The transfer of Zeeman coherence between excited atomic states is discussed, and the similarity between transfer of coherence by radiative and collisional processes in an isotropic environment is emphasized.

An approximate integral form of the close-coupling formalism is used to calculate the cross sections for capture of electrons from helium atoms by protons. Results for the ground-state and excited-$2s$-state capture cross sections are obtained with the effect of the proton-nucleus interaction included, and compared with experimental and other theoretical results. The effects of the post and prior forms of interaction on the cross sections are studied in detail. The effect of the exchange integral on the capture cross sections is also reported. It is found that the inclusion of the ground-state transition in calculating $2s$-state capture cross section enhances the cross section values only in the low-energy region. The present values of the capture cross sections for the ground and excited $2s$ states are in very good agreement with the experimental observations at high as well as low energies. In the low-energy region the nature of the experimental curve has been correctly reproduced for both cases. Results for the differential capture cross sections in the forward direction and the total elastic cross sections are also reported.

Earlier investigations by our group on the ${\mathrm{H}}^{+}$-H collision problem using an approximate form of the Faddeev equations have been extended to include the $2p$ states in both channels in the coupling scheme. Calculations have been performed with and without the proton-proton interaction. Results for the total charge transfer with proton-proton interaction are found to be reliable above 50 keV. Inclusion of $1s$, $2s$, and $2p$ states in the coupling scheme is not sufficient to predict the correct nature of the $1s\to 2s$ and $1s\to 2p$ excitation and capture cross sections by the present method.

We have calculated the second-order interaction between the spin-orbit coupling perturbation $H_{\mathrm{so}}\propto r^{-1\mathrm{}}\left(\frac{dV}{\mathrm{dr}}\right)\overrightarrow{1}·\overrightarrow{\mathrm{s}}$ acting on the core electrons and the exchange Coulomb interaction between the valence and core electrons. This calculation was previously carried out for two alkali $\mathrm{nd}$ states ($\mathrm{Na} 3d$ and $\mathrm{Rb} 4d$), and was shown to result in the observed inversion of the fine-structure interval $\Delta \nu$ for these $d$ states. This calculation is extended to excited $\mathrm{np}$ states, and it is shown that the radial integrals have opposite sign to those for $\mathrm{nd}$, resulting in a small increase of the calculated $\Delta \nu$ (by ∼10-20% in all cases). Specific results have been obtained for several excited $\mathrm{np}$ states of Na, K, Rb, and Cs, and give agreement to within 20-30% with the experimental fine-structure splittings $\Delta {\nu }_{\mathrm{expt}}$.

Analytic self-consistent-field Hartree-Fock wave functions for ${\mathrm{Cs}}^{+}\left({}_{}{}^1{}_{}{}^{}S\right)$ and $\mathrm{Cs}\left({}_{}{}^2{}_{}{}^{}S\right)$ have been calculated by Roothaan's expansion method. The virial theorem is satisfied to six significant figures for both ${\mathrm{Cs}}^{+}$ and Cs. Results for the total electronic energies of ${\mathrm{Cs}}^{+}$ and Cs and the first ionization potential of Cs are compared with those of Fraga et al., calculated by numerically integrating the integrodifferential equations of Hartree and Fock. Our result for the first ionization potential of Cs is closer to the experimental value than that of Fraga et al. Employing those analytic expansions, the diamagnetic susceptibility ($\chi$) and nuclear magnetic shielding constant ($\sigma$) are calculated for both ${\mathrm{Cs}}^{+}$ and Cs.

This calculation demonstrates that the combined configuration-interaction-Hylleraas (CI-Hy) variational method of Sims and Hagstrom can be applied to the ${}_{}{}^1{}_{}{}^{}S$ ground state of the neon atom. Coordinates $r_{\mathrm{ij}}$ have been included in the wave function so as to correlate explicitly the motion of all pairs of electrons in the atom. An energy of - 128.8298 hartree has been obtained from an 83-term wave function (73.5% of the correlation energy). An analysis of the pair correlation energies shows that it is more difficult to represent the electronic correlation in $p$-$p$ and $s$-$p$ pairs than $s$-$s$ pairs using Hylleraas functions. More experience with CI-Hy calculations on atoms containing as many as ten electrons is required before the method can compete with and give higher accuracy than the conventional CI calculations.

We discuss the systematics of energy levels of high-angular-momentum Rydberg states of alkali-metal atoms, and show that they are well described by a quantum-defect model. Polarization of the core electrons by the valence electron is shown to be the dominant contribution to the quantum defect. As an example, recently observed splittings between the $l=3,4,\mathrm{and} 5$ levels in various Rydberg states of sodium are analyzed to yield values for the core polarizabilities. Effective values of the dipole and quadrupole polarizability of 1.0015(15) and 0.48(15) a.u., respectively, are obtained. Implications for the precise determination of the structure of highly excited Rydberg states in alkali atoms are discussed.

The recent electronic orbital tableau ("jawbone") formulas of Harter and Patterson for matrix representatives of elementary generators of $U\left(n\right)\mathrm{}$ in the canonical basis are shown to be simply related to our expressions for the latter, which are based on a simplified Gelfand tableau formalism pertinent to $N$-electron problems, a brief survey of which is given in a form particularly suitable for computer implementation.

Cross sections for proton-hydrogen-atom scattering have been calculated for protons incident in the energy range 15-200 keV. The impact-parameter Schrödinger equation was solved approximately with an expansion in Sturmian functions; the expansion contained a total of six $s$-state and six $p$-state functions centered about each proton. Results are presented and discussed for excitation to the $n=2\mathrm{}$ level, for charge transfer to the ground state and the $n=2\mathrm{}$ level, and for ionization.

The magnitudes, velocity dependences, and $Z$ dependence of projectile $K$ x-ray cross sections measured for 20-56-MeV ${\mathrm{F}}^{7+,8+}$ incident on ${\mathrm{H}}_2$ and He are well reproduced by direct Coulomb excitation theories, in contrast with previous evidence for multistep excitation processes.

The recently proposed analytic methods by Thomas and Chan, which reduce the Glauber amplitude for charged-particle-neutral-atom collisions to a one-dimensional integral representation involving the modified Lommel function, are used to evaluate the cross sections for the elastic scattering of electrons by metastable ($2{}_{}{}^1{}_{}{}^{}S$, $2{}_{}{}^3{}_{}{}^{}S$) helium atoms. The results are compared with some other theoretical calculations.

A semiclassical approximation to the off-shell $T$-matrix elements $t_1(p,p^{\prime };E)$ for potential scattering is derived for the case of local potentials. The approximation satisfies the off-shell unitarity relation. The advantage of the semiclassical description is twofold: It permits fast numerical calculations and allows also a classical understanding of the matrix elements. Classically allowed (oscillatory) and classically forbidden (exponentially damped) regions in the $p$, $p^{\prime }$ plane are discussed. Numerical examples are presented for purely repulsive potentials.

We have determined projectile and target $K$ x-ray cross sections from a variety of targets spanning the periodic table and bombarded by 12-60-MeV Br, 200-330-MeV Kr, 15-80-MeV I, 326-470-MeV Xe, and 90-110-MeV Pb. Most targets were thick solids, but, to assure proper extraction of cross sections, some thin solid and gas targets have also been used. The present paper mainly gives experimental details and describes the method of cross-section determination. In subsequent papers various features of the target dependence of the cross section will be examined in terms of atomic and molecular models of inner-shell excitation processes.

The multiphoton excitation of rubidium has been investigated over the 4600-6500-Å wavelength region with a tunable dye-laser source having a linewidth better than 0.1 Å and a space-charge ionization detector sensitive to a few ions per second. Multiphoton transitions have been observed to occur both through intermediate atomic states and through intermediate continuum states of the rubidium molecule. In the former case two-photon transitions have been observed from the $5{}_{}{}^2{}_{}{}^{}S$ ground state of atomic rubidium to higher-lying $n{}_{}{}^2{}_{}{}^{}D$ levels for values of $n$ ranging from 9 to 34 and to $n{}_{}{}^2{}_{}{}^{}S$ levels for values of $n$ from 11 through 20. The fine-structure intervals of the $n{}_{}{}^2{}_{}{}^{}D$ levels for $n=9\mathrm{} \mathrm{to}c 13$ were measured together with the line-strength ratios and were found to be in good agreement with the predictions of a simple theoretical model. At the shorter wavelengths hybrid two-photon resonances were observed to be excited through resonant intermediate continuum states of ${\mathrm{Rb}}_2$. As a result the dispersion curve for two-photon absorption in rubidium showed what appears to be resonant intermediate $p\pi \left({}_{}{}^3{}_{}{}^{}\Sigma _{u1\mathrm{}}^{}{}_{}{}^{}\right)$ and $0_g^{+}$ terms dissociating to give a $5P_{\frac{3}{2}}$ atom and resulting in the strong development of features corresponding to the $5{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\to n{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2},\frac{5}{2}}^{}{}_{}{}^{}$ part of the diffuse series, for $n\le 50$ in absorption and the $5{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\to n{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ part of the sharp series. Components to $32{}_{}{}^2{}_{}{}^{}D$ and $30{}_{}{}^2{}_{}{}^{}S$ were recorded to a precision of 0.3 ${\mathrm{cm}}^{-1\mathrm{}}$ and quantum defects for these previously unobserved terms were derived. The corresponding hybrid two-photon resonances involving intermediate states dissociating to give a $5{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ atom were not observed in the wavelength interval available in this experiment.

We have recently shown that irradiation of a molecular system by laser light whose frequency is resonant with the separation of the ground state and an excited electronic state at some particular value of the internuclear separation can produce photodissociation and subsequent fluorescence on an atomic emission line. We use this phenomenon in conjunction with established Rydberg-Klein-Rees (RKR) potential curves to determine the relative electronic transition moment between the ${}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ (ground) and ${}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ (excited) states as a function of internuclear separation, and find it to be constant. We simultaneously measure the dissociation energy of the ${}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ excited state in ${\mathrm{Na}}_2$. A simple semiclassical analysis, shown to be derivable from a full quantum-mechanical treatment, is used, and its range of validity is determined on the basis of WKB estimates.

The effect of recoil on the frequency of the spontaneously emitted photons in resonance fluorescence processes is examined. The rate of fluorescence is calculated in the limit of a weak external field. It is found that conservation of energy and linear momentum for the entire scattering process determines the frequency spectrum of the fluorescence. A simple experiment is proposed to measure the frequency shifts due to recoil.

Second-harmonic (SH) generation by paramagnetic samples at microwave frequency is considered, and the dependence of its intensity on the total number $N$ of active centers is experimentally investigated. The reported results show a $N^2$ dependence of the SH intensity near the resonance condition and a higher $N$ dependence in the far wings of the SH line. A qualitative explanation is suggested in which the observed effect is related to the internal correlations established among the spins during the SH generation process, as theoretically investigated in the following paper by Persico.

Absorption of a microwave photon by a system of $N$ two-level atoms followed by reemission, and absorption of two microwave photons followed by emission of a single photon of double frequency are considered. Interatomic correlations and dephasing effects are taken into account, and it is shown that they have different relative importance in different parts of the cross-section curve: On resonance, dephasing effects are expected to prevail, while far from resonance the opposite is true. This behavior is shown to be reflected in a different angular and $N$ dependence of the emission curve in the center and in wings of the line. These predictions are compared with the experimental results on second-harmonic generation of the preceding paper by Boscaino, and shown to be in at least qualitative agreement.

We discuss multistep resonant photoionization of atoms and photodissociation of molecules. We derive a condition under which induced atomic or molecular coherence can always be neglected, allowing accurate analysis of the multiphoton process by simple rate equations. The condition is realizable in practice, and consistent with large ionization and dissociation rates.