The Glauber approximation is known to be in appreciable error at all angles when applied to the elastic electron-atom scattering at medium and lower energies. It is shown that this is not due to the frozen-target approximation but mainly a result of the inadequate semiclassical treatment of close-encounter collisions in the Glauber approximation. A simple method is proposed to correct this inadequacy and is applied to $e$-H elastic scattering at energies from 20 to 100 eV. A remarkable improvement over the Glauber approximation is obtained, and the results agree with experiments very well at all angles where measurements are available.

The lifetime spectra of positrons annihilating in helium gas have been obtained over the temperature range 4.6-300 K and the density range 0.016-0.030 g/${\mathrm{cm}}^3$. The spectra are decomposed into slow-positron and orthopositronium annihilation components which are presented and discussed separately. At low temperatures, the density and temperature dependences of the data are found to depart markedly from the usual behavior observed at room temperature. Simple quantitative treatments are given of the cluster model for the slow-positron data and of the cavity model for the ortho-positronium results.

Lifetime measurements of slow-positron and ortho-positronium ($o$-Ps) annihilation have been made in argon and neon gases at room temperature and below. The argon experiments cover the temperature range 115-300 K and the density range 0.0356-0.0726 g/${\mathrm{cm}}^3$ (≃ 20-40 amagat). The slow-positron spectra in argon exhibit a departure from free-positron annihilation below 200 K. The departure becomes more marked as the temperature is lowered. No deviation from free $o$-Ps pickoff annihilation is observed in argon at low temperatures. The neon measurements cover the temperature range 30-300 K and the density range 0.032-0.89 g/${\mathrm{cm}}^3$ (≃ 35-980 amagat). No effect of temperature on the slow-positron spectra throughout the temperature and density ranges investigated in neon is observed. The spectra are very exponential with a corresponding decay rate which is temperature as well as time independent and is directly proportional to density over the ranges investigated. The $o$-Ps data are more eventful in that the $o$-Ps lifetime at near-liquid densities is approximately 20 nsec, a factor of nearly 4 greater than the value obtained using the pickoff-annihilation coefficient obtained at lower densities. This is evidence for positronium-induced cavities in low-temperature neon. A brief discussion of the argon and neon results is given in the context of the explanations offered for the low-temperature effects observed in helium gas.

The theory for the rotational excitation of symmetric-top molecular ions by electron impact is formulated within the Coulomb-Born approximation. Analytical expressions are derived for the rotational transitions induced by dipole and by quadrupole interactions. The cross sections are large and finite at threshold and decrease with increasing electron-impact energy. The validity of the present theory for the description of low-energy collisions is examined. Numerical calculations are reported for the excitation of the hydronium ${\mathrm{H}}_3$${\mathrm{O}}^{+}$ ion.

The Feshbach projection-operator technique is investigated using second quantization to construct approximate optical potentials with Tamm-Dancoff-approximation and random-phase-approximation descriptions for closed-shell targets. We interpret a recent many-body theory of elastic scattering (due to Schneider, Taylor, and Yaris) as an approximate form of the equations of this work. Possible applications and extensions of the method are also described.

We derive quantum numbers $K$ and $T$ which label asymptotic potential-energy curves in $e^{-}$-H scattering. Zero-order channel states are constructed group theoretically so that the dipole interaction ${\mathcal{r}}_{1}cos{\theta }_{12}$ is diagonal in a product space of hydrogenic orbitals for 1 and spherical harmonics for 2. $K$ and $T$ are analogous to the "electric quantum number" and the $z$ component of angular momentum in the linear Stark effect for H, and are closely related to quantum numbers described recently for doubly excited He. Channels supporting resonances are predicted from a perturbation expansion of eigenvalues of the effective centrifugal barrier operator $2r_{1}cos{\theta }_{12}+l_2^2$ in terms of $K$ and $T$. Comparison with exact ${\mathrm{H}}^{-}$ results and experiment is excellent, and the method accounts for previously unexplained degeneracies with respect to total parity. A rigorous result is that only channels with $K>\mathrm{}0\mathrm{}$ can support an infinity of states below threshold. An approximate selection rule for coupling between neighboring channels suggests that decay of ${\mathrm{H}}^{-}$ resonances goes preferentially to channels such that $\Delta K=\pm 1$, $\Delta T=0\mathrm{}$. Application of the method is also made to $p$-H scattering channels for which the zero-order basis nearly diagonalizes the long-range centrifugal barrier.

We report observations of x radiation from 1.0 to 4.5 keV produced by the collision of ${\mathrm{K}}^{+}$ ions of 0.5 to 3.0 MeV with thick targets. Characteristic lines of the beam or the target or both are observed, depending on the target. These lines are superimposed on a continuum that is exponential in form. The relative dependence of the line yields on atomic number and the continuum on photon energy can be reproduced without the use of an adjustable parameter, if one assumes that the processes are controlled by the Fourier spectrum experienced by an orbital electron that results from the passage of a uniformly moving charged particle. A mechanism is proposed that allows this control to function in producing $K$-shell vacancies. The formulas are applied to other data and are shown to reproduce the relative $Z$ dependence for projectiles of 0.01 to 2.5 MeV/amu with $Z_1$ ranging from 17 to 82.

Cross sections for electron capture into each excited state of He up to $4{}_{}{}^{1,3}{}_{}{}^{}D$ by ${\mathrm{He}}^{+}$ impact on He in the energy range 100-10 000 keV have been calculated by means of the first Born approximation (Bates's version). A Gaussian technique previously developed for evaluating two-center integrals occurring in the Born amplitude has been used. One-parameter, variational wave functions are derived for each excited state of helium up to $4{}_{}{}^{1,3}{}_{}{}^{}D$. Some of the excited ${}_{}{}^1{}_{}{}^{}S$ cross sections are found to be affected by almost a factor of 2 by the choice of 1 ${}_{}{}^1{}_{}{}^{}S$ helium wave function and orthogonality of the excited state ${}_{}{}^1{}_{}{}^{}S$ functions to this function. The observed departure of the ratio of triplet to singlet cross sections from the statistical weight of three is related partly to the interference between a one-electron process of capture into an excited state of helium and a two-electron process of capture into the ground state with the original ${\mathrm{He}}^{+}$ electron excited, and is related partly to the difference between the variational singlet and triplet excited one-electron wave functions. At energies of about 100 keV, agreement with available experimental results is generally good; however, for the $3{}_{}{}^1{}_{}{}^{}P$, $4{}_{}{}^1{}_{}{}^{}P$, and $4{}_{}{}^1{}_{}{}^{}D$ states, the disagreement exceeds the estimated experimental uncertainty.

Matrix variational calculations, reported previously, of $e$-He inelastic scattering, have been extended into the near-threshold regions for excitation of the metastable states $2{}_{}{}^3{}_{}{}^{}S$ and $2{}_{}{}^1{}_{}{}^{}S$. Wigner cusp and rounded-step structures are computed at these thresholds for elastic and inelastic processes not involving the threshold channels. Excitation cross sections are computed for the threshold channels. The present computed results are compared with available experimental data, and found to be in general qualitative and quantitative agreement. A new estimate is derived of the rate coefficient for deactivation of $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$ by thermal electrons: a constant value 2.525 × ${10}^{-9\mathrm{}}$ ${\mathrm{cm}}^3$/sec for $T\le 1053$ °K.

An experiment that tests a novel method for deflecting molecular beams using inhomogeneous resonance fields is described. The idea is easily understood in classical terms. Imagine that the rotating electric dipole moment of a polar diatomic molecule is placed in an electric field. In a static field the $\overrightarrow{\mu }·\overrightarrow{\mathrm{E}}$ interaction averages to zero due to the rotation of the molecule. If, however, the field rotates at the same frequency as the molecule, the field and molecule remain aligned and the $\overrightarrow{\mu }·\overrightarrow{\mathrm{E}}$ interaction does not average to zero. If the field is spatially inhomogeneous, then there is a net force $-\nabla \left(\overrightarrow{\mu }·\overrightarrow{\mathrm{E}}\right)$ on the molecule. This force can be used in making a molecular beam deflector. Resonance deflection of molecules in the $J=0\mathrm{} \mathrm{and} 1$ rotational states of a molecular beam of CsF has been observed. The deflection is produced by passing a collimated molecular beam of CsF through the center of a T${\mathrm{E}}_{111}$ microwave cavity which is oscillating at the $J=0\mathrm{}\to 1$ transition frequency, 11.019 GHz. The deflection of the $J=0\mathrm{} \mathrm{and} 1$ molecules can be detected as a decrease in the undeflected on-axis beam or as an increase in the off-axis beam. The theory of the effect as well as potential applications are also discussed.

Absolute cross sections for the excitation of the $2P$ states of atomic hydrogen in charge-exchange collisions of protons in argon and nitrogen were measured by observing the Lyman-$\alpha$ radiation emitted in transitions from this state. Because of the lack of light standards in the vacuum ultraviolet region of the spectrum, the major problem of the measurements was the absolute calibration of the Lyman-$\alpha$ photometer. This calibration was obtained from coincidence measurements of ${\mathrm{H}}_{\alpha }$ and Lyman-$\alpha$ photons in the presence of an electric field. The measurements were corrected for the effect of Doppler shift on the photometer sensitivity. For the evaluation of the coincidence measurements, the branching ratio of ${\mathrm{H}}_{\alpha }$ transitions to the $2S$ state and the polarization of Lyman-$\alpha$ radiation, emitted in cascade processes, were needed. These quantities were obtained from quantum-mechanical calculations for a hydrogen atom in a weak electric field. Cross sections for the $2P$ states were obtained in the energy range from 0.5 to 30 keV. The $2P$ cross sections in argon had maxima of 2.34 × ${10}^{-17\mathrm{}}$ and 2.84 × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ at 3.35 and 11.86 keV, respectively, and in ${\mathrm{N}}_2$ maxima of 2.17 × ${10}^{-17\mathrm{}}$ and 2.10 × ${10}^{-17\mathrm{}}$ were observed at 3.39 and 11.3 keV, respectively. The energy dependence of the measured cross sections is in agreement with that of published measurements. Differences in the absolute values are discussed.

Radiative lifetime measurements of 13 vibrational levels of the $B{}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ state of ${\mathrm{N}}_2$ have been obtained at 50 eV incident electron energy and 30 mTorr ${\mathrm{N}}_2$ gas pressure using a 50-μsec electron excitation pulse. Two radiative decay components with lifetimes of approximately 5 and 25 μsec are observed in each case. The short-lived component is identified as the contribution from direct excitation of the $B{}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ state. The long-lived cascade contribution is observed to decrease from 37% of the total $B{}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}\to A{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}(v^{\prime }, v^{\prime \prime })$ radiation for the $v^{\prime }=0\mathrm{}$ vibrational level to 15% for the $v^{\prime }=12\mathrm{}$ level and is consistent with theoretical predictions by Cartwright et al.

The photodetachment cross section of the negative hydrogen ion is calculated for incident photon wavelengths in the range 1130 to 14040 Å. The free-state wave function of the bound-free transition is calculated from the simplified Kohn-Feshbach variational method. The bound-state wave function is given by Rotenberg and Stein, who used the Hylleraas correlated wave function with a "tail function" added to it. The agreement between the results from the length and velocity formulas in the present work is found to be considerably better compared to earlier theoretical results. The overall agreement with experimental results also shows some improvement. The cross section is found to rise and fall sharply in the closed-channel resonance region at the positions of the two singlet $P$ resonances. The shape parameter $q$ is also calculated for each resonance state.

The eikonal approximation has been used to investigate the elastic scattering of electrons by hydrogen molecules. In addition to the static potential, the effects of polarization and exchange have been included through potentials. The total and the differential cross sections have been calculated in the energy range 9.4-100.0 eV and compared with the experimental and other theoretical values. It is found that the eikonal approximation predicts reliable results for incident electron energies ≲ 20.0 eV.

The method of complex basis functions proposed by Rescigno and Reinhardt is applied to the calculation of the amplitude in a model problem which can be treated analytically. It is found for an important class of potentials, including some of infinite range and also the square well, that the method does not provide a converging sequence of approximations. However, in some cases, approximations of relatively low order might be close to the correct result. The method is also applied to $S$-wave $e$-H elastic scattering above the ionization threshold, and spurious "convergence" to the wrong result is found. A procedure which might overcome the difficulties of the method is proposed.

Using hyperspherical coordinates and adiabatic expansion methods, we obtain the potential curves for the electron-hydrogen system in ${}_{}{}^1{}_{}{}^{}S$ states. From the lowest potential curve we compute the ground-state energy of ${\mathrm{H}}^{-}$ to be -1.0547 Ry. We also compute the elastic scattering phase shifts at low energies from the same potential curve. Results are very good at low energies. The variations of important correlation effects as the system expands are also investigated.

This work reports the first detailed examination of the noncharacteristic x-ray distribution produced during 1-MeV Ar bombardment of silicon. A crystal spectrometer was used to observe the characteristic and noncharacteristic x rays. It is shown that to within 5 eV the noncharacteristic x-ray band is continuous and tails off in the region of 1.4 keV, as required by the molecular x-ray interpretation. We have obtained the true shape of the noncharacteristic x-ray band in the energy range 675-1550 keV by using a rubidium acid phthalate crystal spectrometer calibrated for its relative efficiency. The observation of a broadened argon $L$ line spectrum and multiple satellite line in the Si $K$ spectrum shows that a high degree of excitation is produced in the $L$ shells of both argon and silicon during the collision.

The cross section ${\sigma }_{\mathrm{MT}}$ for the elastic momentum transfer of electrons with neon atoms in the electron energy range $3\times {10}^{-3\mathrm{}}\le u\left(\mathrm{eV}\right)\le 5\times {10}^{-1\mathrm{}}$ has been deduced from measurements of the microwave absorptivity of a transient cryogenic afterglow plasma. A least-squares fit of our experimental data by the modified effective range formula gives a zero-energy scattering length of $(0.24\mathrm{}\pm 0.015)a_0$, where $a_0$ is the Bohr radius.

Inner-shell vacancy production in the target recoil interaction can distort the observed impact-parameter dependence of x-ray production in heavy-ion collisions when measured in thin-foil targets. Approximate expressions are presented for the energy and scattering-angle dependence of the recoil contribution. A numerical example is given for Al $K$— x-ray production in Al foils. The recoil correction is estimated for $L$— x-ray production in I + Te collisions and compared with the data of Stein et al.; the unexpected rise in the probability they observed at small impact parameters could possibly be accounted for by this mechanism.

Time-resolved spectroscopy of excited mediums following electrical discharges in helium/xenon mixtures, in which xenon is the minority constituent, show enhancement in the emission of all the ionic-xenon levels relative to that observed in pure-xenon discharges. The time characteristics depend on the helium pressure and the decay follows the molecular helium emission. The total pressure ranges between 20 and 300 Torr, of which the xenon pressure is up to 1 Torr. The discharge has a peak current density of 500 A/${\mathrm{cm}}^2$ and it flows for about 100 nsec. It is suggested that helium plays an active role in the generation of excited xenon ions by transferring excitation energy to xenon. The acceptors can be ${\mathrm{Xe}}^{+}$ in its ground state and neutral Xe in its metastable state. In the investigated discharges both, ${\mathrm{Xe}}^{+}$ and metastable Xe* exist in high densities for up to 5-10 μsec into the early afterglow. During this period, atomic helium metastables and molecular helium states such as $a{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$, $A{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$, and $B{}_{}{}^1{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ are also highly populated and in fact constitute an energy store. The molecular states of helium can resonantly transfer energy through the bound-free transitions to ground-state ${\mathrm{Xe}}^{+}$ to form excited xenon ions ${\mathrm{Xe}}^{+*}$ with an estimated cross section of 4 × ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$—a resonable order of magnitude considering the large enhancement observed in Xeii emission. Penning ionization and charge transfer have only little effect on observed enhancement.