A procedure is given whereby for simple diatomic molecules the rotational $g$ factor can be determined from transport measurements alone. The values so obtained agree to within 15% with those obtained from molecular-beam techniques. For ${\mathrm{N}}_2$ and CO, the values of $g_{\mathrm{rot}}$ obtained are - 0.285 and - 0.301, respectively, to be compared with, respectively, - 0.2593 and - 0.2691 as obtained from molecular-beam magnetic resonance.

Calculations have been made of the energy levels and other properties of the states $n{}_{}{}^1{}_{}{}^{}S$, $n{}_{}{}^3{}_{}{}^{}S$, $n{}_{}{}^1{}_{}{}^{}P$, and $n{}_{}{}^3{}_{}{}^{}P$, $n=2\mathrm{} \mathrm{to} 5$, for atoms belonging to the helium isoelectronic sequence up to $Z=10\mathrm{}$, and also for the higher excited $S$ states of helium. The theoretical term values, including the contributions from the mass-polarization correction and the relativistic effects of order ${\alpha }^2$ are listed. A detailed comparison with the experimentally determined energy differences between $S$ and $P$ states for He I up to F VIII shows a satisfactory agreement in almost every case, provided that we include an estimate of the Lamb-shift correction to the $S$-state energy level when considering transitions involving the $1{}_{}{}^1{}_{}{}^{}S$, $2{}_{}{}^1{}_{}{}^{}S$, or $2{}_{}{}^3{}_{}{}^{}S$ states.

Corrections to the Hartree-Fock (HF) theory which arise as a result of electrostatic configuration interaction are calculated for a heavy ion ${\mathrm{Pr}}^{3+}$. The effect of configuration interaction upon the $4f^2$ configuration is represented by effective two-body operators of the form $\Sigma k^{}{a}_k{C}_1^{\mathrm{}\left(k\right)\mathrm{}}{C}_2^{\mathrm{}\left(k\right)\mathrm{}}$. These operators are evaluated using perturbation theory and graphical methods. The effect of the operators of even rank is to depress the values of the Slater $F^k$ integrals below their HF values. The two-body operators of odd rank do not appear within the ordinary HF theory. The Trees parameter $\alpha$ is the coefficient of an operator of this kind. It is found that the corrections to the Slater integrals converge slowly. The contributions to the operators of odd rank converge properly, however, and we obtain the values $\alpha =28\mathrm{}$, $\beta =-616\mathrm{}$, and $\gamma =1611\mathrm{}$. This may be compared with the empirical values $\alpha =24\mathrm{}$, $\beta =-586\mathrm{}$, and $\gamma =728\mathrm{}$. The value of $\gamma$ is determined empirically by the position of a single level, ${}_{}{}^1{}_{}{}^{}S$. It is suggested that the free-ion ${}_{}{}^1{}_{}{}^{}S$ level has not been properly identified.

A procedure is presented that uses perturbation theory to calculate correlation corrections for atomic polarizability when the atom is described by a local potential in the starting approximation. Zeroth-order polarizabilities and first-order correlation corrections for them have been calculated for Mg, Na, Ne, Be, Li, and He atoms using the Hartree-Fock-Slater potential and another local potential. For most of the atoms, the corrections are found to be significantly large. Implications are discussed.

We have measured the hyperfine relaxation time of cesium vapor in the presence of foreign gases. We have therefore been able to measure the diffusion coefficient $D_0$ and the cross section $\sigma 〈\overrightarrow{\mathrm{S}}·\overrightarrow{\mathrm{I}}〉$ of hyperfine relaxation due to the collisions with the foreign gas. The values of $D_0$ for He, Ne, Ar, and ${\mathrm{N}}_2$ are 0.204±0.04, 0.153±0.014, 0.134±0.02, and 0.073±0.015 ${\mathrm{cm}}^2$/sec at 0°C and 760 Torr, respectively. The cross sections are 2.80±0.3, 9.27±0.9, 104±10, and 55.2±4.4 in units of ${10}^{-23\mathrm{}}$ ${\mathrm{cm}}^2$ for He, Ne, Ar, and ${\mathrm{N}}_2$, respectively. We have also improved on the measurement of the spin-exchange cross section ${\sigma }_{\mathrm{ex}}$ obtaining the value (2.18±0.12)×${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$. We compare the problems arising in the study of hyperfine and Zeeman relaxation and we discuss the results.

Cross sections for $K$ x-ray production in carbon are presented for collisions involving incident ${\mathrm{C}}^{+}$, ${\mathrm{N}}^{+}$, ${\mathrm{O}}^{+}$, ${\mathrm{Ne}}^{+}$, ${\mathrm{Ar}}^{+}$, ${\mathrm{Kr}}^{+}$, and ${\mathrm{Xe}}^{+}$ in the energy range 20 keV-1.5 MeV. Thick-target x-ray yield data are also included. The cross-section measurements are in excellent agreement with a simple theoretical model based on the Landau-Zener theory of level crossing.

Calculations and measurements of energy dissipation by protons at energies above ∼ 100 keV are presented. The calculations, which make use of a statistical model of the atom, are based on a refinement of a procedure suggested by Lindhard and Scharff. The theoretical section of the present paper is concerned with energy straggling, as stopping powers were dealt with in an earlier publication. Measurements of stopping power and energy straggling for 100-500-keV protons have been made in various gases, viz. hydrogen, helium, air, neon, argon, and krypton. The stopping-power data are in good agreement with theory and earlier experimental work. For the heavy gases, the experimental straggling values are seen to be an increasing function of energy, as expected from theory. In a more quantitative comparison, however, some discrepancy between theory and experiment is observed.

A modified close-coupling formalism has been applied to the electron—atomic-hydrogen system. We investigate various possible choices of pseudostates which are used to augment the eigenfunction expansion. As a test of the appropriateness of these choices we have evaluated various bound and scattering properties of the electron—atomic-hydrogen system and have computed photodetachment cross sections for ${\mathrm{H}}^{-}$ as well. We find that pseudostates which emphasize short-range interactions are superior to those which incorporate long-range polarization effects when one computes elastic scattering phase shifts in the nonresonant region below the $n=2\mathrm{}$ threshold. Excellent photodetachment cross sections for ${\mathrm{H}}^{-}$ are also obtained using initial and final states obtained from a modified close-coupling formalism which includes these short-range pseudostates.

Experiments on the uv photoabsorption of Xe have determined level positions, line intensities, Landé $g$ factors, intensity profiles in the auto-ionization region, and the branching ratio of photoelectron groups. This paper expresses all these data in terms of a single set of theoretical parameters which pertain to collisions of the $e+{\mathrm{Xe}}^{+}$ system with $J=1\mathrm{}$ and characterize the five close-coupling eigenchannels of this system. Values of the parameters, obtained by fitting the experimental data, provide (1) values of the zero-energy scattering eigenphases, (2) evidence that the orbital angular momentum of the free electron ($l=0\mathrm{} or 2$) is a good quantum number to within ∼ 2%, and (3) evidence that the $\mathrm{LS}$ coupling classification of the $e+{\mathrm{Xe}}^{+}$ complex holds approximately, but only for $l=2\mathrm{}$. The whole analysis correlated diverse experimental data into a unified pattern and can be extended to other values of $J$ and $l$ to other rare gases and to spectra of other elements.

Analogies between Coulomb excitations of nuclei and ionic molecules by charged projectiles are utilized to calculate vibro rotational excitations of $\mathrm{H}_2^{}{}_{}{}^{+}$ molecular ions by $e^{+}$ impact by a semiclassical method developed in the nuclear case. The coupling between vibrational-rotational states of target molecules can very significantly affect the scattering cross sections for either kind of excitation on the other. In this paper we have shown that the effect of such coupling may be included very conveniently, under the present model, whenever applicable. In a subsequent paper we intend to publish results for the experimentally more accessible systems, including the ${\mathrm{H}}^{+}$ + $\mathrm{H}_2^{}{}_{}{}^{+}$ system.

Relative abundances of multiply charged neon, argon, and krypton ions produced by x rays of energies 0.28, 1.5, 5.4, and 8.0 keV have been measured with a time-of-flight mass spectrometer. Effectively monoenergetic x rays were obtained by a filtering technique whereby two filters with transmissions matching at all energies except at the $K$ characteristic line of the x-ray tube target material were alternately placed in the x-ray beam. The data when corrected for charge-dependent discrimination effects are consistent with previous measurements and, except for neon, with calculations which include the electron shakeoff mechanism in addition to Auger transitions. The results for neon at 0.28 keV confirm the need for including electron correlation effects in the description of the ionization process. Other discrepancies between theory and experiment can be explained by considering the energy dependence of partial photoionization cross sections calculated by Rakavy and Ron.

The absolute cross sections for the excitation of the Oi(${}_{}{}^3{}_{}{}^{}S$) and Ni(${}_{}{}^4{}_{}{}^{}P$) resonance states by electron impact on atomic oxygen and nitrogen have been measured over the aeronomically important energy range from threshold to 150 eV. The peak excitation cross sections for these states were found to be 1.2 × ${10}^{-16\mathrm{}}$ and 6.2 × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$, respectively. At low energies, the total Oi(${}_{}{}^3{}_{}{}^{}S$) and Ni(${}_{}{}^4{}_{}{}^{}P$) cross sections exhibited well-developed peaks near 15 and 25 eV, respectively, indicating that cascade processes probably play an important role in exciting the Oi(${}_{}{}^3{}_{}{}^{}S$) and Ni(${}_{}{}^4{}_{}{}^{}P$) states.

Dissociative electron attachment frequencies have been determined for bromine in the presence of helium using microwave cavity techniques. Initial ionization was produced by a single light pulse from a hydrogen flash lamp. The value for the electron attachment coefficient $k$ determined from the attachment frequency data is $k=0.82\mathrm{}\times {10}^{-12}$ ${\mathrm{cm}}^3$ ${\sec }^{-1\mathrm{}}$ ±10% at 296 °K. The electron-ion ambipolar diffusion coefficient ($D_{a+}p$) for $\mathrm{Br}_2^{}{}_{}{}^{+}$ in helium was found to be 795 ${\mathrm{cm}}^2$ Torr ${\sec }^{-1\mathrm{}}$ ± 10% at 296 °K. The positive-ion-negative-ion ambipolar diffusion coefficient for this ion was found to be 380 ${\mathrm{cm}}^2$ Torr ${\sec }^{-1\mathrm{}}$ ± 10% at 296 °K under the conditions where the only significant negative ion present was ${\mathrm{Br}}^{-}$.

The Euler-Lagrange variational method is applied to plane-wave factors as they appear in the parametric time-dependent Schrödinger-equation model for atom-atom scattering. The resulting Euler-Lagrange equations provide a prescription for determining a general plane-wave-factor function of the electron coordinates and time.

It is shown that, as the complex energy approaches its real physical value, the dominant part of the amplitude for ionization derived from the Faddeev equations is a product of a known singular factor and the physical scattering amplitude. This information suggests a method of calculating ionization amplitudes from the Faddeev equations. Corrections to the dominant term for this and another amplitude are discussed. Some numerical tests of the method as applied to a simple model are given.

A standard formalism of quantum electrodynamics is used to investigate the interaction between two neutral atoms. The study is based on an approximate solution of the two-particle Green's function. The frequency distribution of the photon scattering is obtained. We also consider the self-stimulation effect when both atoms are in excited states.

The interaction of a bound electron with external radiation fields of finite intensity is treated with the standard quantum-electrodynamical (QED) formalism of Feynman and Dyson. We first construct an equation for a bound electron in finite-intensity radiation fields, such as those encountered in early molecular-beam experiments and in recent masers and lasers. The Green's function for the equation so obtained enables us to compute the induced transition probabilities for various systems of interest. In this paper, we carry out the calculations on the two-level and three-level systems explicitly, where we find that, to order $e^4$, the QED method based on forward scattering and the semiclassical treatment differ. As we consider only the interaction of electrons with low-energy photons, we may ignore the virtual photon processes, in accordance with the low-energy theorem. As a result, this treatment contains only finite calculations. We demonstrate explicitly that our results are in qualitative agreement with the molecular-beam experiments of Kusch, for which the semiclassical treatment of Salwen fails to predict the results. Consequently, we expect an intensity-dependent effect which can be properly explained only by QED and not by the semiclassical treatment. We also include the effect of nonelectromagnetic relaxation on the induced transition probability of a two-level system, for which we obtain an expression slightly different from that used by Ramsey for the hydrogen maser. Finally, we derive some expressions which will be of interest in experiments related to lasers and masers.

In a previous paper, the stabilization method of calculating resonance parameters was applied to a one-dimensional model problem of potential scattering. The method is here extended to compound-state resonances in elastic scattering, and its application to a model problem for a target with two bound states is examined. The resonance parameters are calculated by two methods which use information obtained in the diagonalization of the exact Hamiltonian in appropriately chosen sets of square-integrable basis functions: One is presented for the first time here; the other is similar to the procedure used in the potential-scattering problem. In addition to the stabilization method, we have applied to the model problem some other techniques, which have been previously proposed for the calculation of resonance parameters. The availability of the exact solutions enables us to make some preliminary assessments of the reliability and the difficulty that might be expected from these approximation methods.

The existence of liquid crystalline order in two dimensions is discussed. It is shown that, contrary to a previous contention, a theory based on the lowest-order approximation to the virial expansion of the free energy (the Onsager limit) indicates that a nematic ordering transition does occur. The effects of the fluctuations in order are considered, and it is shown that the usual elastic theories cannot hold in two dimensions. I attempt to construct a microscopic discussion based on the Bogoliubov inequality, but find that it cannot be applied straightforwardly to this case.

A relationship between the Brueckner and Jastrow many-body theories, which was previously derived for three- and four-particle wave functions, is shown to be valid for any number of particles.