Auger rates are estimated for some circular orbits of the $\alpha {\pi }^{-}{e}^{-}$, $\alpha K^{-}{e}^{-}$, and $\alpha \overline{p}{e}^{-}$ atoms. It is found, as conjectured by Condo several years ago, that the Auger rate for a circular orbit depends sensitively on the multipolarity of the transition. In some instances, the multipolarity may be required by energy conservation to be large enough to permit a ${\pi }^{-}$ or a $K^{-}$ meson to decay rather than to eject an electron. In particular, the estimated Auger rates for those circular orbits of the $\alpha {\pi }^{-}{e}^{-}$, $\alpha K^{-}{e}^{-}$, and $\alpha \overline{p}{e}^{-}$ atoms with binding energies most nearly equal to that of a He atom are, respectively, 2×${10}^{12}$, 4×${10}^5$, and ≲${10}^3$ ${\sec }^{-1\mathrm{}}$. Radiative rates are also computed.

Excitation cross sections for the collisions $\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$,+Ne, Ar, $\mathrm{Kr}\to \mathrm{H}(2s, 2p_0, 2p_{\pm })+\mathrm{N}\mathrm{e},\mathrm{ }\mathrm{A}\mathrm{r},\mathrm{ }\mathrm{Kr}$ are calculated over the velocity range of 0.3-5.0 a.u. in the distorted Born, two-state (for argon only), and four-state impact-parameter approximations that do not allow for electron exchanges between the colliding atoms. The results are compared with earlier first Born and scaled first Born calculations and with experimental data. The four-state cross sections, while greatly reduced from the first Born results, are still between three and ten times greater than experiment. Polarization fractions are also calculated from the four-state cross sections and compared with experimental data and with previous calculations.

Many-electron perturbation theory has been used to investigate the contribution to atomic correlation energies from high-order terms. The treatment analyzes several aspects of the inhomogeneous-electron-gas and the electron-pair approaches. It discusses in detail the coupling of electronic angular momenta with the multipolar components of the Coulomb interaction. The results are expressed in terms of renormalized propagators, which include partial perturbation summations to infinite order. Calculations have been carried out for the neon atom to ascertain the importance of contributions from many-body ring diagrams. Numerical results indicate that the ratio of many-body to two-body correlation energies is about 0.10 for the $2p$ subshell of NeI and that the many-body correlation energy has a positive sign.

A simple modification of the Thomas-Fermi statistical model for electrons in atoms and ions is presented, which corrects one of the model's major deficiencies, namely, its overestimation of the electron density near the nucleus. Exploiting the fact that near the nucleus the potential is nearly Coulombic, boundary conditions are derived from wave mechanics and incorporated into the model equations. The resulting equations are expressed in integral form and solved by a straightforward iterative technique. Results for total atomic energies show marked improvement over the corresponding results obtained from the Thomas-Fermi model, with only a slight increase in the required computational effort. The procedure is extended to obtain a relativistic statistical model of the atom. Numerical results show good agreement with wave mechanics in total energy calculations and in the form of the density near the nucleus. The relativistic effects are of greater magnitude than exchange or inhomogeneity corrections to the Thomas-Fermi model for large $Z$ atoms.

Differential scattering cross sections for excitation of helium by electron impact from its ground state to its $2{}_{}{}^1{}_{}{}^{}P$ excited state have been measured at four incident electron energies in the range 26-55.5 eV for scattering angles between 10° and 70°, and at 81.6 eV for scattering angles between 10° and 80°. These differential cross sections have been placed on an absolute scale by normalizing them to the experimental absolute integral cross sections of Jobe and St. John. These experimental differential and integral cross sections have been compared with the results predicted by the Born approximation, and by several other first-order approximations in which direct excitation is calculated in the Born approximation and exchange scattering by various Ochkurlike approximations. The calculations provide reliable tests of these scattering theories since they are made using the accurate generalized oscillator strengths of Kim and Inokuti. As expected, these first-order theories are poor near threshold and exchange is important at high scattering angles for all energies. Further, the absolute magnitude of the calculated integral and small-angle differential cross sections is too large and is within 50% of experiment only at energies greater than 80 eV. These first-order models are in qualitative agreement with the experimental angular dependence at 34-81.6 eV for scattering angles between 10° and 40°. At higher scattering angles (corresponding to momentum transfers greater than about 1.6 a.u.), the calculated differential cross sections fall well below the experimental ones. The phase between the direct and exchange scattering amplitudes was found to be important at all energies, and is apparently not predicted correctly by any of the first-order models examined here. Some approximations for the exchange (e.g., Ochkur approximation and the post interaction form of the Ochkur-Rudge approximation) were found to be better for integral cross sections and some (e.g., prior Ochkur-Rudge approximation) were better for differential cross sections. The use of good analytic self-consistent-field (SCF) wave functions for both the ground and excited states was tested by computing generalized oscillator strengths from them and comparing these results with the calculations using the accurate generalized oscillator strengths. The SCF functions yield differential cross sections in quantitative disagreement (20%) with the accurate results, although the energy and angle dependence of the cross sections is predicted qualitatively correctly.

A general approximation method is developed for the treatment of bound quantum systems in the presence of an intense external electromagnetic field of long wavelength. The method is based upon a unitary transformation which approximately removes the electromagnetic field from the problem. The accuracy of the technique increases with the number of photons involved in any given process; and in the case of large photon number, the results have a simple, concise form resembling first-order perturbation theory. It is possible to handle intense-field problems with small numbers of photons also, but then the formalism takes on a complexity analogous to the corresponding perturbation expressions for the same number of photons. The theory is extended to the case where two electromagnetic field modes are present, one or both of which may be intense. Bound-bound transitions in a hydrogenlike atom are calculated as an illustration of the application of the method. One of the explicit nonlinear effects to appear is an intensity-dependent deviation of the transition probability behavior from $I^n$ for $n$-photon transitions, where $I$ is the field intensity. It is demonstrated that intensity effects are much more probable with bound electrons than with free electrons.

Cross sections have been measured for production of ${\mathrm{He}}^{+}$ ions by the collision of 10- to 30-keV ${\mathrm{He}}^0$ atoms in the triplet metastable state with target atoms of Xe, Kr, ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, Ar, Ne, and He. Fast ${\mathrm{He}}^0$ atoms are produced in the first of two gas targets in which various neutralizer gases may be present at low density. The fractions of ${\mathrm{He}}^0$ produced in the triplet metastable state in these various neutralizer gases are known. The fraction of fast ${\mathrm{He}}^{+}$ emerging from a second target containing Xe, Kr, ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, Ar, Ne, or He is analyzed as a function of the density of the second gas target, and the cross sections for ionization of ${\mathrm{He}}^0$ atoms from the metastable triplet state are determined. Typical values of the cross sections at 30 keV are 110±40, 37±17, 122±58, 86±42, 18±12, and 65±31 in units of ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ for gas targets of Xe, Kr, ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, Ar, Ne, and He, respectively.

When focusing a 4-GW, fast-rise-time, nsec-range laser onto a solid deuterium target, neutron production is observed. We give evidence for nuclear fusion reactions, measure the electronic temperature, and estimate the number of neutrons for each laser shot.

Inelastic energy ($Q$) profiles and ionization probabilities are measured for ${\mathrm{N}}^{+}$-Ar and ${\mathrm{O}}^{+}$-Kr collisions using the coincidence techniques of Kessel and Everhart. Incident-ion energies from 10 to 150 keV and scattering angles from 9° to 40° for ${\mathrm{N}}^{+}$-Ar collisions, and from 25 to 230 keV and 10° to 40° for ${\mathrm{O}}^{+}$-Kr collisions, are studied. The range of average $Q$ values ($\overline{Q}$) is from about 100 eV to about 1 keV for both cases. The average number of electrons lost in the collision varies from about 0.6 to 1.3 for nitrogen and from 3.3 to 4.6 for argon in the ${\mathrm{N}}^{+}$-Ar collisions. For the ${\mathrm{O}}^{+}$-Kr collisions, the ranges are zero to 1.7 and 2.6 to 6.6 for oxygen and Kr, respectively. For ${\mathrm{N}}^{+}$-Ar collisions, a plot of $\overline{Q}$ versus the distance of closest approach shows an abrupt increase of about 115 eV at about 0.15 Å. A study of the natural linewidths of the coincidence profiles indicates the presence of unresolved structure in this vicinity. For the ${\mathrm{O}}^{+}$-Kr collisions, $\overline{Q}$ was found to depend on both the distance of closest approach and the collision velocity, but not strongly on the scattering angle at higher energies.

The cross section for the excitation of the (0, 0) first negative band of ${\mathrm{N}}_2^{+}$ by electron impact has been measured, using photon-counting techniques, in the energy range from threshold to 3 keV and extrapolated to 10 keV by means of a Bethe-Oppenheimer relation. In order to avoid polarization effects, the primary measurements were made at the "magic angle" of 54° 44′; complementary measurements at 90° were also obtained for comparison purposes. The excitation cross section for the (0, 0) band reached its maximum value at an energy of about 100 eV where it was (1.74 ± 0.17) × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$. The ratio of the total ionization cross section to the excitation cross section was nearly constant over the energy range from 30 eV to 10 keV, and had a value of 14.1.

Using a proportional counter as an x-ray detector, thin-target yields, as well as $K$ x-ray production and ionization cross sections, were determined for Ca, Ti, and Ni when bombarded with 2-28-MeV protons. Broad maxima in the cross sections were found at approximately 8.5, 10.4, and 16.6 MeV for Ca, Ti, and Ni, respectively, in agreement with theoretical calculations based on the Bethe-Born approximation. The shape of the cross-section-versus-bombarding-energy curve agrees well with theory. However, the absolute values of the cross sections were observed to be higher than predicted by theory when the generally accepted value for the effective charge ($Z-0.3\mathrm{}$) was chosen.

Inelastic energy-loss spectra induced by impact of ${\mathrm{H}}^{+}$, ${\mathrm{H}}_2^{+}$, and ${\mathrm{Ar}}^{+}$ on ${\mathrm{N}}_2$ have been measured at incident ion energies of 20-120 keV, with an energy resolution of about 2 eV. Prominent peaks are observed at energy losses of 9.5 and 13.8 eV. The first of these is well resolved and is attributed to excitation of the Lyman-Birge-Hopfield (LBH) system of ${\mathrm{N}}_2$. The peak at 13.8 eV is believed due primarily to excitation of the $b{}_{}{}^1{}_{}{}^{}\pi _u^{}{}_{}{}^{}$ band of the Worley-Jenkins series. The locations of these features on the energy-loss scale do not agree with results of the electron impact work of others and, in general, show trends with projectile velocity that are consistent with an assumed enhancement of excitation to higher vibrational states with the heavier particles. Collision cross sections for excitation of the two peaks are presented, as well as the total ionization cross section and the cross section for total inelastic processes in the case of proton impact.

We present a method for calculating the elastic scattering of electrons from atoms and molecules using the many-body Green's-function techniques of Martin and Schwinger. The procedure involves the self-consistent solution of a pair of equations; one for the one-particle Green's function and the other for the response function of the target in the time-dependent Hartree-Fock approximation (random-phase approximation). That both equations are one-dimensional provides a great computational advantage over more conventional techniques. We discuss the physical nature of our approximation and a numerical scheme to implement our theoretical discussion.

The Raman and infrared bands for superwater are correlated with the previous proposal that superwater consists of stable ice-II-type water clusters, whereas normal water consists of stable ice-I-type water clusters. The strong Raman band for superwater at 620 ${\mathrm{cm}}^{-1\mathrm{}}$ and its shoulder at 640 ${\mathrm{cm}}^{-1\mathrm{}}$ correspond to the strong infrared band for ice II at 642 ${\mathrm{cm}}^{-1\mathrm{}}$ and its shoulder at 660 ${\mathrm{cm}}^{-1\mathrm{}}$. The slight shift can be attributed to temperature variations (from -173 to 25°C) of the infrared band. Examples are given to show that stretching frequencies (2500-4000 ${\mathrm{cm}}^{-1\mathrm{}}$) of hydrates or aqueous salt solutions can be shifted to bending frequencies (around 1400 to about 1600 ${\mathrm{cm}}^{-1\mathrm{}}$) because of imposed stresses on hydrogen bonds. These stresses also involve a change in the librational bands, such as a shift from 153 cm to 410 ${\mathrm{cm}}^{-1\mathrm{}}$ for concentrated HCl solutions. Consequently, the reduction of bands between 2500 and 4000 ${\mathrm{cm}}^{-1\mathrm{}}$ and the appearance of both low-frequency bands at 1400 and 1595 ${\mathrm{cm}}^{-1\mathrm{}}$ and strong librational bands at 620 and 640 ${\mathrm{cm}}^{-1\mathrm{}}$, in going from normal water to superwater, can be explained on the basis of imposed stresses on hydrogen bonds in superwater. That is, the hydrogen bonds in ice-II structures of superwater will have greater stresses than those in ice-I structures of normal water. Hence, for superwater, but not for normal water, the bending-frequency bands at 1400 and 1595 ${\mathrm{cm}}^{-1\mathrm{}}$ become more important dissipators (or absorbers) of photons than the stretching-frequency bands between 2500 and 4000 ${\mathrm{cm}}^{-1\mathrm{}}$. Results on concentrated salt solutions show that one bending-frequency band can be shifted to a different one when greater stress is imposed on the hydrogen bonds. In contrast, the hindered rotational bands (600 ${\mathrm{cm}}^{-1\mathrm{}}$ or so) do not shift. Consequently, the 642-${\mathrm{cm}}^{-1\mathrm{}}$ band of ice II can be correlated with superwater, but the bending-frequency bands of ice II at 1690, 1066, and 960 ${\mathrm{cm}}^{-1\mathrm{}}$ cannot. The 1690-${\mathrm{cm}}^{-1\mathrm{}}$ band of ice II most likely corresponds to the 1595-${\mathrm{cm}}^{-1\mathrm{}}$ band of superwater, and the 1066- and 960-${\mathrm{cm}}^{-1\mathrm{}}$ bands of ice II to the doublet at 1400 ${\mathrm{cm}}^{-1\mathrm{}}$. Experimental data on superwater show that both the ionic model of Lippincott and co-workers and the tetramer model of Bolander and co-workers are erroneous. The very small spread of relaxation times in normal water and the spontaneous settling of superwater from normal water at low temperatures support the proposed cluster-aggregate model for both normal and superwater. Stable clusters would produce cooperative effects in relaxation times and an inability of ice-I clusters (normal water) to interact with ice-II clusters (superwater).

Coupling between longitudinal and transverse waves is examined for an unbounded homogeneous cold plasma in which the several plasma constituents are in relative drift with respect to one another. For mutual relativistic streaming along the direction of a homogeneous dc magnetic field $B$, a dispersion relation is derived. For the special case of two equal counterstreaming electron beams, the extraordinary wave-dispersion law is compared with Lee's nonrelativistic result. For $B=0\mathrm{}$, the dispersion relation is analyzed in some detail, especially as regards the polarization of the unstable eigenmode, and compared with results of Neufeld. We show, both analytically and numerically, that radiation effects are relatively insignificant, except for highly relativistic streaming velocity and for a beam-plasma frequency comparable to that of the background plasma.

Terms up to order ${\left(\frac{\Gamma }{k_{B}T}\right)}^5$ in the high-temperature expansion of the orientational specific heat of ortho-para alloys of solid ${\mathrm{H}}_2$ or ${\mathrm{D}}_2$ are evaluated. Good agreement is obtained between theory and experiment using a Padé approximant and effective values of the quadrupolar coupling constant, $\frac{{\Gamma }_{\mathrm{eff}}}{{\Gamma }_0}=0.83\mathrm{}$ for ${\mathrm{D}}_2$ and $\frac{{\Gamma }_{\mathrm{eff}}}{{\Gamma }_0}=0.80\mathrm{}$ for ${\mathrm{H}}_2$, where ${\Gamma }_0$ is the value for a rigid lattice. These values agree with other determinations of ${\Gamma }_{\mathrm{eff}}$, whereas the $T^{-2\mathrm{}}$ approximation for the specific heat yields anomalously small values of ${\Gamma }_{\mathrm{eff}}$.

The dependence of the recombination coefficient $\alpha$ of ${\mathrm{He}}_2^{+}$ ions and electrons on electron density and gas pressure is measured in helium afterglow plasmas where electron and gas temperatures are equal to 300° K, gas pressure ranges from 10 to 100 Torr, and electron density from ${10}^9$ to 5×${10}^{11}$ ${\mathrm{cm}}^{-3\mathrm{}}$. Electron density decay measured by microwave interferometry is compared with computer solutions of a continuity equation for electrons which takes into account ambipolar diffusion and recombination effects. One finds $\alpha ={\alpha }_2+k_e{n}_e+k_{\mathrm{He}}{n}_{\mathrm{He}}$, where $n_e$ and $n_{\mathrm{He}}$ are the electron and neutral densities, respectively, and ${\alpha }_2\sim 5\times {10}^{-10\mathrm{}}$ ${\mathrm{cm}}^3$ ${\sec }^{-1\mathrm{}}$, $k_e=(2\mathrm{}\pm 0.7)\times {10}^{-20\mathrm{}}$ ${\mathrm{cm}}^6$ ${\sec }^{-1\mathrm{}}$, $k_{\mathrm{He}}=(2\mathrm{}\pm 0.5)\times {10}^{-27\mathrm{}}$ ${\mathrm{cm}}^6$ ${\sec }^{-1\mathrm{}}$. These values compare satisfactorily with results of theoretical computations for a collisional-radiative recombination mechanism including both collisions with electrons and neutrals. The effect of neutrals is particularly noteworthy as far as future experimental work on weakly ionized gases is concerned.

London's stress tensor of the phenomenological theory of superconductivity is identified with the pressure tensor of the gas of superelectrons.

The dispersion of the normal mode at the upper hybrid frequency (Propagating parallel to a uniform magnetic field) in a spatially inhomogeneous plasma has been calculated. The perturbed potential has been solved in $k$ space for the case of a Maxwellian plasma; in the limit $k_{\parallel }\ll k_{\perp }$, the potential function has been shown to satisfy the Whittaker equation. The results obtained are in good agreement with those obtained from a recent experiment.

In an earlier paper, the generalized Langevin approach of Mori and Zwanzig has been applied to generate an exact kinetic equation describing the time correlation of fluctuations in the microscopic phase density for a classical many-body system. In the present work, this kinetic equation is modeled using a single-relaxation-time form for the damping kernel, and the solution of this equation is then studied for large and small values of $k$ and $\omega$. The modeled kinetic equation is used to calculate transverse and lingitudinal current-current correlations in simple classical liquids, and the results are compared with the molecular-dynamics calculations of Rahman for argonlike systems.