Helium-film transfer rates σ have been measured as a function of level difference $z$ and height to the beaker rim $h$ for filling clean glass and neon-coated beakers. Observed transfer rates as a function of level difference or pressure head are described by: $\sigma \mathrm{}\left(z\right)=\frac{1}{[A-B\ln z(\mathrm{cm}\left)\right]}$. For $T=1.65\mathrm{}$ K and $h=7\mathrm{}$ cm, we find $A=(1.80\mathrm{}\pm 0.09)\times {10}^4$ sec/${\mathrm{cm}}^2$ and $B=(8.9\mathrm{}\pm 1.9)\times {10}^2$ sec/${\mathrm{cm}}^2$. For $T=1.28\mathrm{}$ K and $h=7\mathrm{}$ cm, we find $A=(1.35\mathrm{}\pm 0.02)\times {10}^4$ sec/${\mathrm{cm}}^2$ and $B=(8.3\mathrm{}\pm 1.4)\times {10}^2$ sec/${\mathrm{cm}}^2$. Dependence of the transfer rate on film height is $\sigma \mathrm{}\left(h\right)=10\left(\frac{{\rho }_s}{\rho }\right)h^{-(0.26\mathrm{}\pm 0.05)}\times {10}^{-5\mathrm{}}$ ${\mathrm{cm}}^3$. For a glass beaker coated with Ne, the transfer rate is 16% less than the transfer rate for the same uncoated beaker. This is in reasonable agreement with our calculated helium-film thickness for a Ne substrate of $2.3 h^{-\frac{1}{3}}\times {10}^{-6\mathrm{}}$ cm.

Bromine and iodine ions, accelerated to energies between 6 and 15 MeV, were passed through thin gas targets of ${\mathrm{H}}_2$ and He. Nonequilibrium charge distributions were measured, from which cross sections for capture and loss of one or more electrons by the heavy ions were determined by means of a least-squares fitting technique. The cross sections are discussed with regard to their functional dependence on the charge and velocity of the ions. Owing to the unprecedented precision of the results, characteristic irregularities were revealed in the charge dependence of the cross sections for both capture and loss of one and two electrons. These effects are attributed to the influence of shell structure and residual excitation of the ions.

A statistical model, similar to that of Everhart and Kessel, (E-K) is described for ${\mathrm{N}}^{+}$-Ar and ${\mathrm{O}}^{+}$-Kr collisions of the type $X^{+}+Y\to X^{+m}+Y^{+n}+(m+n-1\mathrm{})e$. The E-K model utilizes coincidence data on inelastic energy distributions (usually Gaussian) and average probabilities ${\overline{P}}_n\left(\overline{E}\right)$ for $n$-fold ionization to construct (by an unfolding procedure) intrinsic ionization probabilities $P_n\mathrm{}\left(E\right)\mathrm{}$ for collisions wherein $X$ and $Y$ are of the same species. In the present case of asymmetric collisions, it is necessary to devise a scheme to determine the manner in which the average inelastic energy ($\overline{Q}$) is divided (into ${\overline{E}}^{\prime }$ and ${\overline{E}}^{\prime \prime }$) between the two colliding partners. Three such schemes (shown to be mutually consistent) are presented, one of which assumes that the average inelastic energy associated with an $m$, $n$ event varies linearly with the spectroscopic energy deficits for the ions in charge states $m$ and $n$ (${\overline{Q}}_{\mathrm{mn}}=A+B{U}_m^{\prime }+C{U}_n^{\prime \prime }$), and calculates the required coefficients by a least-squares procedure. Values of ${\overline{E}}_m^{\prime }$ and ${\overline{E}}_n^{\prime \prime }$ are then calculated from the assumption that the outer shell electrons in the two atoms contribute equally to $A$. The E-K model is then applied to each atomic species investigated. Statistical assumptions tested are that ${\overline{E}}_m^{\prime }$ is independent of $n$ (and ${\overline{E}}_n^{\prime \prime }$ is independent of $m$), and that the intrinsic ionization probabilities depend only upon the inelastic energy $E$ received by the atoms even when the atom collides with one of another species. The probabilities obtained for argon ions in ${\mathrm{N}}^{+}$-Ar collisions agree reasonably well with those obtained for ${\mathrm{Ar}}^{+}$-Ar collisions. The data available on the ${\mathrm{O}}^{+}$-Kr and ${\mathrm{Kr}}^{+}$-Kr reactions are somewhat sparse and preclude a thorough analysis, although the results are encouraging enough to warrant further experimental investigation.

Cross sections, differential in ejection energy and angle, for electron emission from nitrogen following proton impact were measured for protons with energies from 0.3 to 1.7 MeV. Electrons were detected at emission angles from 20° to 130° with energies from a few eV to approximately 4000 eV. Cross sections differential in energy were obtained from the doubly differential cross sections by integration with respect to the emission angle. These results were compared with cross sections calculated from binary-encounter theory. Agreement between the calculated and measured cross sections was within experimental uncertainties (25%) throughout most of the energy range of the ejected electrons. $K$-shell ionization cross sections for nitrogen were also estimated from the intensity of the $K$ Auger electrons emitted following proton impact.

Application of positive-ion energy-loss spectrometry has been extended to include experimental determination of absolute excitation cross sections of ground-state helium ions. Helium ion-atom collisions were studied for impact energies ranging between 20-100 keV, in 10-keV intervals. The data were taken with an apparatus resolution between 0.6-0.8 eV full width at half-maximum (FWHM). Cross sections for transitions from ground state to the second and third principal quantum levels of the ion plotted as a function of impact energy were still rapidly increasing at 100 keV. The cross sections at this energy were (1.64 ± 0.28) × ${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$ for ${\mathrm{He}}^{+}\left(1\mathrm{}{}_{}{}^2{}_{}{}^{}s_{\frac{1}{2}}^{}{}_{}{}^{}\right)\to {\mathrm{He}}^{+}\mathrm{}(n=2\mathrm{})\mathrm{}$ and (3.46 ± 0.45) × ${10}^{-19\mathrm{}}$ ${\mathrm{cm}}^2$ for ${\mathrm{He}}^{+}\left(1\mathrm{}{}_{}{}^2{}_{}{}^{}s_{\frac{1}{2}}^{}{}_{}{}^{}\right)\to {\mathrm{He}}^{+}\mathrm{}(n=3\mathrm{})\mathrm{}$.

Using a one-state approximation in the Faddeev equations, the ground-state energies of several three-particle Coulomb systems are computed and compared with the earlier variational results. The simplicity and general applicability of this method are in contrast with the variational techniques. Our results also give an idea of the accuracy involved in a one-state approximation for the Faddeev kernel. Some major numerical difficulties are illustrated. Complete analytical expressions for the Faddeev kernel in the two-state approximation are given in an appendix.

The excitation of ground-state hydrogen atoms to the $2s$ state by the impact of electrons with energies of 1 to 50 Ry (13.6 to 680.3 eV) has been calculated in the distorted-wave approximation with exchange included. The angular distributions of the scattered electrons at 1 and 4 Ry are compared with those derived from the close-coupling calculations by Burke, Schey, and Smith, and are compared with four different plane-wave theories at all energies calculated. Taking the close-coupling results as a standard, it is found that the distorted-wave angular distributions represent an improvement over those of the plane-wave theories.

The atomic-beam magnetic-resonance technique has been used to determine the hyperfine-interaction constants $A$, $B$, and $C$ and electron $g$ values $g_J$ for all previously unstudied atomic levels of ${\mathrm{La}}^{139}$ below 9000 ${\mathrm{cm}}^{-1\mathrm{}}$. The results are analyzed in detail in terms of a set of eigen-vectors spanning the three configurations $5d6s^2$, $5d^{2}6s$, and $5d^3$. Corrections for hyperfine and Zeeman interactions between all low-lying states are carried out in intermediate coupling. The value deduced from the observed hyperfine structure for $Q$, the ${\mathrm{La}}^{139}$ nuclear ground-state electric-quadrupole moment, is influenced strongly by taking account of (a) the large recently found configuration mixing between $5d6s^2$, $5d^{2}6s$, and $5d^3$ and (b) the rather substantial Sternheimer shielding effects. The effects (a) and (b), though both about 30%, are in opposite directions and partially cancel. The value obtained is $Q=(+0.22\mathrm{}\pm 0.03)b$. Although the order of consistency between the experimental results and theory is encouraging, a number of problems remain.

The absorption spectrum of the negative ion of fluorine has been observed in shock-heated vapors of CsF. The photodetachment cross section of the fluorine ion has been measured in the wavelength region between 2100 and 3600 Å. Results are found to be in reasonable agreement with the calculated values of Robinson and Geltman.

The electronic recombination coefficient of ${\mathrm{He}}_3^{+}$ under thermalized conditions at 80 °K is (3.4 ± 1.5) × ${10}^{-6\mathrm{}}$ ${\mathrm{cm}}^3$ ${\sec }^{-1\mathrm{}}$. The electron-temperature dependence of this coefficient is $T_e^{-\chi }$, $〈\chi 〉=1.22\mathrm{}$, $0.98<\mathrm{}\chi <1.60\mathrm{}$. This is applicable when both the gas and ion temperatures are near 80 °K. The fragments of the recombination process have not been identified but the results indicate dissociation into ${\mathrm{He}}_2^{*}$ + He.

We have calculated discrete and continuum generalized oscillator strengths for all the occupied shells of He-Na and the $3s$ and $3p$ continuum generalized oscillator strengths for Ar. The calculations are done with a one-electron common-central-potential unrelaxed-core approximation. The generalized oscillator strengths were used to compute proton-excitation and -ionization cross sections and stopping power, electron-ionization cross sections, and neutral-neutral-ionization and -stripping cross sections. For proton ionization above 200 keV and electron ionization above 200 eV, the calculated cross sections are in better than 20% agreement with experiment. The calculated proton stopping power is lower than experiment by 25% at 100 keV and within 10% at 1 MeV. The computed He-He ionization cross section agrees with the measurement by Wittkower, Levy, and Gilbody, while the computed He-Ar ionization cross section is a factor of 5 higher than the measurement by Puckett, Taylor, and Martin.

The scattering of ${\mathrm{He}}^{+}$ by He, Ne, and Kr is studied in the energy range 1.00-3.00 keV and in an angular region from 0° to about 3°. These studies yield information on the probability of charge exchange $P_0$ as a function of beam energy and scattering angle. For the ${\mathrm{He}}^{+}$ + He case, the positions of the maxima and minima of $P_0$ generally agree with those of previous experiments. A wider range of $P_0$ values is obtained, however, and the current results lend more credence to a two-state resonant-charge-exchange theory for the ${\mathrm{He}}^{+}$ + He collision. In the ${\mathrm{He}}^{+}$ + Ne collision, the charge-exchange differential cross section is found to increase with increasing energy, while the non-charge-exchange differential cross section decreases. An unexpected result of the current studies on Ne is that the positions of the maxima and minima of the scattered neutral He (and of $P_0$) are independent of energy. These results are not consistent with a curve-crossing model for the charge-exchange process, which predicts an angular structure dependent on energy. Studies of the ${\mathrm{He}}^{+}$ + Kr collision show a broad forward He peak with no pronounced structure in the energy and angular region investigated.

The photo-ionization cross sections of the $1{}_{}{}^1{}_{}{}^{}S$ and $2{}_{}{}^1{}_{}{}^{}S$ states of He were evaluated in the energy regions 0.20-2.40 Ry and 3.15-3.30 Ry. The 56-term ${}_{}{}^1{}_{}{}^{}S$ bound-state wave functions obtained by Pekeris were used for the initial states. An expansion into a complete discrete basis set (a modification of the close-coupling method used in electron-atom scattering) was carried out for the ${}_{}{}^1{}_{}{}^{}P$ final-state continuum wave functions. Particular attention was given to the processes where the ejected photoelectron leaves the ${\mathrm{He}}^{+}$ ion in an $n=2\mathrm{}$ excited state. The results obtained from the length and velocity expressions for the photo-ionization cross sections show an agreement to within 1% in the lower-energy region. Good accuracy is achieved for the negative-power moments of the oscillator-strength distributions.

One of the oldest methods suggested for treating the effect of charge polarization on elastic scattering is revived by the use of certain physically reasonable assumptions, and is shown to lead to results, in the limit of small scattering angles and high incident energies, which are in quantitative agreement with experimental and theoretical expectations. The theory is worked out in detail for one- and two-electron atoms, and the extension to more complex systems is also discussed. The effect of charge polarization on the elastic differential cross section for 500-eV incident electrons on He is calculated and compared with the experimental results of Bromberg and the theoretical results of LaBahn and Callaway. The agreement is good over the angular range $0°\le \theta <6\mathrm{}°$ if exchange scattering contributions are included.

The problem of the two-channel positron-hydrogen rearrangement collision is studied with the formalism of the generalized variational bounds. For the zero total partial wave, a reasonably complete treatment of this scattering system is presented, including a detailed discussion of the energy spectrum of the closed-channel Hamiltonian $M$. The coupling of the open channels to the closed channels gives rise to the effective interaction potentials, and these distortion terms are estimated variationally using the bound property of $M$. The orthogonality of $M$ to the open-channel space is maintained by the presence of the energy-shift operator $S$, and the role of $S$ is demonstrated in detail numerically, which produces essential cancellation of various terms. Partly owing to the crudity of the trial functions used, we have not been able to find resonance states below the first excitation threshold. Bounds on the diagonal $K$ matrix elements and eigenphase shifts are presented.

We use the memory-function formalism to investigate ${\tilde{G}}_s (\overrightarrow{\mathrm{k}},\overrightarrow{\mathrm{p}},{\overrightarrow{\mathrm{p}}}^{\prime },t)$, the time autocorrelation function for the single-particle density in phase space and $S_s (\overrightarrow{\mathrm{k}},w)$, the incoherent scattering function of Van Hove. Following a recent treatment for coherent neutron scattering by Akcasu and Duderstadt, we derive a formally exact equation for ${\tilde{G}}_s$. If we assume that the relevant memory function is separable and given by ${\tilde{\varphi }}_s (\overrightarrow{\mathrm{k}},\overrightarrow{\mathrm{p}},{\overrightarrow{\mathrm{p}}}^{\prime },t)={\tilde{\varphi }}_s (\overrightarrow{\mathrm{p}},{\overrightarrow{\mathrm{p}}}^{\prime },o)\tilde{\Phi }(\overrightarrow{\mathrm{k}},t)$, then the equation for ${\tilde{G}}_s$ reduces to a generalized Fokker-Planck equation which can be exactly solved. We use two simple forms for $\tilde{\Phi }(\overrightarrow{\mathrm{k}},t)$, a Gaussian and an exponential, to study the analytical solution both numerically and in various limits. We also compare these results with those obtained in the molecular dynamics computations by Nijboer and Rahman and discuss the extent of validity of the separability assumption for the memory function.

Measurements are reported of ${\left(\frac{\partial P}{\partial T}\right)}_{{\rho }_c}$ on the critical isochore of ${\mathrm{He}}^4$ very close to the critical temperature. The measurements are well represented by an equation of the form ${\left(\frac{\partial P}{\partial T}\right)}_{{\rho }_c}=D+B^{*}t+A^{*}t\ln \mathrm{}\left(t\right)\mathrm{}$, where $t=\frac{(T-T_c)}{T_c}$ in the interval $-0.016<t<\mathrm{}0.013\mathrm{}$. They are used with Moldover's heat-capacity data to calculate ${\left(\frac{\partial \mu }{\partial T}\right)}_{{\rho }_c}$, which is found to be a linear function of temperature in the same temperature interval and to be analytic at the critical point. A comparison of the 1958 ${\mathrm{He}}^4$ vapor-pressure temperature scale ($T_{58}$) with the NBS Provisional Scale 2-20 K (1965) indicates that $T_{58}$ is a very unsuitable temperature scale for ${\mathrm{He}}^4$ critical-point work.

The He II-He I transition has been investigated by measuring the temperature at which the conductivity of He II exhibits a sharp drop. It is found that this temperature is a function of the heat current $Q$. A qualitative explanation in terms of the Ginzburg-Pitaevskii phenomenological theory is suggested.

The ground state of a one-dimensional system of many bosons interacting through a repulsive $\delta$-function potential is studied when the coupling parameter $\gamma$ of the system is small. The procedure is based on the variational analysis in the Bijl-Dingle-Jastrow wave-function space. The ground-state energy, determined in a series form in powers of ${\gamma }^{\frac{1}{2}}$ and truncated after the third leading term, is found to be in fair agreement with exact results of Lieb and Liniger over a range of the coupling parameter extending up to $\gamma =6\mathrm{}$. Two slightly different approaches are considered, and they are shown to be equivalent.

A new method has been designed for obtaining the hyperfine optical pumping of Na vapor. The pumping lamp is placed in a magnetic field and the light emitted in the field direction is used for excitation after crossing a circular polarizer selecting one of the Zeeman lines. This method has two interesting features: (i) The atoms can be pumped either in the lower or in the upper hyperfine sublevel by simply rotating a polarizer by an angle of $\frac{1}{2}\pi$; (ii) the hyperfine pumping is obtained using both the $D_1$ and $D_2$ resonance lines without filtering losses. The pumping efficiency is good and it has been possible to measure the spin-exchange cross section between sodium atoms by studying the hyperfine relaxation rates as a function of the sodium density. The result is ${\sigma }_{\mathrm{ex}}=(1.109\mathrm{}\pm 0.005)\times {10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$.