Cross sections for production and destruction of fast ${\mathrm{He}}^0$ atoms in triplet states have been measured for 10- to 30-keV ${\mathrm{He}}^{+}$ ions incident on gas targets of Kr, ${\mathrm{N}}_2$, and Ne. Values of the fractions of neutral ${\mathrm{He}}^0$ atoms in the triplet metastable state emerging from thin targets of Kr, ${\mathrm{N}}_2$, and Ne are 0.12±0.005, 0.06±0.03, and 0.03±0.02, respectively, for incident ${\mathrm{He}}^{+}$ energies of 30 keV.

The need for an accurate description of the electronic structure of the important laseractive ion ${\mathrm{Nd}}^{3+}$ stimulated this work. We calculated self-consistent-field wave functions by the analytical-expansion method for the ground state of the laser-active ion ${\mathrm{Nd}}^{3+}\mathrm{}(Z=60\mathrm{})\mathrm{}$, $4f^3$, ${}_{}{}^4{}_{}{}^{}I$. The results represent the most accurate wave functions for ${\mathrm{Nd}}^{3+}$ published. All the exponents of the basis functions in the analytical expansion were exhaustively optimized. The virial theorem was satisfied to seven significant figures. Values of $〈{\mathcal{r}}^n〉$ for the $4f$ orbital are included.

An improved form of semiclassical radiation theory is developed which includes the effect of the atom's radiation field back on the atom. This formalism is applied to the problem of a single "two-level atom" interacting with a monochromatic field. The resulting equations are solved without resorting to time-dependent perturbation theory, and are found to predict the behavior of the system over times long compared with the lifetime for spontaneous transitions. Not only stimulated emission and absorption, but also spontaneous emission with the proper Einstein $A$ coefficient, and a frequency shift which agrees at least semiquantitatively with the Lamb shift are described. In addition, several nonlinear effects involving the interference between spontaneous and stimulated radiation are described, and new experiments which might detect such effects are suggested.

Generalized variational expressions are presented for calculating rigorous lower bounds to the true expectation value $〈\Psi \mathrm{}\left|F\right|\mathrm{}\Psi 〉$ of a positive semidefinite operator $F$. These extended formulas, which involve an additional variational function, always lead to an improvement over the results previously obtained. The improvement is illustrated numerically with an application to various properties of the helium-atom ground state.

A simple theory of high-energy neutron scattering from liquid ${\mathrm{He}}^4$ is developed. The inelastic scattering cross section for this process is related, for sufficiently high momentum transfer, to two parameters characterizing the ${\mathrm{He}}^4$ momentum distribution. These two parameters are the average kinetic energy per particle and the fraction of particles in the zero-momentum condensate. Comparison of the theory with recent experimental data indicates that the condensate fraction $\frac{{\rho }_0}{\rho }$ is approximately 0.06 at $T=1.27\mathrm{}°$K.

A unified theory of spin-lattice relaxation in solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is developed by starting from the complete Hamiltonian of the system. The "three-bath model" for the system is presented, and rate equations are derived for relaxation among the baths. A new mechanism for relaxation of exchange energy, viz., the modulation of dipole-dipole interaction by diffusion and by exchange itself, is identified and its relation to other processes derived. By inclusion of this mechanism and the simultaneous consideration of the three baths, the rate equations can be cast in the form that was written down phenomenologically in earlier work by considering the three baths in series. It is shown, however, that if the new mechanism is included in the customary sense in the phenomenological equations, it is not possible to explain the experimental results. A critique of the existing theory of relaxation due to off-diagnoal elements of the exchange operator is given, and an alternative theory presented. Finally, we give an interpretation of the experimental results on the basis of the theory.

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.