Experimental data are presented for $K$-shell x-ray cross sections for electron capture to excited states by bare nuclei of F, O, N, C, and B in the energy range from ∼0.25 to 2.3 MeV/amu. For these projectiles the capture to excited states dominates the capture of the loosely bound electrons available in helium, and the projectile x-ray cross section is closely related to the total capture cross section. The experimental x-ray production cross sections are compared to predictions based on a closed-form electron-capture calculation in the Brinkman-Kramers (BK) approximation, even though the magnitude of the theoretical results is a factor of 7 in excess of experiment. Using a single normalization constant, the calculated cross sections for electron capture to excited states preserved the trends of the experimental data with these bare nuclei over the entire energy range of the experiment. At the lowest energy, the experimental and normalized BK cross sections are still below, but rapidly approaching, the maximum in the capture cross section estimated from calculations for bare nuclei in hydrogen by Salop and Olson using a Landau-Zener model.

Absolute total cross sections for producing ${\mathrm{H}}^{+}$, ${\mathrm{Ar}}^{+}$, ${\mathrm{H}}^{-}$, and $e^{-}$ and the large-angle-scattering differential cross section for ${\mathrm{H}}^{+}$ production have been determined for H + Ar collisions. These determinations were made by combining experimental measurements, described here, and theoretical calculations, described in the following paper. The hydrogen-atom energy range covered extends from 3 keV down to 50 eV. An interesting structured cross section is found for the ${\mathrm{H}}^{-}$ + ${\mathrm{Ar}}^{+}$ ion pair formation reaction. The experimental techniques used are described and the cross sections are compared, where possible, with the data of other investigators. An interpretation of the results, based on the details of the H + Ar interaction, is suggested.

Differential elastic scattering cross-section calculations have been made for H + Ar collisions using classical and eikonal techniques. The calculation procedures are described and compared with existing experimental data. It is shown that the angular distribution of the elastic cross section is similar to that obtained for proton production in such collisions at energies above about 200 eV. By combining the angular dependence of the computed elastic cross section with experimental measurements described in the preceding paper, absolute differential cross sections for proton production have been determined.

The transition-amplitude matrix element within the distorted-wave Born approximation is expanded in terms of the transferred rotational angular momentum in atom-diatom reactive scattering. A full three-dimensional treatment of the reactive scattering is retained in the derivation of differential and total cross sections.

The process of ${\mathrm{H}}^{-}$ formation as a result of double-electron capture by protons from helium atoms has been investigated by an approximate integral form of the close-coupling formalism considering three atomic states and indistinguishability of electrons. The cross sections have been presented for incident proton energies ranging from 5 keV to 1 MeV and have been compared with the previous experimental and theoretical results. Our cross sections agree fairly well with the experimental results over the range of energy investigated. The total elastic and single-electron capture cross sections and the differential double-electron capture cross sections in the forward direction also have been reported.

The cross sections for electron-impact excitation of several states (some of which are autoionizing) involving simultaneous excitation of two electrons in the alkaline-earth atoms (Mg, Ca, Sr, Zn, Cd, and Hg) have been calculated using the Born-Oppenheimer scattering approximation. The nature of the total excitation cross section as a function of energy and of the differential cross section as a function of angle has been studied. The target ground state is represented by a properly antisymmetrized product of (two) one-electron orbitals obtained for the ground state of the atom in the Hartree-Fock-Roothaan approximation. For the final excited states similar products of hydrogenic orbitals have been used. The results are found to be reasonable.

The first-order exact off-shell matrix elements for the scattering processes to a three-body Coulomb system with arbitrary masses in which three-particle states are made of two-body bound states and a third free-particle state have been evaluated. These elements are required if one is interested in applying the tractable form (Sloan and Moore) of the Lovelace-Faddeev equations. The amplitudes have been obtained for both the direct and rearrangement channels. The two-body bound states in both the initial and final states are, however, restricted to be the ground states. It may be mentioned that one can always get the amplitudes for higher excited states by appropriate parametric differentiations. Two other approximate forms of the amplitudes have also been given. In all, the forms the matrix elements in the direct channel are found to be singular in the forward scattering angle. The expressions devoid of singularities have been obtained in the present investigation.

Extensive new data on the even-parity, $J=0\mathrm{}$ and $J=2\mathrm{}$ states of Sr have been obtained using multiphoton ionization spectroscopy. Revised term values for previously observed $5s9d{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}D_2^{}{}_{}{}^{}$, and $5s13d$ to $5s16d{}_{}{}^3{}_{}{}^{}D_2^{}{}_{}{}^{}$ states are presented in addition to term values for newly observed ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ states up to $5s21s$, ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ states up to $5s60d$, and ${}_{}{}^3{}_{}{}^{}D_2^{}{}_{}{}^{}$ states up to $5s37d$. The new data clearly show an avoided crossing between the ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}D_2^{}{}_{}{}^{}$ series near the $5s16d$ levels. A strong $J=2\mathrm{}$ autoionizing resonance is also observed, ∼450 ${\mathrm{cm}}^{-1\mathrm{}}$ above the first ionization limit. Multichannel quantum-defect theory (MQDT) parametrizations of the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$, ${}_{}{}^1{}_{}{}^{}P_1^o{}_{}{}^{}$, ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$, and ${}_{}{}^3{}_{}{}^{}D_2^{}{}_{}{}^{}$ bound-state Rydberg series are also presented, including calculated term values for these series. The MQDT analysis of the $J=2\mathrm{}$ series in Sr differs from the earlier analysis of Ca in that both configuration interactions and recoupling between ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}D_2^{}{}_{}{}^{}$ series must be treated simultaneously. Further, it is found that all of the major perturbations of the $J=2\mathrm{}$ bound states can be reproduced without including any interactions due to a $4d^2{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$, even though $3d^2{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ is a major perturber of the ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ series in Ca.

Selective field ionization of the $\left|m_j\right|$ fine-structure levels of highly excited $p$ and $d$ states of Na has been used to measure the fine-structure (fs) intervals and tensor polarizabilities of the $p$ states from $n=16\mathrm{} \mathrm{to} 19$ and $d$ states from $n=15\mathrm{} \mathrm{to} 17$ by rf spectroscopy. Using a two-step photo-excitation scheme we selectively excite one fs state of a $p$ or $d$ level and set the ionizing field so that it will field ionize the other fs state but not the one pumped by the lasers. Consequently, as the rf frequency is swept through the fs resonance, a substantial increase in the ionization current is observed. Our measurements show that the $p$ fs intervals follow an (${n^{*}}^{-3\mathrm{}}$) rather than an $n^{-3\mathrm{}}$ scaling law ($n^{*}$ is the effective principal quantum number). The polarizabilities of both $p$ and $d$ states are in good agreement with calculations using a Coulomb approximation. The measurements of the $d$-state polarizabilities now cover a wide enough range of $n$ to confirm the theoretical prediction of an $n^7$ scaling law.

The collisional angular-momentum mixing of $n=5-15\mathrm{}$ Na $d$ states with the $l>\mathrm{}2\mathrm{}$ states of the same $n$ has been studied using He, Ne, and Ar as collision partners. At rare-gas pressures of ∼1 Torr, the $l\ge 2$ states are thoroughly mixed and the mixture decays at the average radiative lifetime of all the $l\ge 2$ states of the same $n$. Using ∼1 Torr of neon to collisionally mix the $l\ge 2$ states, the average lifetime for $l\ge 2$ was measured for each $n$ and compared to the theoretical prediction for hydrogen, with which it is in excellent agreement. The cross section for $l$ mixing by each of the gases is found to increase sharply from $n=5\mathrm{} \mathrm{to} 10$ and decrease above $n=10\mathrm{}$. The magnitudes of the $l$-mixing cross sections are found to correlate with the low-energy scattering lengths of the collision partners.

We have used radio-frequency spectroscopy in conjunction with a multistep optical excitation scheme involving a cw dye laser to measure the fine-structure intervals in the $6{}_{}{}^2{}_{}{}^{}F$ and $7{}_{}{}^2{}_{}{}^{}F$ states of Rb. We find that the fine-structure intervals $\delta w$ (in MHz) are $\delta w\left(6\mathrm{}{}_{}{}^2{}_{}{}^{}F\right)=-486\mathrm{}\left(4\right)\mathrm{}$ and $\delta w\left(7\mathrm{}{}_{}{}^2{}_{}{}^{}F\right)=-347.6\mathrm{}\left(10\right)\mathrm{}$.

The foil-excitation method has been employed to determine lifetimes, transition probabilities, and $f$ values for $\Delta n=0\mathrm{}$ dipole transitions between the $n=2\mathrm{}$ states of the highly stripped ions, ${\mathrm{S}}^{12+}$ and ${\mathrm{S}}^{13+}$. The fine-two structure interval between the $J=\frac{1}{2} \mathrm{and} \frac{3}{2}$ levels of the $1s^{2}2p{}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}$ term in ${\mathrm{S}}^{13+}$ was also determined, and the result confirms recent astrophysical observations.

The allowed electric dipole transitions $2{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}-2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ and $2{}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}-2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ in heliumlike argon (${\mathrm{Ar}}^{+16\mathrm{}}$) have been observed in a foil-excited beam with a vacuum-ultraviolet monochromator. The wavelengths of these transitions were measured, and the lifetimes of the excited states determined by a time-of-flight technique. The results are $\lambda (2\mathrm{}{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}-2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{})=560.2\mathrm{}\pm 0.9$ Å, $\lambda (2\mathrm{}{}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}-2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{})=660.7\mathrm{}\pm 1.1$ Å, $\tau \left(2\mathrm{}{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)=1.62\mathrm{}\pm 0.08\times {10}^{-9\mathrm{}}$ sec, and $\tau \left(2\mathrm{}{}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}\right)=4.87\mathrm{}\pm 0.44\times {10}^{-9\mathrm{}}$ sec.

A study has been made of the Compton scattering of 1.12-MeV gamma rays by $K$-shell electrons of tin, tantalum, gold, lead, and thorium. $K$ x rays of target atoms were detected in coincidence with the scattered gamma rays. A careful investigation of false coincidences has been carried out. The ratio $\frac{d{\sigma }_K}{d{\sigma }_F}$ of the $K$-shell electron cross section to the Compton cross section for a free electron at rest was determined at several angles between 25° and 120°. The cross-section ratio in the case of gold and thorium is less than 1 at 25°, larger than 1 in the neighborhood of 90°, and close to 1 at 120°. The experimental results are compared with theoretical calculations based on the incoherent-scattering-function approximation and a relativistic version of the impulse approximation. There is a need for a comprehensive relativistic calculation incorporating the effects of electron binding in intermediate states.

Measurements are reported of the pulse-height distributions of photons of initial energy 1.12 MeV after Compton scattering through 60° and 100° by $K$-shell electrons of Au, Pb, and Th. The energy distributions of scattered photons, obtained in the case of Au and Pb targets by a deconvolution of the detector response function, show a rise for energies lower than about 0.25 MeV, a broadening of the Compton line, and a negligible shift of the Compton peak. On account of natural radioactivity of the Th target, the corresponding pulse-height distributions are not precise enough to make the deconvolution procedure worthwhile. The energy distributions are compared with theoretical calculations based on the nonrelativistic impulse approximation. It is clear that a relativistic calculation incorporating the effects of electron binding in intermediate states is required.

The power of the Young tableau scheme for labeling a complete spin-adapted basis set in the theory of complex spectra lies in one's ability to evaluate matrix elements of irreducible tensor operators directly in terms of the tableau labels and shapes. We show that the matrix-element rules stated by Harter for one-body operators can be easily derived from simple vector-coupling considerations. The graphical method of angular momentum analysis is used to derive closed-form expressions for the matrix elements of two-body operators. This study yields several interesting new relationships between spin-dependent operators and purely orbital operators.

An integral representation for the coupled propagating electromagnetic modes in a spatially dispersive medium is presented, which generalizes the Sommerfeld-Brillouin theory. Analysis of this representation predicts the existence of a new exciton precursor in the transient response; numerical estimates are given for exciton polaritons in CdS. Use of this representation also permits an investigation of signal propagation velocities in regions of anomalous absorption near a resonance of the medium. Inclusion of spatial dispersion leads to a predicted order-of-magnitude enhancement of signal velocities compared to that in the local optics case.

Polarization rotation effects in atomic sodium vapor are studied both experimentally and theoretically. Two pulsed dye laser beams propagate collinearly through a cell containing sodium vapor. The direction of polarization of a linearly polarized dye laser beam of frequency ${\omega }_1$ is found to be rotated by a circularly polarized beam of frequency ${\omega }_2$. This rotation is due to the difference in refractive index at ${\omega }_1$ for right and left circularly polarized light which is produced by the circularly polarized beam. When ${\omega }_1+{\omega }_2$ is tuned near the $3S-5S$ two-photon transition of atomic sodium, this difference is primarily due to the dispersion associated with the two-photon transition. Other sources of polarization rotation which were identified include (i) real transfers of population to excited atomic levels due to collisionally induced transitions and (ii) optically induced atomic energy-level shifts. The theory includes both the effects of two-photon dispersion and optically induced energy shifts. The application of the two-photon polarization rotation effect as a fast, optically controlled shutter or modulator and as a sensitive detection technique for two-photon spectroscopy are briefly discussed.

The cooperative spontaneous emission from a completely excited system of $N$ identical two-level atoms is studied under the condition that the cooperation number is conserved. The master equation for such a system has been solved analytically. The exact expressions for the probability distribution and the expectation values of various observable physical quantities are presented. Through a power-series expansion of the exact photon-number expectation value and by using properties of Stirling numbers of the second kind, it is shown that our result agrees with that of Haake and Glauber asymptotically. As by-products, some new identities involving binomial coefficients and Stirling numbers of the second kind have also been obtained. The exact solution of the same master equation for arbitrary initial conditions will be presented in a subsequent publication.

The time development of $N$ two-level atoms linearly coupled to a monochromatic, long-wavelength radiation field is studied. Both systems are assumed to be initially in coherent states, the radiation mode being strongly populated with an average number $n$ of photons larger than $N$. The decay of atomic coherence can be followed up to a time $t^{*}$, after which the perturbation expansion in powers of $n^{-\frac{1}{2}}$ used to solve the problem breaks down. We show that it increases proportional to $t^2$ at large times, as measured from the variances of the components of the total angular momentum of the atoms. The results are briefly discussed in connection with the problem of conversion of incoherent into coherent radiation.