The phenomenon of environment-dependent "fast" depolarization of stopped positive muons is described in terms of a theoretical model. The formalism is similar to that developed by Ivanter and Smilga to describe the "proper muonium mechanism," but has been adapted and expanded to include situations involving more than one strongly depolarizing influence (i.e., muonium and a molecular radical). For a plausible situation in dilute solutions with transverse applied magnetic field, the exact time dependence of the muon polarization is derived formally, with the "residual polarization" emerging as a limit. The result can be applied to the study of muonium chemistry.

A complete discussion is given of our precision measurement of the hyperfine-structure interval $\Delta \nu$ of the ground state of muonium at a weak magnetic field ($\sim 3$ G) using the resolved transitions $(F,M_F)=(1,\pm 1)\to \mathrm{}(0,0)\mathrm{}$, and at a very weak magnetic field ($\sim 10$ mG) using unresolved transitions $\Delta F=\pm 1$. The method of magnetic resonance studies of muonium is used, where a single oscillatory field is employed and the resonance line is swept by varying the applied frequency. This research yielded values for the coefficients of the linear hfs density shifts for muonium in argon and krypton at a temperature of approximately 20°C: ${}_{a\mathrm{M}-\mathrm{A}\mathrm{r}}=-5.00\mathrm{}\left(22\right)\mathrm{}\times \frac{{10}^{-9\mathrm{}}}{\mathrm{torr}}$, $a_{\mathrm{M}-\mathrm{K}\mathrm{r}}=-10.57\mathrm{}\left(39\right)\mathrm{}\times \frac{{10}^{-9\mathrm{}}}{\mathrm{torr}}$, and also for the quadratic hfs pressure-shift coefficients: $b_{\mathrm{M}-\mathrm{A}\mathrm{r}}=8.1\mathrm{}\left(2.5\right)\mathrm{}\times \frac{{10}^{-15\mathrm{}}}{{\left(\mathrm{torr}\right)}^2}$, $b_{\mathrm{M}-\mathrm{K}\mathrm{r}}=8.6\mathrm{}\left(5.9\right)\mathrm{}\times \frac{{10}^{-15\mathrm{}}}{{\left(\mathrm{torr}\right)}^2}$. The value obtained for $\Delta \nu$ is $\Delta \nu =4463.308\mathrm{}\left(11\right)\mathrm{}$ MHz (2.5 ppm), where the 1-standard-deviation error is principally a statistical counting error. Our result for $\Delta \nu$ is in good agreement with other measurements of $\Delta \nu$ and also with the current theoretical value.

Atom-antiatom rearrangement collisions in which the nucleus-antinucleus bound state is formed are important processes in atom-antiatom interactions. We give a general discussion of the atom-antiatom interatomic potential energy $V$ and calculate $V$ for H-$\overline{\mathrm{H}}$, $\overline{p}$-H, and $\overline{M}$-Ar where $\overline{M}$ means antimuonium (${\mu }^{-}{e}^{+}$ atom). We apply the semiclassical and optical-potential methods to determine cross sections for rearrangement collisions. At low energies these collisions are the dominant processes leading to particle-antiparticle annihilation.

Measured and calculated Stark-broadening parameters are compared for spectral lines emitted by singly ionized atoms from lithium through calcium. It is found that the average value of the ratio of the measured to calculated width is 1.06 ± 0.05, and the average value of the ratio of the difference between the measured and calculated shift to the measured width is +0.03 ± 0.07, where the average is over all compared lines. It is shown that only a small error is introduced by using the one-electron approximation (for equivalent electrons) or $\mathrm{LS}$ coupling. The greatest error arises from the incompleteness (and incorrectness) of tabulated energy levels and their classification.

The van der Waals forces between a polarizable particle and a conducting wall and between two polarizable particles are calculated within the theory of classical electrodynamics with classical electromagnetic zero-point radiation. This theory assumes the differential equations of traditional classical electrodynamics but changes the homogeneous boundary condition on Maxwell's equations to correspond to the presence of random classical electromagnetic radiation with a Lorentz-invariant spectrum. The van der Waals force calculations are performed exactly within the nonrelativistic equations of motion for the particles represented as point-dipole oscillators. The classical results are found to agree identically to all orders in the fine-structure constant $\alpha$ with the nonrelativistic quantum electrodynamic calculations of Renne. To fourth order, there is agreement with the perturbation-theory work of Casimir and Polder.

Field gradients have been calculated at 12 values of the internuclear distance from 34-, 66-, and 87-term molecular wave functions expanded in prolate-spheroidal coordinates and $r_{12}$. Convergence of the gradients as the basis enlarges is indicated and the dissociation energy of ${\mathrm{H}}_2$ is in agreement with experiment. Using vibrationally averaged gradients, experimental values for the quadrupole-interaction constant, and estimating the error in the field gradients arising from truncation of the basis, the electric quadrupole moment of the deuteron is found to be 0.2875±0.002×${10}^{-26\mathrm{}}$ ${\mathrm{cm}}^2$, which is 2% larger than the most recent values. This disagreement as well as that among earlier authors is explained. First-order perturbation-theoretic results for the magnetic spin-spin interaction constant for ${\mathrm{H}}_2\mathrm{}(J=1\mathrm{})\mathrm{}$, $\mathrm{HD}\mathrm{}(J=1\mathrm{})\mathrm{}$, ${\mathrm{D}}_2\mathrm{}(J=1\mathrm{})\mathrm{}$, and ${\mathrm{D}}_2\mathrm{}(J=2\mathrm{})\mathrm{}$ are in agreement with experiment and, except for ${\mathrm{H}}_2$, well inside experimental error.

Two-photon emission from heavy elements with a single $K$-shell vacancy (e.g., ${\mathrm{Cu}}^{+}$) is considered. Simple closed-form expressions are given for the spontaneous, singly stimulated, and doubly stimulated two-photon emission rates. The material parameters relevant to these two-photon processes are shown to be the one-photon absorption cross sections and oscillator strengths.

The spectra of carbon $K$- and argon $L$-shell Auger electrons resulting from ionization produced by 0.15-0.50-MeV/amu $\alpha$ particles and deuterons incident on a thin gas cell have been measured. Absolute ionization cross sections were obtained from the Auger-electron yields and, in addition, the yields obtained with equal-velocity projectiles were used to test the projectile $z$ dependence of the ionization process. Intense satellite structure was observed in the Auger spectra and these features were attributed to Auger transitions from multiple vacancy states formed during the collision.

Two uniformly convergent series are introduced to give bounded estimates of the dynamic polarizability in the region below as well as above the first resonance line. Upper and lower bounds on the oscillator strength can also be obtained from these approximations. The series are simple and rapidly convergent.

The decay of an atom in the presence of a static perturbation is investigated. The perturbation couples a decaying state with a nondecaying state. A "hole" appears in the emission line at a frequency equal to the frequency difference between the nondecaying state and the ground state. The effect is explained by analyzing the phase relationships of the radiation emitted by the two coupled states.

A multiperturbation theory for atomic systems is developed. The theory automatically decouples Rayleigh-Schrödinger perturbation theory into multiperturbation partial differential equations for the 2-through-($n+1\mathrm{}$)-electron components of the $n\mathrm{th}$-order wave function. Variational-perturbation equations for these multiperturbation wave functions are derived together with expressions for the multiperturbation energy-expansion coefficients. The "bare-nucleus" hydrogenic function is chosen as the zero-order wave function rather than the more customary Hartree-Fock function. With this choice the mulitperturbation wave functions are independent of the nuclear charge and of the total number of electrons in the system, and are thus completely transferable to other systems. The "cluster-expansion" wave function is analyzed in terms of the multiperturbation wave functions and the connection between cluster-type expansions and ordinary perturbation theory is shown in detail.

A method for calculating the total energy of complex systems, such as molecules, is proposed. It is a perturbation expansion with two novel features. First, the starting point is an approximate state (rather than an approximate Hamiltonian) and the expansion is in the orbital correction to that state (rather than in a perturbing Hamiltonian). This permits application to complicated molecules where there is no soluble unperturbed Hamiltonian resembling the real system. The second feature is the evaluation of the total energy without the diagonalization of a Hamiltonian matrix. This is accomplished in a way analogous to, but basically different from, the use of the invariance of a trace under a similarity transformation. This permits the treatment of arbitrarily large systems. The principal approximations in the theory are a self-consistent-field approximation to the electron-electron interaction and the truncation at second order of an expansion which would be exact if carried to all orders. If the method were applied to metals, with the approximate starting states taken as orthogonalized plane waves, the theory becomes rigorous nonlocal pseudopotential theory. In molecules linear-combination-of-atomic-orbitals (LCAO) starting states are envisaged and the theory is a systematic improvement upon (as well as simplification of) LCAO theory. Pseudopotentials do not play a central role in the application to molecules, though their use will improve the accuracy and the improvement may be an important one. The results of application of the method to the central hydrides, methane and hydrogen fluoride, by Meserve are given.

When an atom emits or absorbs radiation in the presence of perturbing atoms, satellite bands frequently appear in the spectrum. Such bands may occur when the active atom is subject to equal forces in the two states involved in the transition for some particular configuration of perturbers. In this work a semiclassical approach is used to derive an approximate expression for the one-perturber spectrum in the two-state adiabatic approximation. The expression, which involves an average over Airy functions, is readily adapted for rapid numerical evaluation. Also, an analytic expression for the rate of decline in intensity on the classically forbidden far side of the satellite is found. The semiclassical one-perturber line shape for satellite bands is compared with the classical and quantum-mechanical counterparts for the case of resonance broadening of the Lyman-$\alpha$ line in absorption. The semiclassical line shape is found to be much more realistic than the classical shape in which the satellite appears as a singularity. The semiclassical treatment provides an interpretation of the shape of a satellite band in terms of the intermolecular potentials, a possibility not evident in the exact quantum-mechanical treatment.

The multiphoton transitions in the hydrogen atom are investigated by taking into account the higher-order terms arising from the $S$-operator expansion. These higher-order effects originate induced shifts and induced breadths on the virtual-atomic-energy levels. It is shown that these perturbations play an important role for resonant multiphoton processes. In this case, the theory predicts a particular flux dependence of the transition rates. Furthermore, the well-known dispersion curves are strongly modified in the neighborhood of any resonance. Thus the transition rates can exhibit several peaks. Numerical results are given for a three-photon bound-free transition from the $2S$ state of hydrogen.

Measurements have been made to determine $\gamma$-ray attenuation coefficients very accurately by using an extremely-narrow-collimated-beam transmission method which effectively excluded corrections due to small-angle and multiple scattering of photons. The measured mass attenuation coefficients with maximum errors less than 3% for 34 elements in the range from hydrogen to lead are given.

$K$ x-ray yields have been measured for ten elements ranging from Fe ($Z=26\mathrm{}$) to Au ($Z=79\mathrm{}$) using 30-100-MeV $\alpha$ particles. The new data were combined with some earlier measurements and a smooth-curve fit was performed on the x-ray production cross sections plotted as a function of target atomic number. These "smoothed" cross sections were used in comparisons with the predictions of plane-wave-Born-approximation (PWBA) and binary-encounter-approximation (BEA) calculations and resulted in the observation of a systematic atomic-number-dependent deviation between experiment and theory. By comparing the measured cross-section data to the universal BEA curve at velocity ratios in which the mean electron velocity was calculated "semi-"relativistically, over-all agreement within ± 16% was attained for all elements studied.

An experimental investigation has been made of the formation of excited hydrogen atoms by charge-transfer neutralization of ${\mathrm{H}}^{+}$ and collisional dissociation of ${\mathrm{H}}_2^{+}$ and ${\mathrm{H}}_3^{+}$. Data are presented for the formation of $\mathrm{H}\mathrm{}\left(3s\right)\mathrm{}$ induced by ${\mathrm{H}}^{+}$, ${\mathrm{H}}_2^{+}$, and ${\mathrm{H}}_3^{+}$ impact on the noble gases; for ${\mathrm{H}}_2^{+}$ impact on ${\mathrm{H}}_2$, ${\mathrm{D}}_2$, ${\mathrm{N}}_2$, and Ar, the measurements include formation of $\mathrm{H}\mathrm{}\left(3s\right)\mathrm{}$ and $\mathrm{H}\mathrm{}\left(3d\right)\mathrm{}$ states. Projectile energies range from 100 to 600 keV. The cross sections for producing hydrogen in the $n=3\mathrm{}$ states have been determined by quantitative measurement of collisionally induced Balmer-$\alpha$ emission. The contributions from the $3s$, $3p$, and $3d$ states were separated by a method employing the different lifetimes of each state. Data are consistent with previous measurements made at lower energies. In dissociation the cross sections are generally the same for the formation of the $3s$ and $3d$ states; they show a slow decrease as a function of projectile energy. Cross sections for formation of $\mathrm{H}\mathrm{}\left(3s\right)\mathrm{}$ by charge transfer show the expected rapid decrease with increasing energy. Differences between cross sections for various target gases suggest that the internal structure of the target atom will be an important factor in any prediction of these cross sections.

The Ge $L{\alpha }_{1,2}$ and $L{\beta }_1$ spectra obtained by ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ ion bombardment at 3.0 and 5.0 MeV have major satellite peaks which correspond in energy with those appearing in photon- or electron-excited spectra. Many new satellite peaks can be observed in the ion-induced spectra because of enhanced multiple-vacancy production. An interpretation based on Hartree-Fock-Slater calculations for multiple $3d$ vacancies gives over-all good agreement for the observed satellite groups for both $L{\alpha }_{1,2}$ and $L{\beta }_1$ spectra; however, multiplet calculations are necessary to identify the various satellite components. The continuous satellite structure produced by ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ bombardment on Ge at 3.0, 5.0, and 10.0 MeV shows strong self-absorption effects. Published absorption data and variable-take-off-angle experiments were both used to correct for self-absorption. Satellite peaks occur at energies corresponding to multiple ${\mathrm{}\left(3d\right)\mathrm{}}^n$ plus $N$-shell vacancies where $n$ has values of 4, 5, and 6. Satellite lines have also been identified corresponding to production of ${\mathrm{}\left(2p\right)\mathrm{}}^2$ vacancies by neon bombardment.

A general formalism is presented for the description of elastic scattering of electrons from hydrogenlike atomic systems. The total wave function for the two-electron system is put forth as a multiconfiguration expansion in terms of suitably normalized orthogonal orbitals. These radial orbitals, as well as the coefficients of the expansion, are determined variationally via a system of coupled integrodifferential equations. The formalism is applied to the calculation of elastic electron-hydrogen scattering in the energy range below the first resonance for the ${}_{}{}^1{}_{}{}^{}S$ state of the two-electron system. Accurate phase shifts are obtained with short expansions, as the newly introduced orbitals obtained by numerically integrating the integrodifferential equations account quite adequately for short-range correlation.

A systematic study of the cross sections for $K$-shell ionization by 2.0-MeV-electron impact has been made as a function of atomic number. The cross sections for 32 elements from V ($Z=23\mathrm{}$) to Bi ($Z=83\mathrm{}$) were first measured relative to each other, and then were normalized to 43 b at Sn ($Z=50\mathrm{}$). Thus systematic errors usually associated with absolute measurements were minimized and did not obscure minor variations in the $Z$ dependence of the cross sections. The measured values drop from 353 b at V to 9.9 b at Bi. The general trend of the $Z$ dependence of the data is in agreement with theoretical predictions of Kolbenstvedt. However, variations in cross sections by as much as 30% from one element to the next are not accounted for by the theory.