The Compton profile of the ground state of molecular hydrogen is calculated using the Liu 39-configuration-interaction (CI) wave function to confirm the experimental results of Eisenberger. This is in contrast to previous theoretical results obtained with the Hartree-Fock and Das-Wahl CI wave functions. The merits of these wave functions and also the best-over-lap wave function are discussed.

Theoretical formulas with higher-order perturbation terms are given for the rotational levels of ${}_{}{}^2{}_{}{}^{}\mathrm{II}$ states, and are applied to the OH free radical. By analyzing existing data values of several molecular parameters including the rotational constant $B$, the spin-orbit coupling constant $A$ and $\Lambda$-doublet constants $\alpha$ and $\beta$ are obtained for some vibrational states. The magnetic $g$ factors are discussed and analyzed. A recent experiment on laser magnetic reasonance (LMR) is also discussed.

The diffusion of an optically injected electron-hole plasma parallel and perpendicular to an applied magnetic field has been studied in germanium. The density gradient within the crystal has been measured directly by an infrared-beam-absorption technique. Diffusion measurements made parallel to the magnetic field are adequately explained by the theory. For values of ${\omega }_c\tau >3.5\mathrm{}$ (where ${\omega }_c$ is the electron cyclotron frequency and $\tau$ is the electron scattering time with the lattice), the diffusion across the magnetic field is more rapid than that predicted by a theory that takes into account the anisotropic magnetoconductive properties of germanium. If we express the observed diffusion coefficient as the sum of the computed collisional coefficient plus a term $D_{\mathrm{excess}}$ representing the additional diffusion, we find that at the largest achievable values of ${\omega }_c\tau$, $D_{\mathrm{excess}}$ is within a factor of 2 of the Bohm value $\frac{\mathrm{kT}}{16eB}$ ${\mathrm{cm}}^2$ ${\sec }^{-1\mathrm{}}$.

Calculations are presented for the photoionization cross section of the neutral iron atom for photon energies from threshold to 10 keV. Our results are based upon the use of nonrelativistic wave functions and the dipole approximation. Correlations are included to low orders by the use of many-body perturbation theory; and the cross section including correlations is found to differ greatly from that obtained from the Hartree-Fock approximation. Hartree-Fock results are also presented for comparison. We roughly estimate our cross section, including correlations near threshold, to be accurate to within a factor of 2 when integrated over a few eV.

Polarization analysis of electrons extracted from a weak helium discharge in which the $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ metastable atoms are spin oriented by optical pumping indicates that the reaction $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\right)+\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\right)\to \mathrm{He}\left(1\mathrm{}{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\right)+{\mathrm{He}}^{+}+e^{-}$ is the predominant source of ionization in the discharge. The reaction conserves spin angular momentum and therefore produces polarized electrons. The process has been exploited to produce continuous beams of electrons with polarization as high as 10%. For a source-gas pressure of 0.035 torr, a continuous 4-μA beam with 8% spin polarization has been realized. Electrons extracted from the late afterglow of a pulsed discharge have 17% polarization at an optimum pressure of 0.1 torr.

Conservation of spin angular momentum in the reaction $\mathrm{He}\left(2\mathrm{}{}_{}{}^2{}_{}{}^{}S_1^{}{}_{}{}^{}\right)+\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\right)\to \mathrm{He}(1\mathrm{}{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}+{\mathrm{He}}^{+}+e^{-}$ is demonstrated quantitatively in the afterglow of a helium discharge by measuring the dependence of the electron production rate upon $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ spin-state populations, which are manipulated by an optical-pumping technique.

The process of photoionization of polarized alkali atoms in an atomic beam has been studied for potassium and lithium. Depolarization processes associated with photoionization of alkali molecules and optically excited atoms were discovered. After eliminating these depolarization mechanisms, the measured photoelectron polarization agreed within an accuracy of 3% with the predicted polarization based on the current theory for this electric dipole process. Using a polarized ${\mathrm{Li}}^6$ atomic beam and a pulsed uv light source, we have produced an intense and highly polarized electron beam with 2×${10}^8$ electrons in 1.5 μsec and with a polarization of 0.78, which is a suitable prototype injector source for a high-energy electron accelerator.

A multiconfiguration Hartree-Fock method has been used to compute low-lying autoionization states of ${\mathrm{Li}}^{-}$ and ${\mathrm{Na}}^{-}$. The electron-detachment potentials for these systems have also been computed and agree well with a similar calculation by Weiss. The present formulation permits a simple construction of projection operators used in determining autoionization states for $e^{-}$-alkali-atom systems. For ${\mathrm{Li}}^{-}$ three autoionization states have been found below the $1s^{2}3p$- level and four below the $1s^{2}3p$ level. Only one autoionization state is found for ${\mathrm{Na}}^{-}$.

A procedure which combines the methods of variable-phase and $R$-matrix theory is formulated for multichannel scattering processes. $R$-matrix theory is used to obtain the logarithmic derivative of the scattering functions at a radius $a$, beyond which all exchange potentials are negligible. Variable-phase theory is used to construct a radially dependent reaction matrix which is integrated from $a$ to infinity. The method is applied to a two-channel model which has some of the features of the low-energy electron-hydrogen problem. Essentially exact results are obtained with as few as 40 $R$-matrix states (20 per channel).

Photoionization calculations in the noble gases Ne($L$ shell), Ar($L$ and $M$ shell), Kr($M$ and $N$ shell), and Xe($M$, $N$, and $O$ shell) using Hartree-Fock (HF) wave functions for the outgoing photoelectron are reported. Total cross sections are presented and compared with experiment. Subshell cross sections are also given and unusual features are pointed out in an effort to stimulate direct measurements of subshell cross sections via the technique of photoelectron spectroscopy. The relation between our work and the intrachannel coupling of the Fano continuum configuration-interaction theory is discussed. The asymmetry parameter $\beta$ of the angular distribution of the photoelectrons, $1+\beta$ $P_2(cos\theta$, is calculated in HF-length, HF-velocity, and Hartree-Slater (HS) approximations. The results show remarkable agreement among the $\beta \text{'}\mathrm{s}$ resulting from the several approximations despite the rather different cross sections they predict. Good agreement with recent experimental results is found and the need for further experimental work is pointed out. Extremely oscillatory behavior of the energy dependence of $\beta$ is found and the reasons for such behavior are discussed.

Cross sections for the ejection of electrons, differential in electron energy and angle of emission, have been measured for energetic protons on molecular hydrogen. Electron-energy distributions are presented for ten angles between 20 and 130 deg for each of five proton energies between 0.3 and 1.5 MeV. The results are compared with calculations based on binary-encounter theory, the Born approximation, and the Faddeev equations. Qualitative agreement with the latter provides supporting evidence for the inclusion of a long-range electron-proton interaction in the collision theory for proton energies as high as 1.5 MeV.

Cross sections have been measured for the emission of Lyman-$\alpha$ radiation in collisions of 1-25-keV hydrogen atoms with He, Ne, Ar, Kr, and Xe owing to excitation of the fast atom to the $2p$ and $2s$ states. The intensity of Lyman-$\alpha$ emitted spontaneously from collisionally excited $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$, was measured at 54.7 or 125.3° with respect to the H beam in an essentially field-free collision chamber with an oxygen-filtered photometer calibrated by reference to previous results for ${\mathrm{H}}^{+}$ on Ar. After a small correction for cascade effects, the data yield the cross sections for population of the $2p$ state in these collisions. An electric field, oriented in the direction of the beam, was applied within the collision chamber to quench collisionally excited $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$, and the resulting increase in Lyman-$\alpha$ radiation has been used to derive the cross sections for formation of the $2s$ state. The viewing geometry and the electric field orientation were designed to minimize the effects of polarization of the light emitted from $\mathrm{H}\mathrm{}\left(2p\right)\mathrm{}$ and $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$, and of changes in polarization when the quenching electric field was applied that might otherwise lead to large errors in the $2s$ cross section. The cross sections increase in magnitude and degree of structure with increasing atomic number of the target. Except for collisions with Ne, excitation of $\mathrm{H}\mathrm{}\left(2p\right)\mathrm{}$ is always more probable than excitation of $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$. A relationship between the emission and stripping cross sections is presented, the relative probabilities of excitation and stripping being rather independent of target. Our results are compared with previous measurements made at higher energies and with theoretical estimates of these cross sections. The present extension of previous results to lower energy has revealed new structure in the energy dependence of the cross sections for the heavier targets. Existing theoretical treatments of these collisions fail to yield either the magnitude or energy dependence of the cross sections at energies below 5 keV.

The $\frac{1}{Z}$ expansion method is used to calculate the eigenvalues of the $2p3p{}_{}{}^3{}_{}{}^{}P$ and $2p3d{}_{}{}^{1,3}{}_{}{}^{}D$ states of the helium isoelectronic sequence. The results are compared to variational calculations for neutral helium. Wavelengths are predicted for a number of transitions originating in doubly excited states of the heliumlike ions up to Fe xxv. The results for neutral helium are compared to recent beam-foil experiments and alternative line identifications are made. The predicted wavelength for the $2p3d{}_{}{}^3{}_{}{}^{}D-2\mathrm{}{p}^2{}_{}{}^3{}_{}{}^{}P$ transition is 3014 Å, in close agreement with the line observed by Berry et al. at 3012 ± 2 Å.

Relative differential cross sections for inelastic scattering of C${\mathrm{O}}^{+}$ by Ar have been examined with a high-resolution ion-beam apparatus in which a C${\mathrm{O}}^{+}$ beam interacts with a neutral-Ar beam and the energy, mass, and angular distribution of scattered ions are measured. Maxima in the inelastic energy-loss spectra occur at energies corresponding to C${\mathrm{O}}^{+}$ spectroscopic vibrational spacings. The probabilities of multiquantum vibrational transitions are found to increase with both reactant-ion kinetic energy and scattering angle. Cross sections for vibrational excitation at small scattering angles are adequately described by a semiclassical oriented-nonlinear-encounter model in which an impact-parameter treatment is used to estimate collisional energy transfer for a forced oscillator, and time-dependent wave functions employed to evaluate vibrational transition probabilities. The energy width of the inelastic peaks indicated that simultaneous vibrational-rotational excitations occur. Weakly inelastic processes are observed below the threshold for vibrational energy loss, corresponding to rotational excitation with the relative importance of rotational transitions increasing with decreasing energy and scattering angle.

The frame-transformation theory is applied to a calculation of electron scattering from ${\mathrm{H}}_2$ in the energy range of 1-10 eV. Results are presented for differential as well as integrated cross sections for pure vibrational and rotational-vibrational excitation processes. Our calculations are in very satisfactory agreement with experiment and are subject to easy interpretation.

Ion-molecule reactions between Ba and some atmospheric molecular ions have been studied using a merging-beams apparatus. The interaction energy $W$ (i.e., relative kinetic energy in the center-of-mass system) was varied from 0.1 to 10 or 20 eV. The processes investigated were Ba + ${\mathrm{O}}_2^{+}$ → Ba${\mathrm{O}}^{+}$ + O, Ba + ${\mathrm{N}}_2^{+}$ → Ba${\mathrm{N}}^{+}$ + N, and Ba + N${\mathrm{O}}^{+}$ → Ba${\mathrm{N}}^{+}$ + O and Ba + N${\mathrm{O}}^{+}$ → Ba${\mathrm{O}}^{+}$ + N. There is evidence that each process proceeds via a direct rather than a complex mechanism. In particular, in the center-of-mass system most of the product ions are scattered in the direction of the reactant Ba. Analysis of the kinetic energy of the products indicates that they are formed with considerable internal energy. The relative cross section for each of the reactions decreases as $W$ increases. At $W=0.1\mathrm{}$ eV the absolute cross section for each process is of the order of ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$. Studies were made of the dependence of the cross section on internal excitation of the reactants.

The techniques of tensor algebra customarily applied to exploit spatial symmetry are applied to exploit permutational symmetry of the $N$-electron problem. In the approximation of no spin-orbit coupling, the results are nontrivial and give a further reduction of what is normally regarded as the reduced matrix element with respect to spatial symmetry alone. The required $3-j$ coefficients of the permutation group are evaluated in an appendix so that intermediate group-theoretical indices that have no direct physical significance are eliminated from the formulation. The spin integral for any operator can always be reduced to known integrals of the fundamental Pauli operators. Thus all matrix elements can be reduced to a corresponding spin-free form with known weighting coefficients. An explicit expression is given for the matrix element of an operator suitable for evaluating spin-own-orbit coupling or spin density at the nucleus. A recursion relation for the Clebsch-Gordan coefficients of bipartition representations of $S_N$ in terms of its subgroups and the $9-j$ sympols of $\mathrm{SU}\left(2\right)\mathrm{}$ is developed in the appendix. For one of the representations being the totally symmetric representation, the Clebsch-Gordan coefficient is known and the recursion relation (the group-orthogonality relation in this case) can be considered as giving nontrivial sum rules on the $9-j$ symbols of $\mathrm{SU}\left(2\right)\mathrm{}$.

The distribution of atom-atom collisional excitation among various levels of the helium atom is determined. The determination is made by analyzing absolute measurements of the optical electron excitation cross sections of 63 levels at 100 eV electron energy and 63 mTorr pressure. Factors pertaining to our method of obtaining absolute optical cross sections are discussed in some detail. Collisional-excitation transfer on the $n=3\mathrm{}$ level is found to be slight with a cross section for $3{}_{}{}^1{}_{}{}^{}P$ to $3{}_{}{}^1{}_{}{}^{}D$ transfer of less than 1.2 × ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$. A detailed analysis is made on the $n=4\mathrm{}$ level and collisional excitation transfer cross sections are found to be (4.7±1.5) × ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$ for $4F$ to $4D$ transfer and (2.3±0.6) × ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$ for $4{}_{}{}^1{}_{}{}^{}P$ to $4F$ transfer. The pressure dependence of the apparent electron excitation cross sections of 47 levels is also presented at 100 eV electron energy. Our work shows that the apparent cross sections of levels with large principal quantum numbers decrease as the pressure increases, an effect opposite to that observed for levels of low principal quantum number. A short discussion explains these phenomena in terms of a cyclic energy-exchange process which includes electron excitation, imprisonment of resonance radiation, collisional excitation transfer, and radiative transfer. In the course of this investigation it was necessary to obtain values for the electron excitation cross sections of the $n{}_{}{}^1{}_{}{}^{}P$ series up to $n=10\mathrm{}$. The values showed good agreement with Born-approximation theoretical cross sections.

The effects on scattering parameters of approximate cluster functions which appear in the asymptotic boundary conditions are examined by a model calculation of the elastic electron-hydrogen scattering. It is shown that (i) the resonance energies calculated with functions which are orthogonal to the approximate open-channel functions could be spurious, (ii) the phase shifts could deviate from the correct values as much as the relative error in the cluster functions, and (iii) the threshold mismatch may cause an enhancement of phase shifts. An improved pseudostate expansion is studied in which the prediagonalization of the cluster energy matrix is emphasized. This is seen not only to improve the threshold energies and incorporate the effect of the continuum states, but also to optimize the input functions in a given calculation. An additional diagonalization of the closed-channel energy matrix provides a set of quasistates for the resonance and distortion potentials.

Several recently proposed general extensions of thermodynamic scaling are compared and a single comprehensive form suggested.