We comment on a recently published paper of Gupta and Sutherland on the thermodynamics of the sine-Gordon chain. We present a short alternative derivation of the various thermodynamic functions in the high-and low-temperature limits. While our mathematical results essentially agree with theirs, we propose a different physical interpretation.

In heavy-ion collisions, the molecular electronic dipole moment is accelerated and may emit continuum x rays even in the absence of inner-shell vacancies. Semiclassical calculations of the bremsstrahlung intensity are made for 200-MeV Kr + Ti encounters using hydrogenic two-center wave functions to calculate the molecular dipole moment. The bremsstrahlung is confined to x-ray energies below the Kr $K$ x-ray lines.

Static electric dipole polarizabilities are computed for all states of the ground electronic configurations of C, N, and O atoms. The method used first obtains perturbing orbital functions by an approximate variational calculation of the polarizability, and then uses these orbitals to define virtual excitations for calculations by superposition of configurations. One-electron virtual excitations and transitions involving these orbitals are included in the $N$-electron variational wave function. Excellent agreement is obtained with the experimentally known polarizabilities of the $\mathrm{N}\left({}_{}{}^4{}_{}{}^{}S_{}^o{}_{}{}^{}\right)$ and $\mathrm{O}\left({}_{}{}^3{}_{}{}^{}P\right)$ ground states, and with prior theoretical results for these atoms and for $\mathrm{C}\left({}_{}{}^3{}_{}{}^{}P\right)$. Polarizabilities of the ground-configuration metastable states $\mathrm{C}({}_{}{}^1{}_{}{}^{}D, {}_{}{}^1{}_{}{}^{}S)$, $\mathrm{N}({}_{}{}^2{}_{}{}^{}D_{}^o{}_{}{}^{}, {}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{})$, and $\mathrm{O}({}_{}{}^1{}_{}{}^{}D, {}_{}{}^1{}_{}{}^{}S)$ are computed at the same level of approximation.

A theoretical multichannel treatment of dissociative recombination is presented, with application to $e$+N${\mathrm{O}}^{+}$ recombination. The conventional "indirect" and "direct" dissociative recombinations are treated together on the same footing. The physically meaningful eigenchannel parameters in the multichannel theory, for the NO system, are here determined by fitting to a wealth of spectroscopic data. The results are then compared with some previous theoretical predictions as well as recent experimental data, and a possible reconcilement is suggested for the discrepancy in the ($e+\mathrm{N}{\mathrm{O}}^{+}$) recombination rates given by afterglow and stored-ion measurements.

Elastic electron-hydrogen scattering at intermediate energies is analyzed with a modified Glauber amplitude proposed earlier by this author and the Glauber exchange effect included through a recent eikonal formula by Foster and Williamson. The results of the calculation are found to be in very good agreement with experimental data. This work, therefore, confirms rather clearly that the deficiency of the Glauber amplitude when applied to these atomic processes, stems mainly from the inadequacy of the second-order term of its eikonal expansion in representing the second-Born term and that the Glauber exchange effect is of a considerable magnitude and, hence, cannot be neglected in these processes, especially at very large scattering angles.

The continuum-distorted-wave (CDW) approximation has been used to calculate the electron-capture cross sections $Q\left(\mathrm{nl}\right)\mathrm{}$ when a fast proton collides with a helium target atom. The range of the projectile energy is from 25 keV to 3 MeV and the electron-capture states considered are $nl=1s, 2s, \mathrm{and} 2p$. Of specific interest here is the sensitivity of these cross sections with respect to a systematic improvement in the description of the target ground-state wave function, both up to and beyond the Hartree-Fock level. Large changes were found to occur in the magnitude of each $Q\left(\mathrm{nl}\right)\mathrm{}$ as we progress from a simple one-parameter wave function for He up to a configuration-interaction description: The latter wave function accounted for about 99% of the electron correlation energy. Values of the total capture cross section were determined and compared with experiment over the available energy range of 100-2990 keV. The correlated results were, overall, in good agreement with experiment—especially in the high-energy region.

An accurate numerical calculation of $K$-shell hole production by light ions is presented for nonrelativistic target atoms in the projectile energy region ${\eta }^{\frac{1}{2}} (=\frac{\hslash v}{Z_n{e}^2})\lesssim 1$. Both hydrogenic and Hartree-Fock targetatom potentials were investigated. After correcting a computer error in some of our initial results published recently, good agreement is found for proton impact absolute cross sections and for the projectile atomicnumber dependence of the cross section. We also present simple analytical formulas which fairly well reproduce our results for target atomic numbers ranging from $Z_n=13\mathrm{} \mathrm{to} 30$. This will hopefully facilitate the use by experimentalists of this rather involved calculation, which includes up to 54 basis functions. An interesting result of the comparison between the calculated and experimental atomic-number dependence of the cross section is that it suggests charge-transfer contributions to $K$-shell hole production are at least as large as given by the Brinkman-Kramers (BK) approximation. This requires that a great deal of electron stripping occurs as the projectile tries to leave the atom with its captured electron, because experimentally measured cross sections for charge transfer are considerably less than the BK. A simple model is presented which shows that this is to be expected.

The rotational transitions in H${\mathrm{D}}^{+}$-H${\mathrm{D}}^{+}$ collisions have been studied by using the Coulomb excitation theory of Alder et al. The energy range of the calculations extends from 0.1 to 1 eV so that the probability of vibrational excitation at the higher energies is small and at the same time the effect of short-range anisotropies in the ion-ion interaction potential is insignificant. Since $\frac{V}{E}$ is ≪ 1, the first-order perturbation theory used for our calculations is valid. The rotational transitions induced by the interactions of the charge, dipole, and quadrupole moments of the two molecular ions have been considered. In addition to the single transitions of the ions, simultaneous transitions as well as resonance transfer of energy have been considered. The results have brought out interesting features regarding the relative importance of the various types of transitions involved.

The ${\mathrm{Ne}}^{+}$-He and ${\mathrm{He}}^{+}$-Ne collisions have been studied by means of optical spectrometry in the projectile energy range 10-150 keV. Very similar and regular oscillations in the Rydberg-state total cross sections are found for He I in both collisions and for singlet as well as triplet excitation. These oscillations are well described by the Rosenthal model. The Hei $4d{}_{}{}^{1,3}{}_{}{}^{}D$ states display two superimposed oscillations for center-ofmass collision energies above 6.4 keV. We interpret this as the opening of a third exit channel, believed to be the He i $4f{}_{}{}^{1,3}{}_{}{}^{}F$. No (or very little) structure is found in the Rydberg-state total cross sections for He ii, Ne i, Ne ii, or Ne iii levels.

We show that the minimization of the variance integral provides a method for the determination of scattering wave functions which uses discrete basis functions exclusively. By using a separable representation of the scattering potential only one new class of matrix elements appears in the evaluation of the variance integral which is not already required in the diagonalization of the Hamiltonian. The choice of Gaussian basis functions for the expansion of the scattering wave function should make the method particularly applicable to electron-molecule scattering. Some advantages and limitations of the method are discussed.

This paper summarizes the usual assumptions made in applying dispersion relations to electron-atom scattering. It is shown that in the static exchange approximation, electron exchange gives rise to a third-order pole, and the position and strength of this pole are calculated. It is then argued that this singularity is a feature of the exact scattering amplitude. Finally a numerical study is carried out which confirms the existence of additional left-hand singularities.

The present paper, one of a four-part series, examines $K$-vacancy cross sections in collisions of symmetric and near-symmetric systems produced with 12-60-MeV Br, 200-330-MeV Kr, 15-80-MeV I, 326-470-MeV Xe, and 90-110-MeV Pb beams. Cross sections are discussed from the point of view of molecular-orbital formation during the collision. In that model, the summed $K$-vacancy cross sections of both collision partners represents essentially the total $2p\sigma$ vacancy cross section in the outgoing part of the collision. Experimental summed cross sections using solid targets can have appreciable contributions from multiple-collision effects, which are computed in detail. Proposed single-collision mechanisms of $2p\sigma$ vacancy formation are also examined, but none can be established with certainty. The sharing of $2p\sigma$ vacancies on the outgoing part of the collision between the $K$ shells of two collision partners is found to agree well with a previously derived formula based on the Nikitin-Demkov long-range coupling model.

The first Born approximation (FBA) is applied to the calculation of single-electron-loss cross sections for various ions and atoms containing from one to seven electrons. Screened hydrogenic wave functions are used for the states of the electron ejected from the projectile, and Hartree-Fock elastic and incoherent scattering factors are used to describe the target. The effect of the target atom on the scaling of projectile ionization cross sections with repect to the projectile nuclear charge is explored in the case of hydrogenlike ions. Also examined is the scaling of the cross section with respect to the target nuclear charge for electron loss by ${\mathrm{Fe}}^{+25\mathrm{}}$ in collision with neutral atoms ranging from H to Fe. These results are compared to those of the binary-encounter approximation (BEA) and to the FBA for the case of ionization by completely stripped target ions. Electron-loss cross sections are also calculated for the ions ${\mathrm{O}}^{+i}\mathrm{}(i=3-7\mathrm{})\mathrm{}$ and ${\mathrm{N}}^{+i}\mathrm{}(i=0-6\mathrm{})\mathrm{}$ in collision with He targets in the energy range of ∼0.1 to 100 MeV/nucleon. These results are found to be in excellent agreement with the available data near the peak of the ionization cross section.

We discuss $K$-vacancy production in the higher-$Z$ collision partner in very asymmetric heavy-ion collisions. In terms of an atomic model this process would be described as $1s$-vacancy production, but in terms of a molecular model it would be called $1s\sigma$-vacancy production. Experimental results from our work with 12-60-MeV Br, 200-330-MeV Kr, 15-80-MeV I, and 326-470-MeV Xe beams, and the work of others with lighter projectiles, are used for comparison with available theories and prescriptions for $K$-vacancy production. We discuss the binding correction model of Basbas et al., and semiempirical scaling law proposals made by Foster et al., Meyerhof et al., and Andersen et al. Since none of these prescriptions systematically reproduce the experimental $1s\sigma$-vacancy cross sections, we have developed a more detailed formula which stresses the transient united-atom formation during a heavy-ion collision. Other factors influencing $1s\sigma$-vacancy formation, such as Coulomb deflection, charge exchange, and electronic relativistic effects, are discussed.

Depolarization effects in pulsed photoionization of state-selected lithium atoms have been observed. Experimental evidence and theoretical analysis demonstrate that these effects are produced by resonant excitation of the $2{}_{}{}^2{}_{}{}^{}P$ state. Based upon the analysis, it is argued that resonant excitation of the $2{}_{}{}^2{}_{}{}^{}P$ state with circularly polarized cw laser light followed by broad-band pulsed ionizing radiation can be used to produce an intense highly polarized electron beam with longitudinal polarization.

The problem of a two-photon resonance coupled to a one-photon resonance through a common energy level is treated by a multiple-time-scale perturbation theory which reduces the many-level system to an effective three-level system. The one-photon resonance produces dynamic Stark splitting (Autler-Townes effect) in the two-photon resonance condition; this feature is exploited to suggest a means for measuring transition dipole moments. The combined one- and two-photon resonance conditions restrict the resonantly interacting molecules to a small range of velocities, thus eliminating Doppler broadening. The analytical solution for the density matrix of the effective three-level system shows that (1) the lowest level can be depopulated and (2) the distribution of population between the upper two levels can be set at will by appropriate choice of the one-photon detuning or the field strength. These features are used to suggest an up-conversion scheme.

Differential cross sections for incoherent scattering by $K$-shell electrons have been measured, using coincidence techniques, for incident photons having energies of 662, 320, and 145 keV. Observations were made of the spectral distributions of scattered photons emerging at scattering angles ranging from 20° to approximately 140°. Target materials were iron, tin, holmium, and gold at 320 keV; tin and gold at 662 keV; and iron and tin at 145 keV. A typical spectrum generally displays a scattered quasi-Compton peak which is usually much narrower than would be expected from the bound-state electron motion. Rather than monotonically increasing with atomic number, the peak width typically reaches a broad maximum between $Z=50\mathrm{}$ and $Z=67\mathrm{}$ and then decreases with increasing atomic number. The peak, also typically, reaches a broad maximum width for scattering angles between 45° and 60°. No Compton defect is observed to within ±20 keV. Underlying the quasi-Compton peak is a continuum which diverges at the low end of the scattered-photon spectrum for the following cases: gold, holmium, and tin targets for 320-keV incident photons; gold and possibly tin targets for 662-keV incident photons. This infrared divergence (IRD) is expected on general grounds and has been predicted. The observed IRD continuum is very nearly isotropic.

Starting from the treatment of Fano for the behavior of the total cross section in a photoionization (or electron-ion scattering) experiment in the vicinity of a resonance, we present a theoretical formula for the behavior of an individual final-state channel in the neighborhood of a resonance. This result is then used to derive another theoretical formula for the behavior of the ratio of two partial cross sections (i.e., the branching ratio) in the vicinity of a resonance. This branching-ratio formula depends on the profile parameters $q$, $\Gamma$, and ${\rho }^2$ for the resonance, on the branching ratio outside the resonance, and on two new parameters which are explicitly related to scattering-matrix elements and phase shifts.

First observations are presented to the optically thin and reabsorption free-hydrogen resonance line Lyman-$\alpha$, emitted from a dense equilibrium plasma ($n_e\approx {10}^{23}$ ${\mathrm{m}}^{-3\mathrm{}}$, $T_e\approx {10}^4$ K). In the core of the line (wavelength range up to three half-widths) the Stark profiles are determined nearly exclusively by the central Stark component, which is broadened significantly more strongly than predicted by the theories. The experimental Ly-$\alpha$ Stark widths are larger by a factor of about 2.5 than theoretical ones.