Spin relaxation of optically pumped ${\mathrm{Rb}}^{85}$ and ${\mathrm{Rb}}^{87}$ atoms colliding with light-noble-gas atoms is shown to be strongly influenced by an anomalous relaxation process which we attribute to the formation and destruction of bound and quasibound Van der Waals molecules. The anomalous relaxation rate has been measured and analyzed in Ne, complementing an earlier study in He. Relative rates of formation of complexes in two- and three-body collisions have been determined. The correlation time for the quasimolecular interaction in Rb-Ne has been found to be 6.7 × ${10}^{-10\mathrm{}}$ $p^{-1\mathrm{}}$ sec, where $p$ is the Ne pressure in Torr. Nuclear-spin-independent cross sections for the relaxation of $〈S_z〉$ in sudden binary collisions of Rb atoms with noble-gas atoms have been measured to be (units of ${10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$: $\sigma (\mathrm{Rb}-\mathrm{He})=3.1\mathrm{}$ $\sigma (\mathrm{Rb}-\mathrm{Ne})=19\mathrm{}$ $\sigma (\mathrm{Rb}-\mathrm{Ar})=630\mathrm{}$ $\sigma (\mathrm{Rb}-{\mathrm{N}}_2)=83\mathrm{}$. Relaxation in sudden binary collisions is shown to follow the theoretically expected nuclear spin dynamics: two relaxation rates in the ratios 8:1 for ${\mathrm{Rb}}^{87}$ and 18:1 for ${\mathrm{Rb}}^{85}$ have been measured. Diffusion coefficients of Rb in the various buffer gases have been measured to be (units of ${\mathrm{cm}}^2$/ sec, at 305°K): $D_0(\mathrm{Rb}-\mathrm{He})=0.42\mathrm{}$, $D_0(\mathrm{Rb}-\mathrm{Ne})=0.235\mathrm{}$, $D_0(\mathrm{Rb}-\mathrm{Ar})=0.16\mathrm{}$, $D_0(\mathrm{Rb}-{\mathrm{N}}_2)=0.16\mathrm{}$. Nuclear-spin-independent cross sections for the relaxation of $〈J_z〉$ in the $5{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ state of Rb have been measured to be 3.4 × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ for Rb-He, and 5.9 × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ for Rb-Ne. Anomalies, disagreements, and puzzles occurring in earlier measurements of ground-state relaxation in Rb are shown to be largely resolved when considered in the light of the new results.

We report measurements of the lifetime of the metastable $2{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ state in heliumlike silicon and sulphur using the time-of-flight technique. An apparatus was developed suitable for direct beam-foil measurement of mean lives of x-ray emitting states whose lifetimes are in the neighborhood of ${10}^{-12\mathrm{}}$ sec. Silicon beams at 48 and 54 MeV and sulphur beams at 50, 60, and 66 MeV underwent foil excitation in passage through a nickel foil. A high-resolution Doppler-tuned spectrometer was used to study the decay profile of the emitted x rays. The measured lifetimes of the $2{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ state, (6.35 ± 0.33) × ${10}^{-12\mathrm{}}$ sec and (1.57 ± 0.18) × ${10}^{-12\mathrm{}}$ sec for silicon and sulphur, respectively, are in agreement with theory.

Radiative lifetimes of the first ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ state of Mgu, Cau, Znu, Sru, Cdu, and Bau are reported as measured by the Hanle effect in a fast-flowing helium afterglow. They are, respectively, 3.65(0.12), 6.61(0.30), 2.4(0.3), 6.64(0.10), 2.86(0.25), 6.78(0.40) in units of ${10}^{-9\mathrm{}}$ sec. The ions in the afterglow are created by Penning ionization of the neutral metal atoms, thus providing a steady-state, field-free region for observation. Comparisons are made with measurements by other methods, and discrepancies are discussed.

Time-resolved spectroscopic studies have been carried out on various emissions from He-Ar, He-Kr, He-Xe, and He-Ne mixtures to obtain kinetic information and quenching cross sections following charged-particle excitation. Our results are consistent with the pathways model of Payne, Klots, and Hurst in which Jesse effects are due primarily to energy transfer from $\mathrm{He}\left(2\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)$ to an atom or molecule which is consequentially ionized. Quenching cross sections for $\mathrm{He}\left(2\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)$)-Ar, -Kr, and -Xe at thermal (300°K) collision energy were obtained as 22.5, 42, and 70 ${\mathrm{\AA }}^2$, respectively, with an accuracy of 10%. These results are smaller than theoretical calculations which make use of the orbiting approximation, but agree well with experimental data obtained by crossed-molecular-beam methods. Using the same method, we obtained for the first time room-temperature quenching cross sections for $\mathrm{He}\left(2\mathrm{}{}_{}{}^1{}_{}{}^{}P\right)$)-Ar and $\mathrm{He}\left(3\mathrm{}{}_{}{}^1{}_{}{}^{}P\right)$)-Ne, -Ar, -Kr, -Xe (142 ± 42, 42 ± 4, 53 ± 5, 39 ± 4, and 73 ± 7 ${\mathrm{\AA }}^2$, respectively). These results are larger than theoretical calculations based on the dipoledipole mechanism by Katsuura and Watanabe. Quenching cross sections for $\mathrm{He}\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}P\right)$)-Ne, -Ar, -Kr, -Xe, and $\mathrm{He}\left(3\mathrm{}{}_{}{}^1{}_{}{}^{}D\right)$)-Ne were obtained as 32 ± 5, 22 ± 3, 17 ± 3, 67 ± 10, and 30 ± 5 ${\mathrm{\AA }}^2$, respectively.

The radiation emitted by plane of excited two-level atoms is exactly calculated in the semiclassical approximation. The well-known hyperbolic-secant solution is obtained in the limit case of small plane densities.

The interference between the contributions of two Raman resonances to the third-order susceptibility ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ has been observed in a liquid mixture of benzene and cyclohexane. Utilizing three variable laser frequencies, ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}(-{\omega }_3,{\omega }_0,{\omega }_1,-{\omega }_2)$ was measured in a parametric mixing experiment as a function of the intermediate frequencies ${\omega }_0-{\omega }_2$ and ${\omega }_1-{\omega }_2$ which are near different Raman resonances. Detailed Raman spectra are used to give excellent theoretical fits to the experimental curves. The usefulness of this extension of the well-known three-wave mixing, or CARS (coherent anti-Stokes Raman spectroscopy), experiment in calibrating different two-photon cross sections is discussed.

Pulsed radio-frequency transient phenomena of resonant two-level spins are often described by the Bloch equations where the phenomenological dipole ($T_2$) and population ($T_1$) decay times appear. A similar description has been carried over recently into the microwave and infrared regions as well. At visible-ultraviolet wavelengths, however, a more general solution is required because the transition levels do not constitute an isolated system and also spontaneous emission can no longer be disregarded. As a consequence, the lower (1) and upper (2) transition levels are characterized by vastly different decay rates (${\gamma }_1\ne {\gamma }_2$) and the lifetime $T_1$ is no longer a defined quantity. In view of laser-induced coherent transient phenomena now being observed, we present general solutions of the density-matrix equations of motion for an optically resonant two-level system in contact with a multilevel reservoir where ${\gamma }_1\ne {\gamma }_2$. Particular and perturbative solutions involving intensity-dependent damping and frequency shifts are included with applications to echo and nutation phenomena.

A series of metallic gratings, having grating spacing of 2180 Å and known numbers of grooves ranging from 1000 to 4, were seen to produce Smith-Purcell radiation when exposed to a 50-keV electron beam. Bandwidths for the radiation from these gratings were measured and found to be dependent upon the number of grating grooves as well as the beam angle of incidence. This is interpreted as indicating a one-to-one correspondence between grooves in the grating and undulations in the radiated wave train produced by a single passing electron. With this assumption, a height for the zone of effective interaction for the electron is calculated to be ∼1500 Å from the grating surface.

New measurements have been made of coexisting mass densities of isobutyric acid + water with a precision of 20 ppm and within 3.5°C of the critical temperature. The measurements were made using a single sample of composition very close to critical. It is found that the coexistence curve is more symmetric in terms of the difference in volume fraction ($\Delta \phi$) of coexisting phases than in terms of the difference in mass density. The difference $\Delta \phi$ is well fitted for $\epsilon =\frac{(T_c-T)}{T_c}<0.006\mathrm{}$ by the expression $\Delta \phi =B{\epsilon }^{\beta }$, where $B=1.071\mathrm{}\pm 0.023$ and $\beta =0.328\mathrm{}\pm 0.004$. (Uncertainties are given as 3 times the standard deviation.) A new analysis has been made of the recent data of Gopal et al. on the difference in volume fraction of coexisting densities of carbon disulfide + nitromethane. For this system, $\Delta \phi$ can be fitted for $\epsilon <0.2\mathrm{}$ by an extended scaling expression suggested by Wegner's work, $\Delta \phi =B{\epsilon }^{\beta }+B_1{\epsilon }^{\beta +{\Delta }_2}+B_2{\epsilon }^{\beta +2\mathrm{}{\Delta }_2}$. The exponent ${\Delta }_2$ is fixed at 0.5; the fit gives $\beta =0.316\mathrm{}\pm 0.008$, $B=1.63\mathrm{}\pm 0.09$, $B_1=0.77\mathrm{}\pm 0.31$, and $B_2=-2.43\mathrm{}\pm 0.40$. This work suggests that liquid-liquid critical phenomena are consistent with the functional forms obtained from renormalization-group calculations and with asymptotic exponents which are like those presently calculated for the Ising model. The range of asymptotic behavior seems to be larger for a liquid-liquid critical point than for a liquid-gas critical point.

An attempt is made to formulate and develop the idea of renormalization in the context of generalized thermodynamics. Two examples of renormalization of the Van der Waals theory are discussed in detail.

We investigate the behavior of a class of nonlinear one-dimensional fields with symmetric and periodic interaction. The prototypical equation of this class is the sine-Gordon system. These fields have classical and static solutions with localized particlelike properties. We present a general theoretical framework to discuss the stability of these solutions under quantum and thermal fluctuations. It is shown that stability requires a phase transition of the system into an ordered equilibrium state. As an example, we calculate exactly the thermodynamics of the classical system by evaluation of a functional integral, using transfer matrix techniques. The treatment of the boundary condition, or "kink" density, as a thermodynamic variable requires a nontrivial extension of the standard methods. By a remarkable analytic continuation we show that the thermodynamic pressure is given by the eigenvalue of Hill's equation in the first unstable region. In particular, we compute the thermodynamics of the sine-Gordon field, and find that the localized behavior exhibited by the classical system at zero temperature is completely destroyed at finite temperature; i.e., the solutions are unstable with respect to thermal fluctuations.

A formalism appropriate for obtaining a self-consistent handling of the strongly coupled two-component plasma problem is discussed. The divergence of the classical electron-ion pair correlation function is removed with the aid of a phenomenological "soft-core" potential. The important formal development is the introduction of partial linear and nonlinear polarizabilities, their interrelations, and the linear and nonlinear fluctuation-dissipation theorems satisfied by them. The formalism is used to generalize existing strongly coupled one-component plasma theories for the two-component situations. Both the schemes based on the first Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) equation and the fluctuation-dissipation theorems, and the scheme based on the second BBGKY equation and the decomposition of the triplet correlation function are developed into self-consistent two-component equations. Algebraically, the equations appear as a set of three, coupled, nonlinear integral equations for pair correlation functions or polarizabilities.

Time-dependent phase-space density correlation functions in a fluid mixture of hard spheres are analyzed using a coupled set of generalized Boltzmann equations. The matrix of memory functions is expressed explicitly as static, direct-collision, and cross-collision contributions. Low-order matrix elements of the memory functions are calculated, and the results used to discuss the hydrodynamics of the system and to construct kinetic models. Numerical spectra of density fluctuations are presented to illustrate the effects due to dynamical correlations in a mixture.

The nonlinear partial differential equations describing plane, cylindrical, and spherical explosions in a fully ionized electron-ion plasma with heat-flux relaxation and thermal relaxation are reduced to ordinary differential equations by means of novel similarity transformations. The resulting ordinary boundary-value problem for the plasma explosion, with the strong shock conditions as boundary values at the moving shock front, is formulated mathematically. The scaling laws for the plasma fields are presented which show how the plasma properties change with time during the course of the explosion. The importance of electron and ion heat-flux relaxation, which enhances the concentration of thermal energy behind the shock front, is stressed for the understanding of the shock-heating mechanism in fast processes. It is concluded that heat-flux relaxation is an important process for short-time plasma explosions, which determines the discontinuity of the electron and ion temperature fields at the shock front.

A statistical-mechanical theory of the elastic constants of a liquid crystal based on the Onsager expansion is reexamined, with emphasis on the terms linear in the gradients of the director. This gives a microscopic theory of the piezoelectric effect in nematic liquid crystals, and of the spontaneous twisting of a cholesteric. Model cases of tapered rods, bent rods, and threaded rods are considered.

Within the Mori theory, a kinetic equation for the phase-space density of a tagged particle in a classical liquid is derived which describes the particle motion in a self-consistent wave number and frequency-dependent effective potential. It is shown that for small wave numbers $q$ the particle is almost bound in a trapping potential, that at some critical wave number $q_0$ the trapping potential breaks down, and that for large $q$ the particle propagates almost freely. The theory is applied to the calculation of the self-correlation function $S_s(q,\omega )$ for liquid argon and rubidium, and the breakdown of the trapping potential is shown to explain the observed oscillatory $q$ dependence of the half-width of $S_s(q,\omega )$.

Two hydrogen $n$-$\alpha$ transitions, $n=13\mathrm{}\to 12$ at $\lambda 88.7$ μm and $n=12\mathrm{}\to 11$ at $\lambda 69.0$ μm, were observed in a large-diameter $\theta$ discharge at electron densities between ${10}^{14}$ and 3 × ${10}^{14}$ ${\mathrm{cm}}^{-3\mathrm{}}$. Line profiles were measured with a Czerny-Turner infrared monochromator and a Ge:Ga photodetector at liquid-helium temperature. Both $n$-$\alpha$ lines exhibit strong and symmetric satellite features, with intensities comparable to their parent lines and displacements close to the electron plasma frequency ${\omega }_p$. These satellites can be interpreted in terms of plasmonatom collisions if long-wavelength fluctuations in this turbulent plasma are enhanced by a factor ≳ ${10}^3$ above the thermal level at $T_e\simeq 0.7$ eV. As an independent estimate for the level of turbulence, the continuum emission in the regions corresponding to ${\omega }_p$ and $2{\omega }_p$ was measured, and found to be well above the level expected for a thermal plasma. Comparison with fluid theory, after radiative transfer corrections, shows satisfactory consistency with the $n$-$\alpha$ satellite diagnostics.

The weak plasma turbulence theory recently formulated by one of us is applied to parametrically unstable plasmas. A dispersion relation for normal modes of the turbulent plasma is derived. The condition of marginal stability of these modes provides a nonlinear equation describing the quasistationary turbulent spectrum. Two classes of nonlinearities arise: (i) Diagonal corrections, similar to the renormalized frequencies and damping rates of usual weak turbulence theory but which must be computed using the frequencies of the coupled parametric modes, and (ii) coupling saturation corrections which are renormalized mode coupling coefficients related to spectral cross coupling coefficients such as $〈 E(\overrightarrow{\mathrm{k}},\omega )E(\overrightarrow{\mathrm{k}}-{\overrightarrow{\mathrm{k}}}_0,\omega -{\omega }_0)〉$. The coupling saturation theory is applied to the electron-electron decay instability $\omega \sim 2{\omega }_{\mathrm{pe}}$ and strongly inhibits the conversion of pump radiation into plasma waves.

The well-known constant-coupling theory of ferromagnetism has been adapted to the problem of the nematic liquid crystal. A cluster variational formulation of the theory is developed. The calculations are based on an effective pair potential which is derived from the most general form of interaction by taking suitable averages. Expressions for the long-range order, short-range order, energy, and free energy are derived. Numerical calculations have been performed for a variety of effective interaction potentials. The temperature dependences of the order parameters and thermodynamic functions have been determined. As required by experiment, the theory is found to display a first-order nematic-isotropic phase transition. The results of the present theory are compared to those of previous calculations; questions concerning the validity of the mean-field theory have been clarified. The numerical results are also compared to a variety of experimental data.

With the aid of a modified mean-field model, one in which the spatial correlations are handled by means of a conventional classical liquid theory and the orientational ordering alone is subjected to the mean-field approximation, we find it possible to correlate thermodynamic data near the isotropic-nematic transition region. In contrast with the Maier-Saupe theory, we deduce accurately the volume change, latent heat, and maximum supercooling temperature. The theoretical analysis when applied to PAA and MBBA leads to results in quantitative agreement with experiment. We propose that measured data on other nematic and cholesteric liquid cystals be subjected to tests under the same scheme.