The electron-impact double-excitation cross sections for several states of lithium, beryllium, magnesium, and calcium are calculated using the Born-Oppenhemier scattering approximation. The energy dependence of the total cross sections and the angular dependence of the differential cross sections for these parity-unfavored transitions are reported. The maximum values of the total cross sections for excitation of the lowest states ${\mathrm{}\left(\mathrm{np}\right)\mathrm{}}^2{}_{}{}^3{}_{}{}^{}P_g^{}{}_{}{}^{}$ of beryllium, magnesium and calcium are found to be comparable in magnitude to those for single excitations in the same energy range ($\sim \pi a_0^2$). Those for the $\mathrm{}\left(\mathrm{np}\right)\mathrm{}\left(3d\right)\mathrm{}{}_{}{}^1{}_{}{}^{}D_u^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}D_u^{}{}_{}{}^{}$ excitations are found to be of the order of ${10}^{-1\mathrm{}}\pi a_0^2$ for magnesium and ${10}^{-2\mathrm{}}\pi a_0^2$ for beryllium. The highly excited ($1s$) ${\mathrm{}\left(2p\right)\mathrm{}}^2{}_{}{}^4{}_{}{}^{}P_g^{}{}_{}{}^{}$ state of lithium has a maximum cross section of $4\times {10}^{-5\mathrm{}}\pi a_0^2$. The highly excited $\mathrm{}\left(1s\right)\mathrm{}{\mathrm{}\left(2p\right)\mathrm{}}^2{}_{}{}^4{}_{}{}^{}P_g^{}{}_{}{}^{}$ for all these transitions are proportional to ${sin}^2\theta$ and so they vanish in the forward and backward directions. The polarization of the dipole radiation emitted by these doubly excited states is described. Target wave functions are constructed using the Hartree-Fock method. For the ${}_{}{}^1{}_{}{}^{}S_g^{}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}P_g^{}{}_{}{}^{}$ transition in magnesium and calcium, pseudopotential methods were also used to construct the target wave functions. The resulting cross sections agree closely with those computed with Hartree-Fock orbitals.

The Glauber amplitude for describing collisions of charged particles with two-electron atoms, resulting in transitions between spherically symmetrical states, is reduced to a readily computable form. Application is then made to the $2{}_{}{}^1{}_{}{}^{}S\leftarrow 1{}_{}{}^1{}_{}{}^{}S$ transition in helium, for which angular distributions are determined for 26.5-, 34-, 50-, and 83-eV incident electrons. Comparison with experiment shows that the Glauber theory is capable of accurately predicting the angular distributions for even our lowest-energy calculation. In particular the theory predicts the recently observed structure in the differential cross section. The energy dependence of the "apparent" generalized oscillator strength is also demonstrated for incident energies in the range 300-1100 eV.

In the two-state approximation analytic formulas are derived for the inelastic cross section in the limit in which the particle velocity is large relative to the energy defect. These formulas involve a mixing parameter and two eigenphase shifts. For scattering in a $\frac{C\left(X\right)\mathrm{}}{R^n}$ potential, where $X$ is an internal coordinate of the target, the integral cross section is presented in closed form, with parameters given by the elastic-superelastic potential-difference strength, the coupling strength, the velocity, and a cutoff for the singular potential, taken to be the target radius. Results are given for ${\mathrm{H}}^{+}$-${\mathrm{H}}_2$, $e^{-}$-${\mathrm{H}}_2$, and $e^{-}$-${\mathrm{N}}_2$ vibrational excitation. The theory appears to be correct for the high-energy tail of the cross sections.

A theory for exchange of vibrational quanta between molecules is formulated which does not rely on the Born expansion of the $S$ matrix. A transformation is derived which diagonalizes the vibrational operators responsible for exchange. The scattering operator is then expanded in a series of rotational tensor operators which permits evaluation of $S$-matrix elements to all orders. This formulation shows that multiquantum processes, both rotational and vibrational, play an important role when transition moments are large. Numerical calculations for vibrational exchange rates of carbon monoxide are compared with results of the first Born approximation from which they differ significantly. The dependence of the cross section on vibrational-energy defect is much less drastic than that of the Born approximation. The present calculations indicate that cross sections for the exchange of more than one vibrational quantum are substantial, in marked contrast to the Born approximation where they are forbidden. The size of these multiquantum cross sections indicates that they can play an important role in the detailed kinetic modeling of CO lasers.

The absolute cross sections for the single ionization of ${\mathrm{Ba}}^{+}$ ions by electron impact have been measured as a function of incident electron energy over the electron energy range from below threshold (10.001 eV) to approximately 1000 eV. It is found that the cross section increases from 1.94×${10}^{-16\mathrm{}}$ to 3.76×${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ between 15.1 and 18 eV actual incident electron energy. This rapid rise is interpreted as the onset of autoionization. Some indication of structure occurring near the peak of the cross-section curve such as found in the isoelectronic system Cs is observed, but the relative magnitude of the apparent structure is of the same order as the 90% random-error confidence limits and thus cannot conclusively be regarded as being present. The maximum total error in the measurements is estimated to have its greatest value of less than ±20% at 15.5 eV while ±12% is typical of other energies. Of the total error, ±7% is deemed to be systematic. At incident electron energies below threshold, the cross section is found to be zero within 1% of the cross section at 48 eV. The measurements were performed in an all-metal ultrahigh-vacuum crossed-beam facility in which the nominal operating pressure was less than 5×${10}^{-9\mathrm{}}$ Torr. The ion source was a water-cooled surface-ionization-type ion source while the electron source was a modified 6L6GC beam power tube. Continuous-beam techniques were used for the majority of the measurements, but modulated-beam methods were employed as a check. Measurements made by the two techniques agreed to well within the allowable experimental error and showed no systematic variations. Numerous consistency checks were performed to evaluate possible sources of experimental error such as pressure modulation of the background gas, focusing of the ion beam by the electron beam, and errors in the beam-profile determination. The present ${\mathrm{Ba}}^{+}$ ionization data are compared with the existing experimental and theoretical results.

A spin-exchange optical-pumping experiment to study the temperature dependence of the electron-rubidium spin-exchange cross section is reported. In this experiment, electrons were polarized in a weak magnetic field by spin-exchange collisions with optically pumped Rb atoms. The electron-Rb collisions were the principal source of the electron-spin-resonance linewidth, and they also produced a shift in the resonance frequency. The magnitudes of the linewidth and frequency shift are functions of the electron-Rb-scattering phase shifts. The electron linewidth at fixed Rb density was essentially constant over the temperature range 200-840 °K indicating the spin-exchange cross section is well approximated by a $\frac{1}{v}$ velocity dependence. The ratio of the frequency shift to linewidth was 0.075±0.005 at 300 °K with an estimated Rb polarization of (20±10)%, and the ratio was 0.027±0.007 at 600 °K with a Rb polarization of (10±5)%.

Iodine ions, accelerated to energies between 5 and 25 MeV, have been passed through thin targets of hydrogen and oxygen, and nonequilibrium charge-state distributions have been measured in order to obtain charge-changing cross sections. Results of cross sections for capture of one and two electrons, and for loss of one to eight electrons are presented for ions with initial charge states ranging from $2^{+}$ to ${18}^{+}$. Multiple-electron loss of iodine ions has been found to be relatively large in oxygen, but small in hydrogen. This systematic difference reveals the influence of different excitation mechanisms in energetic ion-atom collisions. The dependence of the cross sections on initial charge and velocity of the ions is discussed and, whenever possible, compared with theoretical expectations.

The low-energy scattering by a potential consisting of a long- and a short-range part is discussed. A general expression for the phase shift ${\delta }_L$ is derived starting from the radial Schrödinger equation. Effective-range expansions are presented for partial waves of all orders for the case of a long-range ${\mathcal{r}}^{-8\mathrm{}}$ potential. The quantity ${tan\delta }_L$ is calculated up to and including the term $k^{2L+7}\ln k$. It is found that in the low-energy limit, ${tan\delta }_L$ is proportional to $k^{2L+1}$ for $s$, $p$, and $d$ waves, and ${tan\delta }_L$ is proportional to $k^6$ for all the higher partial waves.

The technique of heavy-ion energy-loss spectrometry has been used to measure excitation cross sections for the $\left(2\mathrm{}{p}^5\right)3s$ and $\left(2\mathrm{}{p}^5\right)3p$ electronic configurations of neon by impact of heavy ions upon ground-state neon. The incident particles used were ${\mathrm{H}}^{+}$, ${\mathrm{H}}_2^{+}$, and ${\mathrm{He}}^{+}$ at impact energies from 20 to 180 keV. The results are compared with previous optical measurements of the emission cross sections of lines from these levels as excited by ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{+}$ impact. Agreement is not good, neither in shape nor in absolute magnitude, for excitation of the $\left(2\mathrm{}{p}^5\right)3s$ configuration. However, agreement is surprisingly good for excitation of the $\left(2\mathrm{}{p}^5\right)3p$ configuration. A curve-fitting technique has been applied to extract relative singlet-triplet cross sections for levels within the $\left(2\mathrm{}{p}^5\right)3s$ configuration. Almost no triplet excitation is observed for ${\mathrm{H}}^{+}$ and ${\mathrm{H}}_2^{+}$ impact. Significant triplet excitation is observed only for ${\mathrm{He}}^{+}$ impact.

Ionization cross sections of forty gases have been measured for electrons of kinetic energies 0.1-2.7 MeV. The measurements are absolute and extensive precautions have been taken to minimize systematic and accidental errors. The energy dependence of the measured cross sections is accurately described by the Bethe asymptotic formula involving two parameters that represent important atomic properties. Comparisons have been made between ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ and between C${\mathrm{H}}_4$ and C${\mathrm{D}}_4$; the observed differences are of the order of 1% and too small to be resolved with certainty. A close comparison has been made between positrons and electrons in Ar at 0.67 and 1.1 MeV; the cross sections are observed to be equal within a probable error of 0.5%.

The emission profiles of the cesium resonance lines broadened by collisions with inert gases have been measured from about 50-1000 ${\mathrm{cm}}^{-1\mathrm{}}$ from line center. The emission is observed from optically excited Cs in a cell whose temperature is varied from about 300-800°K. By measuring the wing intensity relative to the entire line intensity from optically thin Cs, the profiles can be related to theoretical models without knowledge of the cesium density. The quasistatic theory of line broadening, extended to include the distribution of perturber positions about the Cs*, is used to analyze the data. The observed temperature dependence of the emission profiles is associated with the temperature dependence of the perturber distribution in the Cs*-inert-gas adiabatic potential. The quasistatic spectrum depends on the difference between excited- and ground-state adiabatic potentials, so each potential is thereby separately determined from the data. The $X\Sigma$, $A\Pi$, and $B\Sigma$ potentials for the 3.5-5-Å region are given.

A computer-linked spectroscopic system with a high-sensitivity-resolution product has been used to measure the time-dependent net rate of production of neutral helium atoms resulting from the recombination of ${\mathrm{He}}^{+}$ with electrons in a pulsed helium afterglow at neutral pressures of 1.86 and 44.6 Torr. The recombination-rate coefficient of ${\mathrm{He}}^{+}$ as a function of afterglow time has been obtained by dividing these data by the product of the electron and atomic-ion density as determined from intensity measurements of radiation from bound levels in Saha equilibrium with the free electrons. Simultaneous time-resolved measurement of the electron density with a 35-GHz Fabry-Perot resonator has given the recombination-rate coefficient as a continuous function of electron densities without the need of a priori assumptions about that functional form. The electron temperature as a function of electron density in the recombining afterglow was determined from analyses of time-resolved measurements of the intensity distribution of radiation from the continuum states above the $n{}_{}{}^3{}_{}{}^{}P\to 2{}_{}{}^3{}_{}{}^{}S$ Rydberg series in atomic helium. For pressures below a nominal 2 Torr, the resulting parametrization of the recombination-rate coefficient for ${\mathrm{He}}^{+}$ with electrons can be represented as $\alpha =7.1\mathrm{}\times {10}^{-20\mathrm{}}{\left(\frac{T}{300}\right)}^{-4.3\mathrm{}}\mathrm{}\left[e\right]\mathrm{}$ ${\mathrm{cm}}^3$/sec, where $T$ is the electron temperature and [$e$] the electron density. At higher pressures the rate coefficient is found to decrease as a consequence of associative ionization of the excited states.

We calculate the roton-limited mobility of ions in superfluid ${\mathrm{He}}^4$ for temperatures below ∼ 1.7°K. Taking, as a first approximation, a constant ion-roton transition-matrix element, which we treat as an adjustable parameter, we find good agreement with experiment for both positive and negative ions. This model calculation indicates that the most mobile of the recently discovered "exotic" negative carriers is a very light ion.

The narrow-line output of a dye laser on the low-frequency side of the ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ resonance line (7948 Å) of rubidium was self-defocused by passage through dilute rubidium vapor. The defocusing was caused by the electronic nonlinearity associated with "adiabatic following" of the laser field by the pseudomoment of the resonant atoms. By using the corresponding nonlinear dielectric constant, the wave equation was solved numerically and gave excellent quantitative agreement with experiment.

This paper is concerned with the behavior of the autocorrelation and memory functions of statistical mechanics as $t\to \infty$. A simple calculation shows that for a large class of models leading to power-law behavior, the two functions have opposite sign and common functional behavior in the limit $t\to \infty$.

Four approximate formulas, due to Wannier, Kihara, Frost, and Patterson, for the field dependence of ion mobility are tested by comparison with special cases for which accurate theoretical results can be found. The Kihara result, an expansion in ${\left(\frac{E}{N}\right)}^2$, has only limited range. The Frost-Patterson formulas at high fields apply only to rigid-sphere cross sections. The Wannier free-flight theory yields a formula with one parameter that can be chosen once and for all to fit the zero-field Chapman-Enskog result; without further adjustable constants the formula gives reasonable results at medium and high fields (largest deviations less than 20% in the special cases tested), and is applicable to any ion-neutral mass ratio and force law, including the case of resonant charge transfer.

We present measurements of the specific heat $C_{\mathrm{vx}}$ of a mixture of ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ with a nominal concentration of ${\mathrm{He}}^3$, $X_3=0.80\mathrm{}$. Data were taken with a flat calorimeter cell in the vicinity of the gas-liquid critical point of the mixture, which is characterized (at a given $X_3$) by its density ${\rho }_c$ and temperature $T_c$. The data consist of nine isochores within the approximate density range $0.52<\mathrm{}\frac{\rho }{{\rho }_c}<1.20\mathrm{}$ and in the temperature range $-0.1\mathrm{}\le t\le 0.1$, where $t=\frac{(T-T_c)}{T_c}$. Data were taken to within 0.4 mK of the transition temperature on all but one of the isochores. We find that the behavior of the specific heat in the mixture for a given reduced density $\frac{\rho }{{\rho }_c}$ is in general very similar to that seen in pure ${\mathrm{He}}^3$. In particular, the behavior of $C_{\mathrm{vx}}$ along the critical isochore is the same as that for pure ${\mathrm{He}}^3$ in the range ${10}^{-4\mathrm{}}\le t\le {10}^{-2\mathrm{}}$. There the apparent weak divergence is characterized by an exponent $\alpha \approx 0.1$. From thermodynamic considerations of the upper bound of $C_{\mathrm{vx}}$ along a line of singularities in mixtures, the apparent weak divergence we observe does not, however, represent the asymptotic behavior. This question is discussed in the light of the paper by Griffiths and Wheeler and of new calculations by Leung and Griffiths for a binary fluid. The thermal-equilibrium times in the two-phase region were found to be much longer than in the pure ${\mathrm{He}}^3$ fluid, and these are briefly discussed. The thermal diffusivity in this region is found to have a maximum at a density approximately 20% lower than ${\rho }_c$, in rough correspondence to the density of the temperature extremum of the two-phase-region boundary.

A compressibility-consistent integral equation for the radial distribution function $g$ similar to a previously proposed pressure-consistent integral equation is applied to a ${\left(\frac{b}{\mathcal{r}}\right)}^5$ effective potential. The results compare well with those obtained by a molecular-dynamics calculation and are superior to the results of Percus-Yevick 2 and Percus-Yevick 2 XS calculations. The $g$ obtained from this integral equation can be used to compute the sum of the bridge diagrams. These bridge-diagram sums are used in an Euler-Lagrange equation to compute the ground-state Bijl-Jastrow wave function for liquid ${\mathrm{He}}^4$. An interatomic potential of the Lennard-Jones 6-12 type is used. The ground-state energy is found to be -6. 63°K/atom (experiment: -7. 14°K). The equilibrium density is 0. 0205 atom/${\mathrm{\AA }}^3$ (experiment: 0. 02185 atom/${\mathrm{\AA }}^3$). The structure factor and radial distribution function obtained are compared with experimental results.

The two three-body correlation terms occurring in the equation of motion for the density response function are expressed in terms of three-point vertex functions. By neglecting retardation effects in the latter, this leads to frequency-dependent effective kinetic and potential energies $K_{\mathrm{eff}}(\overrightarrow{\mathrm{q}}, \omega )$ and $V_{\mathrm{eff}}(\overrightarrow{\mathrm{q}}, \omega )$. $K_{\mathrm{eff}}$ is expressed by the one-particle correlation functions and $V_{\mathrm{eff}}$ by the density correlation function. $K_{\mathrm{eff}}$ and $V_{\mathrm{eff}}$ determine the density response function $\chi (\overrightarrow{\mathrm{q}}, \omega )$, the poles of which define the phonon-roton spectrum ${\omega }_q$. In addition, an eigenvalue equation is derived which is shown to have two distinct eigenvalues. While the first is again ${\omega }_q$, the second is identified with the diffuse second branch recently found by Cowley and Woods. It is shown that in the limit $q\to \infty$ the two eigenvalues both merge into the free-particle spectrum. The limit $q\to 0$ of the two eigenvalues as well as the end-point singularity of the phonon-roton branch are discussed in a second paper.

On the basis of the formalism developed in a previous paper, several features of the two-branch excitation spectrum observed by Cowley and Woods are discussed. In the long-wave-length limit we derive a $T^4$ dependence of the sound velocity which is in agreement with a $T^3$ law for the specific heat. Furthermore, a simple derivation of the Pitaevskii singularity at the end point $q_c\cong 3.55$ ${\mathrm{\AA }}^{-1\mathrm{}}$ of the phonon-roton spectrum is presented and it is argued that above $q_c$ the excitations are essentially decoupled from the condensate. Finally, the author gives convincing arguments that the diffuse second branch of Cowley and Woods should converge, for $q\to 0$. near twice the roton gap where, however, it should disappear in neutron scattering but show up in Raman scattering, in accordance with experiments by Greytak et al.