Various theoretical and numerical problems relating to heliumlike systems in their ground states are treated. New developments in the numerical solution of the Schrödinger equation permit the solution of 256-body systems with hard-sphere forces. Using periodic boundary conditions, fluid and crystal states can be described; results for the energy and radial-distribution functions are given. A new method of correcting for low-lying phonon excitations so as to extrapolate the energy of fluids to an infinite system is described. A perturbation theory relating the properties of the system with pure hard-sphere forces to those with smoother, more realistic two-body forces is introduced. As in recent work on classical systems the potential is divided into two continuous parts: One is repulsive, one attractive, the latter being treated as a perturbation. The solution for the repulsive part is taken directly from the hard-sphere problem when the radius is identified as the scattering length of the repulsive part of the smooth potential. The convergence for the Lennard-Jones potential is very good. Using our numerical results for the hard-sphere problem, with phonon corrections, together with this perturbation theory, results for energy versus density agree with experiment within our error of (3-10)% except at high crystal densities. We carry further Schiff's recent application of this perturbation theory to ${\mathrm{He}}^3$ and conclude that antisymmetrization by the method of Wu and Feenberg is the reason for lack of agreement with experiment in that system.

The expansion of transport coefficients of gases in powers of the density makes a logarithmic divergence appear in the second-order correction to Boltzmann order term. This divergence arises from the sequences of four collisions among four isolated hard spheres. The number of distinct sequences may be reduced to 10 in the cases of the shear viscosity and the heat conductivity and to 9 for the self-diffusion coefficient. For these three transport coefficients the contributions of two sequences are computed in the first Enskog approximation and given in terms of elementary functions.

The dynamic properties of the molecular model proposed by Maier-Saupe (MS) for nematic liquid crystals are investigated. It is shown that the model predicts diffusive optic soft modes, describing nematic-order-parameter fluctuations which condense at the isotropicnematic stability limit. Since the MS Hamiltonian in its usual form does not exhibit the full symmetry of the high-temperature phase, no symmetry-recovering Goldstone mode is predicted. A rotationally invariant form of the Maier-Saupe Hamiltonian, on the other hand, predicts the existence of two different diffusive optic soft modes in the nematic phase, in addition to a doubly degenerate "magnon" mode which is the Goldstone mode of the isotropicnematic transition.

A cluster expansion is obtained for the coherent and incoherent dynamic structure factors in the case of a simple classical dense fluid. The expansion is useful in the case of fluids where the hard-core repulsive part of the interaction plays an important role. The first term in the expansion is given by the dynamic structure factor of a noninteracting system. The second term is obtained by solving the dynamics of a two-particle system with initial positions given by the pair-correlation function for the full system and initial velocities given by a Maxwellian distribution. The third term is obtained by solving the dynamics of a three-particle system, etc. Keeping only the first two terms, the effect of repeated binary collisions on the dynamic structure factor is studied in the case of a hard-core fluid and a Lennard-Jones (6,12) fluid with liquid-argon parameters. The results are compared with neutron-scattering experiments.

We calculate the Kapitza resistance $R_K\mathrm{}\left(T\right)\mathrm{}$ for a Cu-${\mathrm{He}}^4$ interface using the acoustic mismatch theory of Khalatnikov and of Mazo and Onsager. Included in the calculation are the effects of: phonon attenuation in the Cu as well as impedance matching due to the increased He density near the interface. We calculate $R_K\mathrm{}\left(T\right)\mathrm{}$ for several values of attenuation in the Cu; detailed calculations are displayed for the case of equal attenuations for longitudinal and transverse waves in the solid. Also considered are different attenuation profiles in the Cu. We use a density profile calculated from compressibility data and the Van der Waals attractive force between He and the Cu substrate. Our model includes the effects of a solid layer of He at the Cu surface, i.e., in such a He layer both longitudinal and transverse waves are allowed. Included in our calculations are the effects of different density profiles for the He. The calculations indicate that for suitable choices of the physical parameters, the theoretical results for $R_K\mathrm{}\left(T\right)\mathrm{}$ agree in magnitude as well as $T$ dependence with the experimental data. Unfortunately, the important physical properties have not yet been experimentally determined and definitive test of this theory must await such data.

The photoionization cross section for ${\mathrm{H}}_2$ per atom has recently been reported to be ∼ 45% larger than the atomic cross section at energies of 5.41 and 8.39 keV. This note relates this observation to the differences in electron density at the nucleus in atomic and molecular hydrogen and points out that the enhancement at high photon energies is unique for molecular hydrogen.

Recently Amoruso and Johnson (AJ), using a relativistic formulation, have pointed out that earlier theories of exchange-polarization effects on hyperfine constants in atoms had omitted an important contribution. This contribution would have serious implications for a number of solid-state hyperfine calculations. We show that in a correct Hartree-Fock formulation, the contribution proposed by AJ vanishes exactly, a conclusion that is also substantiated by results of recent many-body perturbation-theory calculations. The need for a reevaluation of relativistic effects on exchange core polarization in Hartree-Fock theory is emphasized.

Beam-foil measurements of the lifetimes of the $2S_{\frac{1}{2}}$ states in hydrogenlike fluorine and oxygen have been performed. The experimental results of 237 ± 17 nsec (fluorine) and 453 ± 43 nsec (oxygen) are in good agreement with the respective theoretical values of 228 and 464 nsec. Our results indicate that meaningful beam-foil lifetime measurements can be made on systems whose lifetimes are in the hundreds-of-nanosecond region and whose decay can be followed over only a fraction of a decay length.

The conservation of angular momentum has been studied experimentally in connection with thermomagnetic torque experiments. It has been determined that the outer cylinder experiences a torque equal in magnitude and opposite in direction to that experienced by the inner cylinder. This result implies that the net angular momentum of the system remains constant.

An extension of an earlier calculation on positronium hydride PsH is presented. In the earlier work, the wave function was expressed as an exponential term $\exp (-A{r}_1-B{r}_2-C{r}_{1p}-D{r}_{2p})+\exp (-B{r}_1-A{r}_2-D{r}_{1p}-C{r}_{2p})$, times a twelve-term polynomial in the interparticle coordinates: $r_1$, $r_2$, $r_{1p}$, $r_{2p}$, and $r_{12}$ (the electrons are labeled 1 and 2; the positron is labeled as $p$). The coefficients in the polynomial were determined by the variational method. In the present work, the number of terms is increased; the coordinate $r_p$ is included in the polynomial; the wave function is tested for the four cusp conditions; and an annihilation rate and the relaxation of the daughter system are calculated. The new binding energy, 0.794 eV, is greater than the earlier result by 0.137 eV. The annihilation rate is found to be 2.22 ${\mathrm{nsec}}^{-1\mathrm{}}$, with the $1s$ state being the most probable daughter-occupation state. The electron-positron, electron-nucleus, nucleus-positron, and electron-electron cusp values are, respectively, -0.4398, -1.065, -0.0102, and 0.1126. The values of the repulsive cusps definitely show that the wave function has not yet converged to the exact function in all regions of three-particle space. A search for a bound excited state of PUSH with the same symmetry of the ground state was unsuccessful.

The superfluid fraction $\frac{{\rho }_s}{\rho }$ of He II in Vycor porous glass has been studied in the range (approximately) 1.6-2.0 K using fourth sound. There is a qualitative difference in the temperature dependence of $\frac{{\rho }_s}{\rho }$ between this work and that obtained for He II in comparable packed powders.

The polarized-orbital method is used to calculate the photoionization cross sections for sodium and potassium in direct analogy to earlier calculations for lithium. However, in the present case, unsatisfactory results are obtained which suggest that the polarized-orbital method has limited predictive capabilities.

An expedient self-consistency scheme for the determination of parameters of atomic analytic potentials is presented. The method is applied to a simplified one-parameter potential. Values of the parameter for the ground configuration of all atoms are given. Rules to estimate the parameter for excited configurations and ions are also provided.

A new calculation of the $M1\mathrm{}$ decay rates of the metastable $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ states of two-electron ions is presented. The calculation is based on the Furry bound-interaction representation of quantum electrodynamics and expansion in powers of $\alpha Z$ is avoided. The basic one-electron states are constructed from solutions to the Dirac equation including the ground-state Dirac-Hartree-Fock potential. Correlation and transverse-photon-exchange effects, both of relative order $Z^{-1\mathrm{}}$, are included in the calculation by the perturbation expansion of the $S$ matrix in powers of $\alpha$. Decay rates calculated to lowest order in powers of $\alpha$ are smaller than previously reported rates. When correlation and transverse-photon-exchange corrections are included in the calculation the resulting rates agree well with previous calculations. We estimate that the present values are more accurate than the older results for $Z>\mathrm{}12\mathrm{}$, while for smaller $Z$ the older results are expected to be better. The close agreement between the present calculations and previous theoretical results confirms the smallness of both higher-order relativistic effects and of higher-order correlation corrections in calculations of this type.

A charge-exchange optical-pumping experiment has been performed to measure the ratio $\frac{g_I\left({}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}_{}^{+}{}_{}{}^{}\right)}{g_J\left({}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}\right)}$. The NMR frequency of free ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}_{}^{+}{}_{}{}^{}$ ions polarized by charge-exchange collisions with optically pumped ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$ atoms was measured along with the ($F=2,M=-2\mathrm{}\leftrightarrow F=2,M=-1\mathrm{}$) Zeeman transition frequency of ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$ in a magnetic field of ∼ 55 G. The magnetic field was produced in a shielded solenoid. The 30-${\mathrm{cm}}^3$ cylindrical optical-pumping cells were filled with a Ne buffer gas, and the ions were produced in a weak continuous electrodeless rf discharge which was run in a sidearm attached to the cells. The NMR frequency was ∼ 76 kHz and the charge-exchange and rf-broadened NMR linewidth was 60 Hz. The Zeeman frequency was ∼ 39 MHz and the Zeeman linewidth was 80 Hz due to the inhomogeneity of the magnetic field. Our result is $\frac{g_I\left({}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}_{}^{+}{}_{}{}^{}\right)}{g_J\left({}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}\right)}=-4.969\mathrm{}934\left(12\right)\mathrm{}\times {10}^{-4\mathrm{}}$, which can be compared with a previously measured value of $\frac{g_I\left({}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}_{}^{+}{}_{}{}^{}\right)}{g_J\left({}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}\right)}=-4.969\mathrm{}9147\left(44\right)\mathrm{}\times {10}^{-4\mathrm{}}$ to obtain the difference in the shielding constants of the atom and ion, $\sigma \left({}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}\right)-\sigma \left({}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}_{}^{+}{}_{}{}^{}\right)=(3.8\mathrm{}\pm 2.6)\times {10}^{-6\mathrm{}}$.

A systematic procedure is proposed for obtaining a correlated multiconfiguration Hartree-Fock (MCHF) wave function for the $1s^{2}2s^2{}_{}{}^1{}_{}{}^{}S$ ground state of Be. With $\Phi _{}^{\mathrm{MCHF}}{}_2{}^{}=a_1|1\mathrm{}{s}^{2}2s^2〉+a_2|1\mathrm{}{s}^{2}2p^2〉$ as a zero-order approximation, a first-order correction ${\Phi }^{\mathrm{}\left(1\right)\mathrm{}}$ is derived consisting of sums of the type $\Sigma {n\ge 3}^{}\Sigma {m\ge 3}^{}{c}_{nm}|\alpha \beta \mathrm{nlm}{l}^{\prime }{}_{}{}^1{}_{}{}^{}S〉$, where $\alpha ,\beta \subset \mathrm{}\{1s,2s,2p\}\mathrm{}$. By transforming the basis of radial functions a "reduced" form consisting of a single sum is obtained for each such double sum. A numerical MCHF procedure is used to compute the separated pair-correlated functions. These functions are then combined in a configuration-interaction calculation. For Be, 99.1% of the correlation was accounted for in 52 configurations, yielding a total energy of - 14.66587 a.u.

The interaction protentials between a spherically symmetric atom (Cs) and a highly conducting surface (gold) or a dielectric surface (glass) are investigated by the atomic-beam-deflection technique. The observed beam profile is least-squares fitted to an $r^{-3\mathrm{}}$ potential. The derived interaction constant for the gold surface is 0.59 and 0.67 of the values predicted by Bardeen and Mavroyannis, respectively. A glass surface is found to have an interaction constant 0.65 that of gold. The measurements have also been obtained for a polar molecule (CsCl). With a gold surface the observed beam profile is almost identical to that for stainless steel (reported earlier) in spite of their difference in dc conductivity. Further, the observed constant for an insulator (glass surface) is 0.86 that of gold. With gold, the interaction constant obtained for a cesium-halide molecule, with a strong permanent dipole moment, is smaller than that for a Cs atom with zero dipole moment.

The stability of a monochromatic constant-intensity laser beam propagating through a resonant medium is considered. It is found that many absorbers should exhibit a region of negative conductivity and, consequently, amplify perturbations. The associated gain is dependent on a number of variable parameters, such as laser-beam intensity, perturbation frequency, relaxation times, degeneracy, transverse mode, inhomogeneous broadening, etc. Putting absorbers inside Fabry-Perot interferometers allows the construction of plane-wave devices with a bistable output.

Configuration-interaction calculations, using only Hartree-Fock discrete-state configurations, are reported for the two perturbed series, $3sn{f}^{3}F$ of Al II and $3s^{2}n{d}^{2}D$ of Al I. While good results are obtained for term values and oscillator strengths in Al II, this is not the case for Al I, where the calculations predict the $3s3p^2$ perturber to be expelled into the continuum. To study this case more closely, superposition of configurations (SOC) calculations, which include all correlation effects, were carried out on the five lowest ${}_{}{}^2{}_{}{}^{}D$ states of Al I. These results indicate that the perturber actually remains in the discrete spectrum, but loses its identity and is smeared out over the entire series. New Rydberg orbitals are extracted from the SOC wave functions which are quite different from the Hartree-Fock but very similar to those of the Coulomb approximation. Various truncations of the SOC functions are also analyzed and the implications for the correlation problem discussed.

Radiative-lifetime studies have been carried out for resonance transitions of silicon I, II, and III in the ultraviolet using an electron-beam phase-shift apparatus. Lifetimes ranging from 0.03 to 220 nsec were determined. Significant discrepancies with earlier results were found for oscillator strengths of certain transitions, e.g., the Si II 1190-1194-ÅA multiplet, the SiII 1808-ÅA multiplet, and the SiIII 1206-ÅA multiplet, which are important transitions in the establishment of the interstellar abundance of silicon. In making these measurements, some very short lifetimes were encountered, requiring that we make strenuous efforts to avoid errors in the reference phase. This led to redeterminations of the radiative lifetimes for the cascade-free transitions in NeII at 462 ÅA and in NII at 1085 ÅA, with lifetimes of 0.15 ± 0.03 and 3.0 ± 0.1 nsec, respectively.