Gibbs's theory of the formation of nuclei in the metastable phase of a two-phase system was reformulated by Cahn and Hilliard in order to eliminate Gibbs's condition that the nucleus be homogeneous up to a sharp boundary with the outside phase. This paper extends the Cahn-Hilliard theory of nucleation to systems having nonclassical Helmholtz free energies. The results of this study show that nucleation in the metastable region follows a completely different pattern than that predicted by Cahn and Hilliard. Most important is the extension of the range of stability of a fluid system close to its critical point. This is in contrast to the Cahn-Hilliard theory in which the region of stability becomes smaller and disappears as the critical point is approached. Recent experimental results of Huang, Vernon, and Wong give good agreement with our theory.

The relative effectiveness of electric and magnetic fields for producing molecular alignment in a nematic liquid crystal has been investigated while changing the magnitudes of the dielectric and conductivity anisotropies. The comparison was made for an ordering of the molecules such that the average angle that a molecule makes with the magnetic field is 45°. The dielectric anisotropy was changed from ${{\epsilon }_{\parallel }}^{\prime }-{{\epsilon }_{\perp }}^{\prime }=-0.2-1.0\mathrm{}$. A relationship involving dielectric, conductivity, and magnetic permeability anisotropies was found to be satisfied in a range of magnetic field strengths of 3-6 kG. If the torque due to the conductivity anisotropy was greater than the torque due to the dielectric anisotropy, stable Williams domains were likely to be observed, but if it was less, stable Williams domains were unlikely to occur. This has been shown earlier for materials exhibiting a negative dielectric anisotropy but this work emphasizes materials with a positive dielectric anisotropy.

A phenomenological scaling theory for incompressible fluid turbulence in the limit of infinite Reynolds number is proposed. The local vorticity and local dissipation are taken as scaling variables with scaling dimensions $\frac{2}{3}-\frac{\zeta }{2}$ and $\frac{\mu }{2}$, respectively. The 1941 Kolmogorov theory corresponds to $\mu =\zeta =0\mathrm{}$. Experimentally, $\zeta$ is small and $\mu \approx \frac{1}{2}$. This choice of scaling variables gives immediate and simple predictions about measured or readily measurable scaling exponents. An additional dimensionality-dependent scaling relation, $\mu =d-\frac{8}{3}+2\mathrm{}\zeta$, is proposed and supported by a physically plausible argument. This relation, which is consistent with experiment, suggests that the 1941 Kolmogorov theory is exact for $2<d<\mathrm{}\frac{8}{3}$ and has small corrections for $d=3\mathrm{}$. Dynamical reasons for this behavior are suggested. The relation of scaling behavior to intermittency of the dissipation is briefly discussed.

Neutron inelastic scattering from liquid ${\mathrm{N}}_2$ at $T=66.4\mathrm{}$ K and saturated vapor pressure is presented in the form of the normalized coherent nuclear-scattering law $S_{n,\mathrm{coh}}(\kappa , \omega )$. Our results at the wave vector, $\kappa =0.1\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$ are consistent with recent computer simulation showing that the sound mode continues to propagate for larger wave vectors than described by linear hydrodynamic theory. At larger wave vectors no evidence is found of propagating phononlike excitations in this liquid, but the observed spectra are broad and centered around the mean recoil energy of a Boltzmann gas. Using Sears' partial-wave expansion to separate the scattering owing to rotational motion from that owing to the motion of the molecular centers, we compare the latter to the result obtained from liquid argon, appropriately scaled according to the principle of corresponding states. The over-all agreement is good, but significant deviations from scaling are observed and briefly discussed in terms of anisotropic interactions. Further, the information obtained on rotational relaxation is compared with recent experiments and theories.

The viscosity of the critical mixture isobutyric acid-water was measured by three different methods used simultaneously. The comparison of the results obtained in this way allows better insight into the anomalous behavior of the viscosity, and also into the question of the "ideal viscosity." One of the most important results consists in the experimental observation of the relaxation of the coupling between viscous and diffusive modes, as predicted by Kadanoff. Also, measurements of the Rayleigh linewidth were performed so that the question of the "high-frequency" viscosity could be discussed. It is shown that each kind of measurement involves a characteristic frequency and wave number, which should be compared with the frequencies characteristic of the critical system. In such a way, as the critical point is approached and consequently all the frequencies changed, a number of modifications can occur in the behavior of the viscosity. In particular there is a decrease in the viscosity, measured at nonzero frequency and a relaxation at the Kadanoff cutoff frequency. Very close to the critical point the viscosity rounds off revealing a cusplike behavior, unless a dependence on the shear gradient is allowed.

It is argued that the method proposed in recent papers by Bunkin and Tugov is not adequate for calculation of the multiphoton transition probabilities in diatomic molecules.

The critical comments by Fedorov, Makarov, and Samokhin on a treatment of multiphoton vibronic transitions in diatomic molecules are discussed and are shown to be unsubstantiated at all points.

An autodetaching state of ${\mathrm{C}}^{-}$ and several autoionizing states of the neutral carbon atom are excited using the collisional-excitation method. The autodetaching ${\mathrm{C}}^{-}$ state lies at 7.44 ± 0.07 eV above the neutral-carbon ground state and has a dominant configuration of $2p3s3p{}_{}{}^4{}_{}{}^{}D$. The observed autoionizing states of carbon are assigned inner-shell-excited configurations of $2s2p^2({}_{}{}^4{}_{}{}^{}P, {}_{}{}^2{}_{}{}^{}D, {}_{}{}^2{}_{}{}^{}P)nl$.

Previous results concerning the evolution of the signal towards light of well-defined phase during the degenerate parametric amplification process are pointed out, as well as how this is affected by damping, the time dependence of the pump, and the additional process of frequency up-conversion.

The hyperfine structure of several highly excited ${}_{}{}^2{}_{}{}^{}D$ states in ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$ and ${}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}$ has been measured. The $D$-state atoms were produced in a two-step-excitation process. In the first step, multiple scattering of the strong alkali-metal $D_1$ and $D_2$ lines from an rf lamp was used to excite atoms into the first excited ${}_{}{}^2{}_{}{}^{}P$ levels. The intense tunable radiation from a cw dye laser was used in the second step to transfer $P$-state atoms into highly excited $D$ states. Level-crossing and optical-double-resonance techniques were used for the determination of the absolute values of the hyperfine-interaction constants. The following results (in MHz) were obtained for the magnetic dipole and the electric quadrupole interaction constants $a$ and $b$: For ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$, $\left|a\right(6\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\left)\right|=7.84\left(5\mathrm{}\right)\mathrm{}$, $\left|b\right(6\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\left)\right|=0.53\left(6\mathrm{}\right)\mathrm{}$ ($\frac{b}{a}>0\mathrm{}$), $\left|a\right({}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}\left)\right|=3.6\left(7\mathrm{}\right)\mathrm{}$, $\left|a\right(7\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\left)\right|=4.53\left(3\mathrm{}\right)\mathrm{}$, $\left|b\right(7\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\left)\right|=0.26\left(4\mathrm{}\right)\mathrm{}$ ($\frac{b}{a}>0\mathrm{}$), $\left|a\right(7\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}\left)\right|=2.2\left(5\mathrm{}\right)\mathrm{}$. For ${}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}$, $\left|a\right(8\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\left)\right|=3.98\left(8\mathrm{}\right)\mathrm{}$, $\left|a\right(8\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}\left)\right|=0.9\left(4\mathrm{}\right)\mathrm{}$, $\left|a\right(9\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\left)\right|=2.37\left(3\mathrm{}\right)\mathrm{}$, $\left|a\right(9\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}\left)\right|=0.5\left(2\mathrm{}\right)\mathrm{}$, $\left|a\right(10\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\left)\right|=1.52\left(3\mathrm{}\right)\mathrm{}$, $\left|a\right(10\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}\left)\right|=0.4\left(2\mathrm{}\right)\mathrm{}$. The $a$ factors generally deviate strongly from the values expected in a one-electron picture of the alkali-metal atom indicating the importance of polarization and correlation effects for these states. For ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$ a comparison with a recent calculation including polarization effects is made. The $b$ factors for ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$ are the first significant values allowing a calculation of an alkali-metal-atom nuclear quadrupole moment from non-$P$-state data.

A method has been developed for computing the eigenvalues of a given potential in the radial equation for diatomic molecules. This method is simple, accurate, and can be applied not only to energy eigenvalues but also to the eigenvalues of any parameter that may be included in the potential. An analytic expression for the potential can be found in terms of simple functions (as the Gaussian function) by the following method: As many parameters as are needed are included in the potential. Then, the values of these parameters are adjusted so that the computed eigenvalues agree with the experimental values. Some parameters are also adjusted in order that the computed rotational constants agree with the experimental values. The rotational constants are computed very accurately by computing rotational eigenvalues, and without using numerical integration of eigenfunctions. The present method was applied to the ground state $X{}_{}{}^2{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ of ${\mathrm{N}}_2^{+}$. The computed dissociation energy agrees with one of the two possible dissociation energies of ${\mathrm{N}}_2^{+}$ and thus determines the correct value.

The relationship between the matrix eigenvalues of the $L^2$ discretization of an operator with a continuous spectrum and Gaussian quadrature is discussed for the radial kinetic energy and for the attractive and repulsive Coulomb Hamiltonians. It is shown that discretization of the radial kinetic energy in a Laguerre- (Slater-) type basis gives a Gegenbauer quadrature, while discretization in an oscillator- (Gaussian-) type basis generates a Laguerre quadrature. Laguerre discretization of the Coulomb problem gives a Pollaczek quadrature in the repulsive case, and a new modified Pollaczek quadrature in the attractive case. The utility of these results is shown in applications to potential scattering and photoionization. Two numerical techniques for obtaining "equivalent quadrature" weights are discussed: a matrix method due to Gordon, and a very simple interpolatory method due to Heller.

Ionization potentials, electron affinities, and term splittings have been computed for the lowest electronic configurations of atoms with $Z$ from 13 to 18. Following approximate Hartree-Fock calculations, correlation energies are computed by variational solution of one- and two-electron Bethe-Goldstone equations, defined in terms of orbital excitations. All computed energy differences are in good agreement with experiment. The energy differences arise primarily from $M$-shell correlations, with very little contribution from $L-M$ interactions, and no substantial $L$-shell effect. Estimates are made of the effects of extending the orbital basis set beyond $f$ orbitals and of including three-particle correlation.

Using Hartree-Fock-Slater wave functions, values of the nuclear hexadecapole antishielding factor ${\eta }_{\infty }$ have been calculated for the following ions: ${\mathrm{Ti}}^{3+}$, ${\mathrm{Mn}}^{2+}$, ${\mathrm{Cu}}^{+}$, ${\mathrm{Zn}}^{2+}$, ${\mathrm{Ge}}^{4+}$, ${\mathrm{Rb}}^{+}$, ${\mathrm{Zr}}^{3+}$, ${\mathrm{Nb}}^{5+}$, ${\mathrm{Tc}}^{2+}$, ${\mathrm{Ag}}^{+}$, ${\mathrm{In}}^{3+}$, ${\mathrm{Sb}}^{3+}$, ${\mathrm{Cs}}^{+}$, ${\mathrm{Hf}}^{3+}$, ${\mathrm{Re}}^{2+}$, ${\mathrm{Au}}^{+}$, ${\mathrm{Hg}}^{2+}$, ${\mathrm{Bi}}^{3+}$, ${\mathrm{Fr}}^{+}$, ${\mathrm{Th}}^{3+}$, and ${\mathrm{Am}}^{2+}$. The radial distortions induced in the core electrons due to nuclear hexadecapole moment were calculated using Sternheimer's perturbation numerical procedure. The contribution to ${\eta }_{\infty }$ due to the $\mathrm{nf}$ shell is much weaker in magnitude than that from the $\mathrm{nd}$ shell. In the three $\mathrm{nd}$ series of ions considered here, maximum values of ${\eta }_{\infty }$ are obtained in the cases of ${\mathrm{Cu}}^{+}$, ${\mathrm{Ag}}^{+}$, and ${\mathrm{Au}}^{+}$ ions, respectively, where the outer $d$ shell is complete and is most external. With the assumption that a large nuclear quadrupole moment may be associated with a significant hexadecapole moment, it is suggested that of the systems examined here containing nuclei with spin $I\ge 2$, ${\mathrm{Bi}}^{3+}$, ${\mathrm{Re}}^{2+}$, ${\mathrm{Sb}}^{3+}$, ${\mathrm{In}}^{3+}$, and ${\mathrm{Mn}}^{2+}$ are likely to exhibit prominently nuclear hexadecapole interaction effects since these have favorable natural abundance, quadrupole moment, magnetic resonance sensitivity, and large ${\eta }_{\infty }$ values.

We derive an approximation for transition moments between excited states consistent with the approximations and assumptions normally used to obtain transition moments betwen the ground and excited states in the random-phase approximation and its higher-order approximations. We apply the result to the calculation of the photoionization cross sections of the $2{}_{}{}^3{}_{}{}^{}S$ and $2{}_{}{}^1{}_{}{}^{}S$ metastable states of helium by a numerical analytical continuation of the frequency-dependent polarizability. The procedure completely avoids the need for continuum basis functions. The cross sections agree well with the results of other calculations. We also predict an accurate two-photon decay rate for the $2{}_{}{}^1{}_{}{}^{}S$ metastable state of helium. The entire procedure is immediately applicable to several problems involving photoionization of metastable states of molecules.

We present calculations of the cross section for quenching of the metastable $2S$ state of muonic hydrogen (${\mu }^{-}p$) in collisions with a hydrogen atom, at collision energies below the threshold for inelastic $2S-2P$ excitation. A quantum mechanical approach based on the adiabatic approximation is used with phase shifts evaluated in the WKB approximation. Below threshold, the dominant quenching process involves Stark admixture of $2S$ and $2P$ states of ${\mu }^{-}p$ during the collision, which is accompanied by a $2P-1S$ radiative transition also during the collision, and consequently the cross section is reduced by several orders of magnitude compared with the inelastic cross section. These results are important to considerations of the possibility of measuring the $n=2\mathrm{}$ fine and hyperfine structures of ${\mu }^{-}p$. We also present quenching cross section results based on this same approach for collisions of the muonic helium ion, ${\left({\mu }^{-}\alpha \right)}^{+}$, on He, relevant to lifetime and fine-structure measurements of ${\left({\mu }^{-}\alpha \right)}^{+}$. Our theoretical results for ${\left({\mu }^{-}\alpha \right)}^{+}$ differ from available experimental lifetime results for ${\left({\mu }^{-}\alpha \right)}^{+}$. We attribute the discrepancy to uncertainties in the values of the interatomic potential used in the calculations.

Following recent reports on strong uv and ir laser transitions in noble-gas mixtures, we attempted to determine the dominant precursor reactions leading to laser action. In this paper we present experimental results of time-dependent spectroscopy of the various species existing in He/Xe mixtures excited by fast transverse electrical discharges. We also present some parametric measurements of the He/Xe laser in the ir region. A plasma model is suggested for explaining the time behavior of the helium and xenon emissions. According to this model, which is justified by the experimental results, ir laser action in the He/Xe mixture is excited mainly by energy transfer from metastable helium atoms and molecules by Penning ionization of xenon atoms.

Within the Born approximation, a general formulation is given for differential cross sections corresponding to electron-impact ionization of an arbitrary $L-S$-coupled atomic system. Expressions for the generalized oscillator strength and total cross section are also given. Correlation effects are explicitly included in the formulation through the use of a configuration-interaction wave function to describe the initial bound target state, and a close-coupling wave function to describe the final free target state. Two independent computer codes have been constructed which allow these functions to be of arbitrary complexity for any atom. The codes use recently developed, but different, techniques for solving the close-coupling equations. Test results are obtained for the helium atom, and they agree well with previous correlated calculations.

Time-dependent spectroscopy techniques have been used to determine the cross sections for the deexcitation of nonmetastable $\mathrm{He}\left(3\mathrm{}{}_{}{}^1{}_{}{}^{}P\right)$ states by collision with Ne, Ar, Kr, or Xe atoms. The measured cross sections in ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ at ${600}_{-100\mathrm{}}^{+200\mathrm{}}$ °K are, for Ne, ${27.6}_{-2.8\mathrm{}}^{+4.5\mathrm{}}$; Ar, ${55.6}_{-7.8\mathrm{}}^{+10.6\mathrm{}}$; Kr, ${49.5}_{-4.8\mathrm{}}^{+8.0\mathrm{}}$; and Xe, ${73.0}_{-8.8\mathrm{}}^{+12.9\mathrm{}}$. These cross sections are compared with theoretical Penning ionization cross sections having values of 20 for Ne, 40 for Ar, 39 for Kr, and 35 for Xe, in units of ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ (at 600 °K).