a radical sort of local nonequilibrium. The partition function is found in exact form, for an arbitrarily large temperature gradient. In an approximation, it is shown that these results reduce to the known ones for equilibrium, and near equilibrium. The same approximation allows us specific equations for the temperature, pressure tensor, and the entropy of the system, in a far-from-equilibrium case, in terms of the new thermal variables of the system. The general entropy functional, and its variation, are discussed.

A study of the influence of a nonlinear viscoelastic medium upon the frequency of cooperative modes in such a medium is presented. The form of the stress tensor is derived by using the well-known Rivlin-Green techniques and the corrected dispersion relations are derived by an application of a perturbation technique upon the set of linearized hydrodynamic equations and a nonlinear viscoelastic stress tensor. The results are applied to glycerol and the possible effects of nonlinearities displayed.

The perturbation technique developed in paper I of this series has been suitably modified for the treatment of the propagation vectors of cooperative modes, rather than their frequencies. The method has been applied to the problem of sonic absorption and propagation in a nonlinear viscoelastic medium. The results show departure from the results predicted by the linear theory.

The self-trapping of light pulses is considered using the classical nonlinear wave equation of Chiao, Garmire, and Townes, modified to include nonlinearities up to sixth order in electric field. A phenomenological approach is adopted in which the nonlinear coefficients are considered without reference to a specific molecular self-trapping mechanism. It is found that filament formation can occur only over a narrow range of values of the nonlinear coefficients. The method can be used as a criterion to test the validity of various self-trapping mechanisms.

The energy spectrum of elementary excitations in liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is studied in the long-wavelength limit by means of the Brillouin-Wigner (BW) perturbation theory for two-phonon processes. Calculation of an additional second-order BW energy correction to the Bijl-Feynman excitation spectrum is carried out by considering contributions from the leading correction to the convolution approximation for the three-particle distribution function. The resulting correction is found to be positive and about 7.9% of the second-order perturbation energy obtained previously with the convolution approximation.

The Propagation of second-sound waves in superfluid helium is considered for temperatures below 0.6 °K. A dispersion relation for the waves is obtained. This relation is valid for frequencies much less than the small-angle phonon-phonon collision rate. In the low-frequency limit the usual second-sound mode with velocity $\frac{c_0}{\sqrt{3}}$ is found $c_0$ is the phonon velocity). At higher frequencies the velocity of this mode increases towards $c_0$ and other modes of lower velocity appear. The nature of these waves is discussed. Finally, several experiments that might give information about the waves are considered.

Numerical calculations show that high conversion of laser light into stimulated Raman light in the forward direction limits the beam diameter of the self-focused light. The dependence of the limiting diameter on material parameters and experimental conditions is calculated. In the experiments we used single-frequency laser pulses of ∼ ${10}^{-8\mathrm{}}$-sec duration. Our measured minimum diameters in liquid benzene, mixtures of benzene C${\mathrm{S}}_2$, and toluene are in fair agreement with values calculated from our steady-state theory. The rapid movement of the focus at the end of the liquid cell gives rise to transient stimulated Raman scattering or transient self-focusing in liquids with long relaxation times. In C${\mathrm{S}}_2$, nitrobenzene, and bromobenzene these transient effects have to be taken into account in the comparison between calculated and measured limiting diameters.

The measurement of the $W$ value, the average energy expended per ion pair, in liquid argon for internal conversion electrons emitted from ${}_{}{}^{207}{}_{}{}^{}\mathrm{Bi}$, is carried out by the electron-pulse method. Comparing with the $W$ value (26.09 eV) for $\alpha$ particles in a gas mixture of argon (95%) and methane (5%), the $W$ value in liquid argon is determined to be ${23.6}_{-0.3\mathrm{}}^{+0.5\mathrm{}}$ eV. This value is clearly smaller than that in gaseous argon (26.4 eV). Such a reduction of $W$ value in liquid argon can be explained by assuming the existence of the conduction band in liquid argon as in solid argon. Under this assumption, the $W$ value in liquid argon is estimated by applying the energy-balance method, which was used for the rare gases by Platzman. The calculated value thus obtained is in good agreement with the experimental result. Following the same method, the $W$ values for liquid krypton and liquid xenon are also estimated.