The effect of spatial correlation of the two valence electrons on the multiplet spacings has been investigated for atoms with the ${\mathrm{}\left(1s\right)\mathrm{}}^2{\mathrm{}\left(2s\right)\mathrm{}}^2{\mathrm{}\left(2p\right)\mathrm{}}^6{\mathrm{}\left(3s\right)\mathrm{}}^2{\mathrm{}\left(3p\right)\mathrm{}}^6{\mathrm{}\left(3d\right)\mathrm{}}^2$ ground configuration. The atom is taken as a two-electron system with each electron moving in a Hartree-Fock effective potential. The zeroth-order wave function is taken to be a Clebsch-Gordan combination of products of one-electron Hartree-Fock orbitals. A variational function of the form $1+c{\mathcal{r}}_{12}+c^{\prime }{({\mathcal{r}}_1-{\mathcal{r}}_2)}^2$ is inserted into this wave function for each of the multiplet members, and $c$ and $c^{\prime }$ are determined by the variational method. When unrestricted Hartree-Fock functions are used as the zeroth-order basis set, good results which are insensitive to $c^{\prime }$ are obtained for the multiplet spacings. The ${}_{}{}^1{}_{}{}^{}G-{}_{}{}^3{}_{}{}^{}F$ spacing is overcorrected by about - 12% compared to +23% without correlation, while the ${}_{}{}^1{}_{}{}^{}D-{}_{}{}^3{}_{}{}^{}F$ spacing is overcorrected by - 3% compared to +34% without correlation.

A classical calculation is given for the kinetic energy of a vortex ring in an inviscid fluid (He II) in the presence of an infinitely extended plane, a coaxial circular disk, and an infinitely extended plane with a coaxial circular aperture. The energy is obtained as an explicit function of the ring position relative to the obstacle being considered. Formulas are given for the velocity components of the vortex-ring motion, the force exerted on an obstacle by a stationary vortex ring, and the impulse of the vortex ring in the presence of the obstacle. In the case of the circular aperture, there is found to be a critical energy (or ring size) beyond which a vortex ring cannot pass through the aperture. The path of the vortex ring near the different obstacles is obtained by numerical computation, departing from the explicit energy expression. The calculation method is easily extended to other axisymmetric configurations and consists of Fourier and Hankel integral-transform techniques in combination with results from the theory of dual integral equations.

Ion-ion neutralization cross sections have been measured for ${\mathrm{N}}^{+}$ + ${\mathrm{O}}^{-}$, ${\mathrm{N}}_2^{+}$ + ${\mathrm{O}}_2^{-}$, and ${\mathrm{O}}_2^{+}$ + ${\mathrm{O}}_2^{-}$. The kinetic energy range, in the barycentric coordinate system covered by the experiment, is between 0.1 and 98 eV with an energy resolution of about 0.1 eV. The products of the neutralization cross section $Q$ times the relative speed $v_{\mathcal{r}}$ are nearly independent of energy, having values close to ${10}^{-7\mathrm{}}$ ${\mathrm{cm}}^3$/sec for all three systems studied, except that below 0.5 eV the ${\mathrm{N}}^{+}$ + ${\mathrm{O}}^{-}$ and ${\mathrm{N}}_2^{+}$ + ${\mathrm{O}}_2^{-}$ systems show a rapid increase of $Q{v}_{\mathcal{r}}$ with decreasing energy. The experiment employs the superposition of positive- and negative-ion beams of several keV energy over a common path length of 33 cm. The beams are subsequently separated and the neutral products of the reaction are measured.

A simplified variational model for collision-dominated recombination of atomic ions is presented. The results are analytical formulas for electron-electron-ion recombination coefficients applicable to atomic systems whose outer electrons conform to one-electron energy-level structure. When combined with radiative transition probabilities, these results yield collisional-radiative recombination coefficients which are then compared with other theories and available experimental studies. In particular, fair agreement is found with Norcross and Stone's elaborate calculations for cesium recombination.

A simplified derivation of the master-graph formulation of the quantum-statistical theory of an interacting quantum fluid is presented. A complete analysis of the self-energy structures arising from both particle statistics and particle interactions simplifies the master-graph expressions for the thermodynamic properties of the fluid. The $x$-ensemble formulation of Lee and Yang is used to treat the degenerate Bose fluid below its Bose-Einstein condensation temperature. The results for a Bose fluid above its Bose-Einstein condensation temperature and for a Fermi fluid are obtained as special cases.

Molecular-dynamic studies of the behavior of the diffusion coefficient after a long time $s$ have shown that the velocity autocorrelation function decays as $s^{-1\mathrm{}}$ for hard disks and as $s^{-\frac{3}{2}}$ for hard spheres, at least at intermediate fluid densities. A hydrodynamic similarity solution of the decay in velocity of an initially moving volume element in an otherwise stationary compressible viscous fluid agrees with a decay of ${\left(\eta s\right)}^{-\frac{d}{2}}$, where $\eta$ is the viscosity and $d$ is the dimensionality of the system. The slow decay, which would lead to a divergent diffusion coefficient in two dimensions, is caused by a vortex flow pattern which has been quantitatively compared for the hydrodynamic and molecular-dynamic calculations.

In a previous paper, the master-graph formulation of the quantum-statistical theory of quantum fluids was developed. If this formulation is used to calculate the equilibrium properties of quantum fluids, apparent divergences are encountered in the low-temperature limit. In the present paper, we transform this theory by means of a $\Lambda$ transformation to overcome these apparent low-temperature divergences. In this transformation, the terms in the theory which gave rise to the apparent low-temperature divergences and which represent the dominant low-temperature contributions are summed explicitly to obtain well-behaved expressions. In addition, a consistent method is developed to obtain the corrections to the dominant low-temperature contributions. Explicit expressions for the $\Lambda$-transformed theory are given for the cases of a Bose fluid above the Bose-Einstein condensation temperature and for a Fermi fluid. Finally, the physical implications of the $\Lambda$ transformation are discussed.

The thermal-conductivity length dependence of helium II in small channels previously reported was found to arise from defects in our channel material. New thermal-conductivity measurements using more nearly perfect capillary channels do not show a length effect.

A realistic model potential is used to explain the low-temperature low-concentration positive-ion mobility. It is suggested that a similar potential could explain the negative-ion mobility.

Cross sections for the production of hydrogen atoms in the $3s$ state by the impact of ground-state hydrogen atoms on nitrogen molecules have been measured in the kinetic energy range 10-35 keV. The cross-section curve appears to have a maximum at the lower energies of about 4 × ${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$. This value is roughly 2½ times less than the maximum cross section for producing $3s$ atoms through electron capture by proton impact on nitrogen molecules in the same energy range.

Results of a search for the electric dipole moment of the thallium atom using previously described techniques and apparatus are reported.

This paper discusses an error in an earlier paper by West and Mizushima.

The ripple theory of surface tension in superfluid helium, originated by Atkins and developed by Brouwer and Pathria, implies a surface instability.

An explicit reduction in the number of terms of the expansion of the reduced two-particle density matrix for atomic systems is shown to occur when the expansion functions are eigenfunctions of $L_z\mathrm{}\left(1\right)+L_z\mathrm{}\left(2\right)\mathrm{}$ and $S_z\mathrm{}\left(1\right)+S_z\mathrm{}\left(2\right)\mathrm{}$.

Using a variationally determined set of atomic orbitals, the validity of pair-correlation approximations is examined for the Ne atom. Summing the usual pair-correlation energies yields 100.5% of the correlation energy. By summing symmetry-adapted pair-correlation energies, 90.2% of the correlation energy is obtained. The complete second-order wave function which includes the Hartree-Fock configurations plus all singly and doubly excited configurations produces 88.6% of the correlation energy.

The ${\mathrm{Li}}^{+}$-He experimental elastic differential cross sections of Aberth and Lorents in the 3.6- to 218-eV energy range have been analyzed and yield a simple repulsive potential. The potential may be parametrized as $V\left(R\right)=2.95\mathrm{}\times {10}^2\exp \mathrm{}(-4.30R)+1.00\mathrm{}\times {10}^3\exp \mathrm{}(-20.4R)\mathrm{}$ in which $R$ is in Å, and the energy is in eV. The estimated error is ±25% for $0.30\AA <R<\mathrm{}0.80\mathrm{}\AA$. The potential is in fair agreement with recent ab initio quantum calculations and the potential of Zehr and Berry who analyzed the energy loss of ${\mathrm{Li}}^{+}$ as a function of scattering path length.

Uncertainty principles for the average fluctuations of momentum and position per particle in an ensemble are derived. For bosons, these results are similar to the usual uncertainty principle, with slight corrections for the correlated motion of the particles. For fermions, a large correction for the Pauli exclusion principle is necessary, which causes $〈p^2〉〈{\mathcal{r}}^2〉$ to be proportional to the two-thirds power of the number of particles in the ensemble.

A relativistic expression for $L_1{L}_2{M}_{4,5}$ Coster-Kronig transition probabilities has been obtained by using the solutions of the Biedenharn symmetric Dirac-Coulomb Hamiltonian. The interaction matrix element yields the well-known nonrelativistic result in the appropriate limit. Numerical results for atoms having $Z$ values between 32 and 41 are compared with earlier calculations. Relativistic effects are shown to be sufficiently pronounced as not to be critically affected by the choice of a screening parameter. The transition probability at the cutoff point is appreciably greater than earlier nonrelativistic values.

The optimum scale factor for the Slater free-electron exchange approximation for atoms has been obtained by minimizing the total electronic energy. In general, the scale factor lies between the Slater and the Gaspar-Kohn-Sham limit of 1 and $\frac{2}{3}$, respectively. The variation that occurs as the different shells are populated is qualitatively understandable in terms of the inhomogeneity of the over-all charge distribution.

Electron transport is considered in the metallic range of metal-ammonia solutions; the scattering centers are (i) ions and ammonia dipoles weakly bound in solvated ion complexes, and (ii) free ammonia dipoles. They form a binary liquid mixture, but only one of the three possible partial structure factors is required. From the orientational degrees of freedom of the dipoles, it can be shown that much of the scattering is incoherent. This, combined with the observation that solvated ions are relatively weak scatterers, accounts in large measure for the high conductivities measured in metal-ammonia solutions.