Several states of Pb were excited and studied in detail by simple optical techniques with data averaging. Cross sections for depolarization of alignment (in ${\mathrm{\AA }}^2$ at 850°K, ±20%: He, 28; Ne, 46; Ar, 73; Xe, 105) and upper limits on quenching cross sections were determined for the ${}_{}{}^3{}_{}{}^{}P_1^o{}_{}{}^{}$ excited state of ${\mathrm{Pb}}^{208}$ by monitoring the reduction in the polarization of the fluorescence as a function of foreign-gas pressure. Optical-pumping Zeeman resonances were detected in optically produced and polarized ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$, and ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ metastable states and $g_J$ ratios determined in ${\mathrm{Pb}}^{208}$: $\frac{g_J\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)}{g_J\left({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)}=1.17698\mathrm{}\left(15\right)\mathrm{}$ and $\frac{g_J\left({}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}\right)}{g_J\left({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)}=0.96158\mathrm{}\left(33\right)\mathrm{}$. The $g_J\left({}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}\right)$ due to Lurio and Landman implies $g_J\left({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)=1.2753\mathrm{}\left(4\right)\mathrm{}$ and $g_J\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)=1.5010\mathrm{}\left(5\right)\mathrm{}$. From the dependence upon foreign-gas pressure of the optical-pumping recovery times after rf depolarization, the following cross sections for depolarization of alignment were deduced for the ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ states, respectively (in ${\mathrm{\AA }}^2$ at 813 °K, ±20%): He, 27, 36; Ne, 27, 35; Ar, 51, 59; Kr, 64, 76; Xe, 123, 159; ${\mathrm{H}}_2$, 26, 39; ${\mathrm{N}}_2$, 73, 88. The ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ quenching cross sections were found to be less than ${10}^{-21\mathrm{}}$ ${\mathrm{cm}}^2$ for the rare gases, ≤1.3×${10}^{-21\mathrm{}}$ ${\mathrm{cm}}^2$ for ${\mathrm{N}}_2$, 24(5)×${10}^{-20\mathrm{}}$ ${\mathrm{cm}}^2$ for ${\mathrm{H}}_2$, and ≤0.3×${10}^{-20\mathrm{}}$ ${\mathrm{cm}}^2$ for $D_2$. The ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ radiative lifetime of 53±30 msec was also extracted. Comparisons are made between some of the above experimental quantities and theoretical predictions.

We have measured the cross section for production of metastable ($2S$) atoms by the process of dissociative excitation of molecular deuterium by electron impact. The measurement includes the quantitative evaluation of detection efficiency, density, and geometrical factors necessary to establish an absolute scale on a purely experimental basis. The method depends on the application of an rf field at the Lamb-shift frequency (1059 MHz) to quench the metastables at the point of excitation. The radiation induced by the applied field is isotropic so that the absolute cross section depends on a simple solid-angle correction. The cross sections at 23.8 and 39.1 eV are 2.97×${10}^{-18\mathrm{}}$ and 3.40×${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$, respectively, with a probable error estimated to be ± 14%. The energy dependence of the cross section was also measured from threshold to 500 eV.

The results of our earlier charge-exchange measurements in ${\mathrm{He}}^{+}$ + He collisions are extended down to scattering angles of 0.05° at energies of 1.00, 2.00, and 3.00 keV. The structure in the probability of charge exchange as a function of angle is clearly demonstrated. At very small angles the incident beam interferes with scattering measurements, and a technique for studying structure in this angular region is described.

Systematic studies of atomic lifetimes and oscillator strengths in the homologous atoms Ga, In, Tl and ${\mathrm{Ga}}^{+}$, ${\mathrm{In}}^{+}$, ${\mathrm{Tl}}^{+}$ have been performed by measuring mean lives of excited atomic states using the beam-foil technique. The lifetimes of the lowest $S$ levels in the neutral atoms, 6.9 ±0.5, 7.5±0.7, and 7.7±0.5 nsec, respectively, for Ga, In, and Tl, are in agreement with recent reported values obtained by Hanle-effect and phase-shift techniques. Identical $f$ values are found for homologous transitions in Al, Ga, In, and Tl, when configuration mixing can be excluded. The experimental results are compared with theoretical data based upon a single-configuration Coulomb approximation for neutral atoms and with a modified self-consistent-field approach for singly ionized atoms.

Reactions involving a few open channels with particle rearrangements are treated by a combination of the theory of sequential projections and the quasiminimum principle. A simple variational procedure of evaluating the resonance energies is proposed, which does not make explicit use of the full open-channel projection operators nor requires the exact Green's function in the coupled static approximation. A part of the open-channel problem is also treated variationally using the double functional, so that the resulting scattering parameters are expected to have the quasibound property. The positron-hydrogen scattering system above the pickup threshold is studied in detail.

Differential cross sections for excitation of the $6{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ and $6p^{\prime }{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ states of mercury have been measured at angles where minima of the generalized oscillator strengths could be expected. The minima appeared for both channels. Contrary to the results of the first Born approximation, their position depends not only on the momentum transfer but also on the primary energy. The confidence of some authors in the reliability of the Born approximation for inelastic scattering is not justified.

An eikonal distorted-wave theory is proposed for inelastic electron-atom collisions at intermediate energies. The primary interaction, responsible for the transition, is treated to first order, while the initial- and final-state interactions are taken into account by using the eikonal approximation. Direct and exchange collisions are both considered. Detailed numerical calculations are performed for the excitation of the $n=2\mathrm{}$ levels of atomic hydrogen by electron impact. The results for the differential excitation cross sections are compared with those obtained in the Glauber eikonal approximation at small scattering angles.

The multiple-scattering theory of Glauber is used to investigate the importance of double scattering in the collisions of fast electrons with diatomic molecules. By representing the atomic potentials as a sum of Yukawa terms, comparisons of scattering amplitudes calculated by the partial-wave analysis and the high-energy approximation (Moliere) are made over a wide range for several atoms. At 40 keV the amplitudes are found to be numerically equivalent to within a few percent, with the agreement worsening with decreasing energy. Calculations for ${\mathrm{N}}_2$ at 0.5 and 40 keV and for ${\mathrm{I}}_2$ and ${\mathrm{U}}_2$ for 40-keV incident electron energies are presented; these results can be regarded as quantitative estimates of the importance of double scattering for a system of two atoms as a function of atomic number. Our ${\mathrm{U}}_2$ calculation is compared with a similar calculation by Hoerni. In contrast to his findings, the double-scattering contribution to the differential cross section is seen to be negative in the small-angle region. In any event, for all cases considered, the multiple-scattering correction is quite small, amounting to no more than ±2% of the differential cross section for any angle of scattering.

The cross sections for $K$-shell ionization of carbon have been measured for incident protons with energies from 0.3 to 2.0 MeV. These cross sections were obtained from Auger-electron yields measured for methane, ethane, ethylene, and acetylene gas targets assuming that each $K$-shell vacancy results in the emission of an Auger electron. The molecular surroundings of the carbon atom were found to influence the $K$-Auger-electron yield; e.g., for 1.0-MeV-proton impact, the carbon-$K$-shell ionization cross section was 1.00×${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$ for acetylene and 1.10×${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$ for ethane. These differences are larger than the estimated uncertainty in the relative values of the measured cross sections (5%). The estimated uncertainty in the absolute value of the cross sections is 20%. A comparison of our Auger-electron yields with published x-ray production cross sections was used to estimate the fluorescent yield of carbon. The fluorescent yield determined from these data was found to vary with proton energy from 0.0016 at 0.3 MeV to 0.0025 at 2.0 MeV.

We have measured the effect of the transfer of excitation on the population of the $3{}_{}{}^3{}_{}{}^{}D$ state of helium. Through careful diagnosis of a proton beam passing through a long target chamber containing helium gas, we have been able to separate the various contributions to the light intensity from the $3{}_{}{}^3{}_{}{}^{}D$ state. Our measurements were performed at target-gas pressures roughly two orders of magnitude lower than those of previously reported measurements. We measure the summation of the excitation-transfer cross sections ${\sigma }_c\mathrm{}\left(n\right)\mathrm{}$ for the transfer from an $n{}_{}{}^1{}_{}{}^{}P$ state to the corresponding $n{}_{}{}^3{}_{}{}^{}F$ state times the branching ratio $B_{\mathrm{n}}$ for radiative cascade to the $3{}_{}{}^3{}_{}{}^{}D$ state, and obtain $\Sigma B_n{\sigma }_c\mathrm{}\left(n\right)\mathrm{}=2.2\mathrm{}\times {10}^{-12\mathrm{}}$ ${\mathrm{cm}}^2$. This measurement enables us to relate the excitation transferred to the $3{}_{}{}^3{}_{}{}^{}D$ state $Q_T \left(3\mathrm{}{}_{}{}^3{}_{}{}^{}D\right)$ to the excitation cross section of the $4{}_{}{}^1{}_{}{}^{}P$ state $\sigma \left(4\mathrm{}{}_{}{}^1{}_{}{}^{}P\right)$. We obtain $Q_T \left(3\mathrm{}{}_{}{}^3{}_{}{}^{}D\right)=(1.5\mathrm{}\times {10}^{-15\mathrm{}} {\mathrm{cm}}^3)N\sigma \left(4\mathrm{}{}_{}{}^1{}_{}{}^{}P\right)$, an expression, which for the low pressures used in this experiment, is linear in the number density $N$.

We study the problem of an electron in a dilute gas of density $\rho$ of hard spheres. The radius of the spheres is $a$. It is shown that a systematic expansion of the Green's function in a series involving the small parameter $\rho a^3$ leads to inconsistencies at low energies. This is attributed to the existence of localized states. We then assume that the problem can approximately be reduced to the motion of a classical particle through a suitably defined smooth, random, energy-dependent effective potential. Physical arguments are given to justify this reduction, although a rigorous proof is lacking. The resulting classical problem is in complete agreement with the Mott-Cohen-Fritzsche-Ovshinsky model of disordered materials, and is simple enough to permit detailed calculations of all quantities of interest. As a test for the validity of our approximations, we apply the theory to compute the mobility of excess electrons in gaseous He. By adjusting two parameters of order unity we get a good fit to the experimental data; the remaining small discrepancies admit satisfactory explanations.

Values for the mobilities of positive and negative charge carriers in normal ${\mathrm{He}}^4$ at the vapor pressure are presented. The interpretation of these measurements in terms of the usual microscopic models for the charge carriers is shown to require the correct hydrodynamic treatment of a modified Stokes-flow problem. Good agreement with experiment is found for both ${\mu }_{+}$ and ${\mu }_{-}$ below 4.2 °K, and new information is obtained about several features of the carrier structures. The behavior of ${\mu }_{+}$ and ${\mu }_{-}$ above 4.2 °K suggests the possibility that the viscosity of normal helium has a peculiar temperature dependence in this range. Sudden drops in ${\mu }_{+}$ and ${\mu }_{-}$ are observed near the critical temperature, and it is argued that this kind of effect may be due to critical-point fluctuations, rather than to changes in carrier structure as has been claimed by other authors.

It is shown that when the second moment of the direct correlation function is negative, the usual Ornstein-Zernike analysis is inadequate. The calculation is extended and it is shown that when both the second and fourth moments are negative, the decay of correlations is oscillatory. It is then argued, following Fisher and Widom, that there will be a locus in the density-temperature plane such that at low temperatures and densities the second moment will be positive and the decay of correlations will be monotonic, while at high temperatures and densities the second and fourth moments will be negative, and the decay of correlations oscillatory.

The optical and dielectric properties of water in the vacuum ultraviolet are presented and discussed. Optical constants at energies up to 14.6 eV were obtained by a Kramers-Kronig analysis using reflectances measured in this study between 9.2 and 14.9 eV and reflectances calculated from data in the literature below 9.9 eV. Structure in the complex part of the dielectric constant and the energy-loss function of water is compared with molecular excitations observed in water vapor. A sum-rule calculation indicates approximately 1 as the effective number of electrons per water molecule participating in absorption processes in the liquid state up to 14.6 eV.

An improved treatment of electron correlations is presented within the framework of a previously developed unified model for Stark broadening by plasma electrons. This treatment employs the method of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy in connection with a closure relation corresponding essentially to the exclusion of simultaneous strong collisions. A line-shape expression is derived for the case that the perturbing electron gas is in thermal equilibrium. This expression depends on the dynamic dielectric constant and on the two-electron correlation function. If the latter is approximated by the linearized Debye-Hückel expression (low-density case), and if the result is simplified for the vicinity of the line center by using second-order perturbation theory for the atom-perturber interaction, the results of earlier treatments of electron correlations are recovered.

The ionization energy loss of relativistic heavy nuclei is calculated using the exact Mott cross section for close collisions. Deviations from the Bloch formula are computed in some typical cases and found to be significant for nuclei with $Z\gtrsim 20$.

An explanation of the anomalous NMR specific heat first seen by Garwin and Reich in non-dilute solid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$-${}_{}{}^3{}_{}{}^{}\mathrm{He}$ mixture is given in terms of the energy of interaction of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$.

In an earlier paper an expression was derived for the memory function associated with the classical phase-space fluctuation function. In this paper, we investigate further the properties of this memory function. We dicuss the region of validity of our approximation, the low-wave-number and -frequency limit, as well as general properties of the memory function. We also discuss the hydrodynamics predicted by the memory function and the associated kinetic equation. We see, for example, that the sound velocity is given by the adiabatic speed of sound calculated thermodynamically from that static energy and pressure evaluated to lowest order in the density. Finally, we discuss two techniques for handling the two-particle Liouville operator that appears in the memory function. One technique is to introduce the Koopman operator which serves as the classical time propagator. The second technique is to introduce eigen-functions of the two-particle Liouville operator. In an appendix the exact form of these eigen-functions is given in terms of Hamilton's characteristic function. These eigenfunctions, to my knowledge, were not available previously.

A method is presented which yields two-photon cross-section values $\delta$ which are independent of the statistical properties of the light beam. A two-cell arrangement is used in which the fluorescence intensity produced by two-photon absorption of a laser beam is compared to that due to one-photon absorption of the harmonic light generated by the same beam in a quartz slab at the top of a Maker fringe. The measurement does not require a calibration of the detecting channels but relies on the knowledge of the one-photon cross section at the harmonic frequency and of the appropriate component of the nonlinear susceptibility tensor ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$. Values of $\delta$ ($\lambda =6943\mathrm{}$ Å) are presented for several organic molecules and compared to those obtained by other methods.

It was recently shown that the kinetic-kinetic part of the Kubo integrands for shear viscosity and heat conductivity behaves as $t^{-\frac{d}{2}}(d=\mathrm{dimensionality})$ for $t\to \infty$. We generalize this result to the complete (kinetic-kinetic + kinetic-potential + potential-potential) Kubo integrands for bulk and shear viscosity and heat conductivity and find explicitly the leading-order term for these autocorrelation functions for $t\to \infty$. The method is very similar to that used in the Landau-Placzeck calculation of the light-scattering cross section of simple fluids. This $t^{-\frac{d}{2}}$ behavior has two consequences that are examined: In two-dimensional fluids it leads to a divergence of Kubo integrals and in three dimensions it yields a nonanalytical low-frequency behavior of the frequency-dependent transport coefficients.