Many-body perturbation theory is used to calculate the parallel and perpendicular dynamic polarizabilities of molecular hydrogen. High-order terms in the perturbation expansion are included and the poles of $\alpha \left(\omega \right)$ are calculated. Results for the dynamic dipole polarizabilities and for the molecular anisotropy are in good agreement with experiment.

Cross sections for production of inner-shell vacancies in atoms by proton impact have been examined in an impulse approximation. The model used includes modifications to account for the nuclear repulsion of the proton. Comparisons with experiment and with other calculations are made. It is found that the model compares favorably with existing Born approximations. If the most recent fluorescent-yield data are used, the present results agree well with experiment for proton energies larger than ∼ 300 times the electron binding energies. Determination of fluorescent yields by means of such experiments is also discussed.

We report here measurements of the absorption coefficient and velocity of ultrasound in the critical liquid-mixture aniline-cyclohexane ($T_c=29.8\mathrm{}°$C) as a function of frequency and temperature. The standard pulse technique was used for the absorption measurements over the frequency range between 1 and 75 Mc/sec. In this range, measurements have been performed at a minimum of 8 and a maximum of 11 frequencies. The temperature range covered is between 30.5 and 36.2°C. Velocity measurements have been performed in the same temperature range but only at 2 and 15 Mc/sec. The experimental data have been analyzed in terms of Fixman's theory. We also include a discussion of this theory, together with a comparison with the more recent works by Romanov and Solov'ev, Kawasaki and Tanaka, and Kadanoff and Swift. Our results are not conclusive, but we have provided further indications that the sound-diffusion coupling, originally suggested by Fixman, is the only mechanism responsible for the excess absorption in a region not too close to the critical one. Some limitation appears for the temperature closest to the critical point.

The exchange constant $J$ is calculated in helium mixtures, using the single-particle theory of Nosanow for atomic configurations likely to yield large enhancements of $J$ over the pure ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ value. ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ atoms near a pair of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ atoms are first considered. Little relaxation (the same as around 1 ${}_{}{}^4{}_{}{}^{}\mathrm{He}$) and change in the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ functions are found. Nonspherical Gaussian functions ${\phi }_{\mathrm{NS}}$ are then used to describe ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ surrounded by 6 ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ as first neighbors in otherwise pure ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. The ${\phi }_{\mathrm{NS}}$ obtained on energy minimization is nearly spherical and little changed from its pure ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ value. From these examples, no enhanced $J$ is predicted for mixtures. This is in agreement with recent high-temperature measurements on ${}_{}{}^4{}_{}{}^{}\mathrm{He}$-rich mixtures, but disagrees with low-temperature measurements of the exchange specific heat which suggest a significantly enhanced $J$.

Time-dependent perturbation theory is used to evaluate the angular distribution of electrons emitted from heavy atoms in collisions with protons and other heavy charged particles. The incident particle is assumed to move on a straight-line trajectory. Hydrogenic wave functions are used for the initial electron state, and continuum Coulomb wave functions for the final electrons. The angular distributions of electrons emitted from $K$ and $L$ shells by a given projectile are compared. The separate contributions of the $L$ subshells to the angular distributions are also calculated.

The propagation of a Gaussian light pulse through a medium having a positive or negative absorption line is examined. Analytical approximations are obtained for the case where the spectral width of the pulse is much smaller than that of the line. It is shown that the pulse remains substantially Gaussian and unchanged in width for many exponential absorption depths, and that the locus of instants of maximum amplitude follows the classical expression for the group velocity, even if this is greater than the velocity of light, or negative. Numerical calculations have been used to examine what happens beyond the limit of usefulness of the analytical approximations.

Metastable He atoms produced by charge exchange of slow ${\mathrm{He}}^{+}$ with He were detected by secondary electron emission from a tungsten target. The cross section for metastable production rose from a threshold near 22 eV to a peak value of 2.2×${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$ ±50% at 27 eV and decreased to a minimum at 32 eV (center-of-mass energy). A subsequent rise was measured up to 110 eV and was attributed to the increased production of ${\mathrm{He}}^m$ and, to a smaller extent, to kinetic emission of secondary electrons at the higher energies.

The diamagnetic susceptibility of an electron gas is reduced by Coulomb interactions below the Landau value in proportion to $\epsilon \beta {{\kappa }_0}^2$, where $\epsilon$ is the plasma parameter, ${\kappa }_0$ is the Debye screening constant, and $\beta =\frac{1}{\mathrm{kT}}$.

The quadrupole polarizability ${\alpha }_q$ which measures the induced quadrupole moment produced by an external field gradient has been calculated for three ions: ${\mathrm{Rb}}^{+}$, ${\mathrm{Cs}}^{+}$, and ${\mathrm{Bi}}^{5+}$, and for the neutral alkali atoms. The present calculations for ${\mathrm{Rb}}^{+}$ and ${\mathrm{Cs}}^{+}$, using the appropriate Hartree-Fock wave functions, represent a considerable improvement over our previous calculations, in which Hartree wave functions (without exchange) were employed. The values obtained for ${\alpha }_q$ of the alkali atoms are very large, ranging from 60.0 ${\mathrm{\AA }}^5$ for Li to 440.8 ${\mathrm{\AA }}^5$ for Cs. In Sec. III, we have collected the values of ${\alpha }_q$ for 11 ions, as obtained using the author's method of direct solution of the inhomogeneous wave equation. Wherever possible, these values have been compared to those obtained by other methods. The agreement is generally very good.

The two-dimensional Magnus formula ${\overrightarrow{\mathrm{f}}}_m=\rho ({\overrightarrow{\mathrm{v}}}_s-{\overrightarrow{\mathrm{V}}}_v)\times \overrightarrow{\kappa }$ can be extended to three-dimensional fluid-core vortices of arbitrary core structure by a precise redefinition of the stream velocity vector ${\overrightarrow{\mathrm{v}}}_s$, vortex velocity vector ${\overrightarrow{\mathrm{V}}}_v$, and circulation vector $\overrightarrow{\kappa }$. For example, ${\overrightarrow{\mathrm{V}}}_v$ becomes the velocity, in a plane slicing the vortex core, of the "center of mass" of the vorticity. The exact three-dimensional formula is derived by analyzing the motion of vorticity relative to the fluid particles - a relative motion caused by the action of nonconservative forces on the vortex core (e.g., the electric force on a charged vortex ring in superfluid helium). The analysis deals with the vorticity field $\overrightarrow{\omega }\equiv \overrightarrow{\nabla }\times \overrightarrow{\mathrm{v}}$ and, thus, can lead to simple formulas and insights in cases where the velocity field $\overrightarrow{\mathrm{v}}$ may be impossibly complicated. Examples introduced are (i) the concept of a "conserved vorticity current," (ii) a possible classical mechanism for the creation or destruction of vortex lines in superfluid helium, and (iii) a simple technique for analyzing the effect of viscosity on the structure of a vortex core.

The dissipation of energy in the flow of an ideal incompressible fluid is described by a theorem whose derivation relies upon the exact three-dimensional Magnus formula discussed in the previous paper. The theorem, which explicitly demonstrates the role of vortex motion in the process of energy dissipation, can be used to calculate the trajectories of vortices. Also derived is a detailed Josephson equation - an extension of Anderson's "new corollary in classical hydrodynamics" - which provides an exact non-time-average relation between chemical potentials and vortex motion.

The classical binary-encounter model for the ionization of ions by impact of electrons given by Thomas and Garcia has been extended to calculate the excitation cross section of ions. The electron-impact excitation cross sections for the $3s-3p$ and the $3s-3d$ transitions in ${\mathrm{Mg}}^{+}$, the $2s-2p$ transition in ${\mathrm{Be}}^{+}$, and the $4s-4p$ transition in ${\mathrm{Ca}}^{+}$ have been calculated. The results are compared with calculations based on the close-coupling and the Coulomb-Born approximations. Our results agree better with close-coupling calculations than with calculations based on the Coulomb-Born approximation.

A general method is presented for calculating the $f$ values for all permitted dipole transitions involving simultaneous photoionization and photoexcitation of helium. The cross section for ions excited into the $n=2\mathrm{}$ state is compared with experiment and with a similar calculation by Salpeter and Zaidi; their result, that the ejected electron is in a $p$ state is confirmed. The probability for the residual ${\mathrm{He}}^{+}$ ion to be excited to a state of principle quantum number $n$ is evaluated for $n=2-10\mathrm{}$, and the probability for the photoelectron to be in a $p$ state is compared with the probability for it to be emitted in an $s$ state. It is found that the inclusion of contributions from simultaneous photoionization and photoexcitation, and from double ionization in the total helium photoionization cross section, improves the agreement between theory and the experimental data at high energies.

We study the coupling of the surface oscillations of a free ${\mathrm{He}}^3$ film to the ${\mathrm{He}}^3$ particles of which the film is composed. A check on the self-consistency of the lowest-order theory of this coupling fails because of an infrared divergence. We, therefore, are led to use exact dynamical equations and find that the infrared difficulty then disappears because the exact theory takes the classical Maxwellian distribution of surface vibration properly into account. The resulting form of the coupling may be used to study the possibility of a superfluid pairing transition in a free ${\mathrm{He}}^3$ film.

A method is provided whereby all the possible results of sequences of three-particle binary collisions may be calculated, given the initial velocities of the three particles. All the one-dimensional bounds on the number of collisions given by Doolen are confirmed. It is further found that only sequences of certain types are possible, the longest of which arises when the lighest particle rebounds between the two heavier particles. If in this instance, we let $\theta$ be the angle between the relative velocity of the first and second pairs of colliding particles and remove the one-dimensional restriction, we find that an upper bound on the maximum number of collisions $n_c$ is given by $\frac{{\pi }_c}{{n_c}^{-1\mathrm{}}}>invcos\left[{\left(\frac{m_B{m}_C}{(m_A+m_B)(m_A+m_C)}\right)}^{\frac{1}{2}}cos\theta \right],$ where $n_c$ is the largest integer which satisfies the inequality and $m_A$ is the mass of the lightest particle.

Spin-projected Hartree-Fock (PHF) wave functions are obtained for the isoelectronic series ${\mathrm{H}}^{-}$, He, ${\mathrm{Li}}^{+}$, and ${\mathrm{Be}}^{++}$, using different orbitals for different spins and general spin-orbitals (GSO), in both cases of pure $s$ character. The GSO energy for He is -2.87887 a.u., accounting for 99.1% of the radial correlation energy. A natural orbital analysis of the GSO function shows that it corresponds to a configuration interaction function with three $s^2$ configurations. The one-electron energies obtained from the PHF equations are given an interpretation as ionization energies. In the GSO case, the one-electron energies are not unique, but an upper limit is obtained.

Oscillatory structure has been observed in total symmetric and asymmetric charge-transfer cross-section measurements involving the alkali-metal atoms. Cross sections with oscillations similar to experimental results had been obtained from impact-parameter calculations using a two-state approximation with an interaction potential difference containing a maximum. This paper describes a physical model of charge transfer relating to the oscillatory electron capture probability. The ${\mathrm{Li}}^{+}$ + Li calculations of Peek et al. are examined and used as an example to relate capture-probability oscillations to those in total cross section. Computed capture probabilities having anomalous oscillations are shown as a function of impact parameter at several velocities. The capture-probability maxima are shown as contours on a plot of impact parameter versus inverse impact velocity. This plot illustrates capture-probability oscillations having a nearly stationary phase over a range of impact parameters, which results in oscillations in the total cross section. Oscillation damping and phase-constant effects are briefly examined to relate experimental results with theory. Near-resonant asymmetric oscillations are also discussed.

An ellipsometric technique has been used to determine the optical constants of sodium-, lithium-, and calcium-ammonia solutions between 0.6 and 2.3 eV in the temperature range of 213 to 233 K. The sodium-ammonia data span the range of the metal-nonmetal transition. The alkali metal solutions of concentration $x\ge 8$ mole percent metal (MPM) are clearly free-electronlike, whereas, the solutions of concentration ≤ 4 MPM strongly indicate the presence of the solvated electron. In the intermediate concentration range ($4<x<\mathrm{}8\mathrm{}$ MPM), the solutions are undergoing the metal-nonmetal transition; and the species governing the optical properties cannot be unambiguously determined, but probably involve both bound and free electrons. The temperature dependence of the optical constants of concentrated ($x\ge 6$ MPM) alkali metal-ammonia solutions was found to be negligibly small, while that of less concentrated solutions was consistent with that observed in the dilute alkali metal solutions. Concentrated solutions of calcium in ammonia (>6 MPM) deviated considerably from the Drude model but still appeared to be free-electronlike, as evidenced by the lack of structure in the absorption. They differed somewhat from the alkali metal solutions of similar electron concentration.

A general formalism is described for treating diabatic coupling processes in highly excited molecular states. The method treats electronic and nuclear motion quantum mechanically, and uses the adiabatic Born-Oppenheimer states as basis function. The present paper concentrates on diagnoses of vibronic coupling matrix elements, with Rydberg and continuum states of ${\mathrm{H}}_2$ as the test cases. The principal contributions come from the excited electron's interactions with the oscillating finite monopole of the ion-molecule core. The electronic factors in the transition amplitudes are definitely dependent on internuclear distance, particularly in the cases of $p$ and $d$ states. The transition amplitudes accumulate their magnitudes over the full classically allowed range of internuclear distance, especially in the cases of $s$ and $p$ states. Specific application is made to vibronic coupling perturbations in $p\sigma$ and $p\pi$ Rydberg states of ${\mathrm{H}}_2$.

Vibrationally induced autoionization and one class of predissociation of electronically excited ${\mathrm{H}}_2$ and its isotopes are treated by a perturbed-stationary-state theory. Autoionization and predissociation rates are given for a number of states of ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$. In addition to direct bound-continuum coupling, consideration is given to effects of higher-order coupling; these effects cause order-of-magnitude changes in isolated cases. The auto-ionization rates vary with principal quantum number $n$ as $n^{-3\mathrm{}}$, directly with vibrational energy $\mathrm{vh}\nu$, and decrease sharply with vibrational quantum change $\Delta v$. As the principal quantum number increases, transitions of successively smaller $\Delta v$ become possible; the net effect of this is to override the $n^{-3\mathrm{}}$ dependence in total autoionization rates. Competition between predissociation and autoionization is examined; the two processes show very different dependence on $n$ and $v$, with the consequence that decay in most regions of ($n, v$) space is dominated by one or the other process; but the two mechanisms are competitive for some ($n, v$) states. The isotope effect also is rather different for the two decay processes, enough so that, in effect, the isotope effect amounts to a qualitative change from one mechanism of decay to the other, with mass change.