Accurate calculations of the frequency-shift cross section for collisions of two hydrogen atoms are presented for a range of temperatures.

The rate of spontaneous emission of radiation by a loosely bound composite system is calculated from quantum electrodynamics correct through terms of relative order ${\alpha }^2{Z}^2$. Recent criticisms by Feinberg and Sucher of the semiclassical method of deriving the higher-order radiation coupling terms are discussed. It is proved that the Breit interaction remains valid in the presence of radiation emission and that the semiclassical and quantum-electrodynamic methods of deriving the higher-order coupling terms always yield the same results to relative order ${\alpha }^2{Z}^2$. We discuss in particular relativistic corrections to allowed and spin-forbidden electric dipole transitions and the $1s2s{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-1\mathrm{}{s}^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ magnetic dipole transition.

The many-body perturbation theory of Brueckner and Goldstone has been used to calculate the total nonrelativistic energy of the CH molecule. We have used a single-center expansion with a complete set of basis states appropriate to the neutral carbon atom. At the equilibrium internuclear separation we calculate the total energy for CH to be -38.482±0.02 a. u. as compared with the experimental value -38.479 a. u. We have also calculated a full potential curve for the ${}_{}{}^2{}_{}{}^{}\Pi$ ground state of CH accurate to second order in the perturbation expansion.

It is shown that the conventional application of the Pauli principle to the qualitative estimation of the relative distributions of electrons with parallel and antiparallel spins is wrong. The Pauli principle induces a local reduction of the probability of finding electrons with parallel spins close together. However, for neutral atoms at least, such electrons have a considerably higher probability of being found at moderate separations and an accompanying reduced probability of being found at higher separations, relative to electrons with antiparallel spins.

A diffuse nuclear charge distribution, with approximately the trapezoidal Hofstadter shape, is used to calculate the effect of the distributed nuclear charge on the magnetic-dipole hyperfine-structure (hfs) interaction between the nucleus and the atomic electron. For a surface or a uniform charge distribution model this effect is known as the Breit-Rosenthal-Crawford-Schawlow correction to the point-charge interaction. The hfs interactions calculated with the diffuse and with the uniform charge distributions differ by over 4% for medium to heavy nuclei. The results, combined with our previously calculated values for the Bohr-Weisskopf correction (the effect on the hfs due to the nonpunctual distribution of nuclear magnetization), allow a more realistic determination of the total hfs anomalies, caused by the extended nuclear electric and magnetic structures, and therefore also of ${\left|\psi \mathrm{}\right(0\left)\right|}^2$, the probability of the electron wave function at the origin.

Expressions are obtained for the collision cross sections governing the relaxation of angular momentum polarizations in the molecular hydrogen isotopes, making use of the fact that energetically inelastic collisions are very infrequent. A number of interrelationships between the collision cross sections of this type, occurring in NMR and in other transport and relaxation phenomena such as the Senftleben-Beenakker (SB) thermal conductivity effect, and depolarized Rayleigh light scattering, are developed and comparisons between calculated cross sections and those obtained from various experiments are given. For example, in $n$-${\mathrm{H}}_2$ at room temperature, the SB effect for the shear viscosity gives a characteristic cross section of (0.47 ± 0.05) ${\mathrm{\AA }}^2$ to be compared with a calculated cross section of 0.32 ${\mathrm{\AA }}^2$, and a cross section of 0.40 ${\mathrm{\AA }}^2$ which can be extracted from NMR measurements. A calculated value of ${\sigma }_{\mathrm{DPR}}$, for the cross section determining the width of the depolarized Rayleigh line, in $n$-${\mathrm{H}}_2$ of 0.48 Å, is obtained, to be compared with the experimental value 0.495 ${\mathrm{\AA }}^2$.

The magnetic hyperfine and $g_F$ constants were calculated for the $c{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}(1s, 2p)$ metastable state of ${\mathrm{H}}_2$ using wave functions determined from the optimal-double-configuration model. The hyperfine constants differ by as much as 24% from previous values obtained using a single-configuration electronic wave function. The hyperfine constants are $a=21.98\mathrm{}$ MHz, $b=471.14\mathrm{}$ MHz, $c=59.37\mathrm{}$ MHz, $d=-12.87\mathrm{}$ MHz, where $a$ and $b$ are the orbital interaction of the electron with the nucleus and the Fermi contact interaction, respectively, and $c$ and $d$ arise from the dipolar interaction of electron and nucleus. With these values for the hyperfine constants, along with the experimental fine-structure splittings and a matrix-diagonalization procedure, the $g_F$ values were calculated and found to be in better agreement with experiment than the earlier theoretical values.

The Pauli approximation for many-electron atoms is derived. This yields an unambiguous expression for the fine-structure splitting and other first-order relativistic corrections to the energy, using nonrelativistic wave functions. A formalism is developed for atoms, based on these results, which is suitable for the evaluation of the fine structure using multiconfiguration wave functions. Fine-structure splittings calculated from Hartree-Fock wave functions are presented for ground states from He through Ar; the remaining energy corrections are also presented. Multiconfiguration results are presented for the lowest ${}_{}{}^2{}_{}{}^{}D$ and ${}_{}{}^2{}_{}{}^{}P$ states of N, accounting for about 80% of the discrepancy between Hartree-Fock values and experimental values.

The fine-structure constant can be determined to high accuracy from precise measurements of the fine structure of the $2{}_{}{}^3{}_{}{}^{}P$ level in helium. One of the necessary calculations is to compute the contributions from the six Breit operators and the mass-polarization operator in second-order perturbation theory. The eighteen spin-dependent perturbations from intermediate ${}_{}{}^3{}_{}{}^{}P$ states are calculated by solving an inhomogeneous Schrödinger equation for the perturbation of the wave function by the variational method. The second-order contributions are then given by a single integral. These corrections are calculated using standard Hylleraas expansions with up to 165 terms for the perturbed wave functions, resulting in contributions to the two fine-structure intervals of the order of ${10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, but only four of the results are sufficiently accurate.

Ag $K$ and $L$ x-ray yields have been measured for 2-30-MeV protons incident on a thin Ag foil target with a Si(Li) x-ray detector (resolution 540 eV at 6 keV). The absolute $K$-shell ionization cross section ${\sigma }_K$ extracted from these measurements has been compared to plane-wave-Born-approximation (PWBA) and binary-encounter-approximation (BEA) calculations and agrees quite well with both over the energy range covered in this investigation. However, the PWBA and BEA predictions of $L$-shell ionization cross sections are low by a factor close to 2 compared to experimental values for ${\sigma }_L$, although both predict an energy dependence for the shape of ${\sigma }_L$ in good agreement with that observed. The disagreement in magnitude is most likely because of the present inadequate $L$-shell fluorescence yields for medium-and low-$Z$ atoms. The $\frac{K\alpha }{K\beta }$ x-ray intensity ratio for proton bombardment of Ag from 2-30 MeV was observed to be constant (4.68±0.33) and consistently slightly below Scofield's calculation (5.09). The unresolved $K\beta$ peak was decomposed into its two major components $K{\beta }_{1,3}$ and $K{\beta }_2$ whose ratio appeared to be weakly dependent on proton-beam energy.

Energy transfer and coherence transfer between two atoms of different species are studied theoretically. The electric dipole-dipole interaction is the mechanism considered for the excitation transfer. A generalized perturbation method for a damping system is used. A general formula is derived for the polarization of the sensitized fluorescence resulting from the excitation transfer. This polarization is shown to be dependent on the angular momenta of the two atoms, and to be independent of their relative velocity as well as of their difference in the energy of excitation. The polarizations are found to be nonzero in many cases which demonstrate the transfer of coherence through collision processes. A general and compact formula is also derived for the polarization of pure fluorescence where excitation exchange has not taken place. The polarization of the sensitized fluorescence is in general smaller than that of the pure fluorescence. This means that the coherence is transferred only partially. Finally, the magnetic field effect has been included. This field depolarization depends on the $g_j$ values and the lifetimes of the excited states of both atoms. The general feature of the field dependence also differs considerably from that of the Hanle effect for resonance fluorescence.

A new method for obtaining absolute differential excitation cross sections in low-energy electron-atom scattering is employed. The method utilizes certain of the kinematic properties of a recoiling-atom beam in an electron-atom crossed-beam configuration to distinguish between elastic scattering events and excitation to various atomic levels. Differential cross sections for elastic scattering and excitation of the $4p$ state of potassium are presented at 1.0, 3.0, 4.4, and 5.2 eV. A combined cross section for the $4s-5s$, $3d$ excitation integrated over a restricted angular range is also presented.

We have measured the cross section for the quenching (i.e., depopulation) of the $2s$ (metastable) state of atomic hydrogen by collisions with atoms of helium and argon. The energy range covered was 0.25-30.0 keV. The experimental technique was to measure the attenuation of a beam passing through the various gases, the detector being a Lyman-$\alpha$ counter viewing a section of the beam where a dc electric field mixed $2s$ and $2p$ states, which essentially converted metastable atoms into Lyman-$\alpha$ photons. For helium as target gas, the cross section was also calculated using a pseudopotential and the eikonal approximation. For helium, the measured cross section falls rapidly as the energy increases from 0.25 to 2.5 keV and remains roughly constant at $7.5\pi a_0^2$ from 2.5 to 30 keV. The theoretical curve is about a factor of 4 below the measured value. Implications of this discrepancy are discussed in the text. For argon, the measured cross section increases from $20\pi a_0^2$ to $27\pi a_0^2$ as the energy increases from 1 to 30 keV.

A technique is described for measuring Compton profiles using a ${\mathrm{Te}}^{123m}$ 160-keV $\gamma$-ray source together with a Li-drifted-germanium detector. By studying He and ${\mathrm{N}}_2$, whose Compton profiles have been previously measured using x rays and theoretically calculated, it is found that the $\gamma$-ray technique gives results which agree with both the theory and the previous x-ray measurements. Measured Compton profiles for Ar and Kr are also presented. These results would have been almost impossible to obtain by the x-ray technique because of the large photoelectric absorption of the low-energy x rays. The Ar and Kr results are compared with atomic Hartree-Fock calculations and found to agree at $q=0\mathrm{}$ within experimental error which is less than 1%. As a result of these studies, it is concluded that all elements and their compounds can now be studied by Compton scattering.

Coupled-channel calculations have been performed at 27.5, 30, and 50 eV for the reaction ${\mathrm{He}}^{+}+\mathrm{He}\to {\mathrm{He}}^{+}+\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)+19.81\mathrm{}$ eV using presently available ab initio potentials for the two lowest ${}_{}{}^2{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ states. The inelastic-scattering differential cross sections have been calculated at these energies and are compared with recent experimental results. Several features are distinguished on the calculated cross sections. All possess low-frequency Stückelberg oscillations and a higher-frequency oscillation due to the nuclear symmetry of the reactants. At the two lowest energies of 27.5 and 30 eV, inelastic rainbow-type oscillatory structure is also observed. The inelastic rainbow structure was due to the maximum on the excited-state potential and the closeness of the collision energy to the thershold for this reaction. The elastic differential cross sections were calculated at 50 eV, and perturbations due to the crossing of the inelastic channel were found superimposed upon the electron and nuclear exchange oscillations.

Absolute cross sections have been measured for the excitation of hydrogen atoms to the $3s$, $3p$, and $3d$ states by the impact of ground-state hydrogen atoms on He, Ne, Ar, ${\mathrm{H}}_2$, ${\mathrm{O}}_2$, and ${\mathrm{N}}_2$ in the energy range from 10 to 35 keV. In this energy range the cross sections for the different angular momentum states are generally the same order of magnitude (${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$). Excitation to the $s$ state is more competitive with the $p$-state excitation at the $n=3\mathrm{}$ level than at the $n=2\mathrm{}$ level. Excitation to the $3d$ state is not as likely as excitation to the $3s$ or $3p$ states. Cross sections for the production of Balmer $\alpha$ radiation have been computed. Polarization fractions for the $3d\to 2p$ radiation have also been measured.

Cross sections have been determined for the destruction of the $3s$ state in atomic hydrogen by 10-, 25-, and 35-keV hydrogen-atom impact on ${\mathrm{N}}_2$, Ar, and ${\mathrm{H}}_2$. The experimental values support the concept of two destruction mechanisms. One mechanism involves the collisional ionization of the excited atom, which has been treated quantitatively by Bates and Walker. The other mechanism involves electron capture by the fast-atom nucleus.

Highly excited states of hydrogen molecules have been formed by electron-capture collisions of 50—450-keV diatomic ions in hydrogen gas. Populations of the excited states ($n\ge 10$) have been determined by passing the molecules through an intense electric field which strips the excited electron from the molecule. The fraction of molecules in states $n\ge 10$ was approximately ${10}^{-3\mathrm{}}$ with ${\mathrm{D}}_2^{*}$ being approximately a factor of 2 greater than ${\mathrm{H}}_2^{*}$. The fractional yield of ${\mathrm{H}}_2^{*}$ varied as the stripping electric field to the $\frac{3}{4}$ power. Results are presented for molecular autoionization, excited-state population dependence on ion-source-electron energy, and state-mixing measurements.