Differential cross sections for the electron impact excitation from the metastable 2 ${}_{}{}^3{}_{}{}^{}\mathrm{S}$ state to the 3 ${}_{}{}^3{}_{}{}^{}\mathrm{S}$ state of helium, at impact energies 50 to 500 eV, are calculated in the two-potential model and the modified Born approximation using Coulomb waves with a screened nuclear charge. The exchange effect is included in the framework of the Ochkur-Rudge approximation. The results are compared with recent theoretical calculations. It is shown that the present approach provides a significant improvement over the plane-wave Born approximation at large scattering angles.

Cross sections for metastable $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ formation by electron caputre in ${\mathrm{H}}^{+}-\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collisions and by excitation in $\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}-\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collisions have been measured over the energy range 1.9-92 keV. A fast beam of ${\mathrm{H}}^{+}$ ions or $\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ atoms was passed through a tungsten-tube-furnace target which contained thermally dissociated hydrogen. Fast metastable $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ atoms formed by collisions in the target were detected downstream using electric field quenching and Lyman-$\alpha$ photon-counting techniques. The present values are normalized at 24.5 keV to the average value of three previous independent measurements of the $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ formation cross section in ${\mathrm{H}}^{+}$-H collisions which agree to within 20%. Measured cross sections for both ${\mathrm{H}}^{+}$-H and H-H collisions contain only one maximum, in contrast with certain theoretical predictions. For ${\mathrm{H}}^{+}$-H the low-energy data are in good agreement with theoretical results based on a multistate molecular treatment of the collision. Above 75 keV the ${\mathrm{H}}^{+}$-H data agree with the Born approximation cross sections. Close-coupling pseudostate predictions lack overall detailed agreement with the present results, although the maximum in the cross section is reproduced well. High-energy ($E>\mathrm{}15\mathrm{}$ keV) coupled-state calculations using a scaled hydrogenic two-center expansion are in good accord with the data. For H-H collisions all theoretical treatments are in poor accord with the present experimental results. Above 40 keV the measured H-H cross section is inversely proportional to the impact energy. This $E^{-1\mathrm{}}$ energy dependence is in agreement with high-energy theoretical predictions. However, above 10 keV the Born approximation predicts structure in the cross section due to simultaneous excitation of the projectile and target which is not observed. The present results are compared with previous experimental determinations, and discrepancies are found to exist.

Cross sections have been computed for the electron-transfer process ${\mathrm{Ba}}^{+}+{\mathrm{Ba}}^{+}\to \mathrm{Ba}+{\mathrm{Ba}}^{++}$, for collision energies ranging from 25 to 500 keV. The straight-line classical-trajectory method has been used, with basis functions obtained by the multiconfiguration valence-bond method. Several numerical procedures applicable to future treatments of similar large systems were developed. The maximum cross-section value is found to be around $27\pi a_0^2$ (2.4 × ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$), and occurs near collision energy 500 keV. The system's transient behavior has also been studied in detail during the collision, and it has been found that most electron-transfer events involve migration of the electron across internuclear distances considerably larger than the ionic diameter.

The contributions to the cross sections for the ionization of $H\left(1s\right)\mathrm{}$ and $H\left(2s\right)\mathrm{}$ atoms in collisions with atomic hydrogen, arising from electron exchange, are evaluated in the Ochkur-Rudge approximation. This is shown to improve considerably the agreement between theory and experiment in the energy range 5-100 keV. A comparison between exchange cross sections in the absence of interference, as obtained by the present method and in previous work employing classical four-body trajectory calculations, is also presented.

The charge states of $\mathrm{H}_2^{}{}_{}{}^{+}$ fragments produced by collisions in several gas targets (${\mathrm{H}}_2$, air, Ar) at various pressures were measured. The bombarding energies were in the range 250-600 keV. The fragments were separated according to their charge by an electrostatic deflector and measured simultaneously by a system of detectors and electronic coincidence circuits. A system of differential equations describing the process as a combination of a molecular dissociation process and a charge-exchange process by atomic projectiles was set up and solved. There is a very good agreement between the theoretical expressions which depend on the ratios of the dissociation, loss, and capture cross sections and the experimentally observed charge states. It turns out that although the cross sections change greatly with the gas target and projectile velocity, the ratio between the atomic and molecular cross sections for the processes remains almost constant.

The hyperfine interaction constants of the $z{}_{}{}^6{}_{}{}^{}P_{\frac{7}{2}}^{}{}_{}{}^{}$ and $z{}_{}{}^8{}_{}{}^{}P_{\frac{7}{2}}^{}{}_{}{}^{}$ levels of the configuration $4f{}_{}{}^7{}_{}{}^{}6s6p$ of the isotopes ${}_{}{}^{151}{}_{}{}^{}\mathrm{Eu}$ and ${}_{}{}^{153}{}_{}{}^{}\mathrm{Eu}$ have been remeasured with the laser-atomic-beam technique. The analysis yields values of -6.80(26)% and -1.00(3)%, respectively, for the hyperfine anomalies. The anomaly in the $z{}_{}{}^6{}_{}{}^{}P_{\frac{7}{2}}^{}{}_{}{}^{}$ level is the largest so far observed and deviates considerably from the ground-state hyperfine anomaly. The experimental values of the hyperfine anomaly are compared with a calculation based on Nilsson-type nuclear wave functions. Possibly the electronic-state dependence of the hyperfine anomaly is due to core polarization.

A molecular-dynamics simulation of the pressure broadening of the sodium resonance line by argon gives an absorption line shape which is compared to results from the Anderson-Talman classical path theory. The system consists of 255 argon atoms and one sodium atom in a box with periodic boundary conditions. The size of the box and the initial velocities are chosen to correspond to a particle density of 2×${10}^{21}$ ${\mathrm{cm}}^{-3\mathrm{}}$ and a temperature of 450 K. The time-dependent difference potential matrix is utilized in an adiabatic approximation to give the molecular-dynamics line shape. Spin-orbit coupling and Doppler broadening are neglected. A Fourier-transform technique is used to evaluate the Anderson-Talman theory line shape for the same system. Remarkable agreement is found between the molecular-dynamics line shape and the line shape obtained from the one-perturber spectrum by means of the Anderson-Talman theory. Comparison of molecular-dynamics line shapes calculated with a scalar and with a vector dipole transition moment shows that relaxation of polarization has a significant broadening effect on the center of the line.

The isotope shift of the transition $2{}_{}{}^3{}_{}{}^{}P-3{}_{}{}^3{}_{}{}^{}D$ between ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is measured to an accuracy of 3 parts in ${10}^3$ using the technique of Doppler-free intermodulated fluorescence spectroscopy. The hyperfine structure of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in the $2{}_{}{}^3{}_{}{}^{}P$ and $3{}_{}{}^3{}_{}{}^{}D$ states is fully resolved and is fit to a magnetic-interaction hyperfine Hamiltonian. After removing the hyperfine interaction and assuming no specific isotope shift in the $3{}_{}{}^3{}_{}{}^{}D$ state, the measured iostope shift agrees with theoretical values when variational wave functions are used to compute the specific mass shift of the $2{}_{}{}^3{}_{}{}^{}P$ term.

We compute new estimates of energy levels of doubly excited states with two electrons in the same shell, for all principal quantum numbers $N\le 5$ and angular momentum values $0\le L\le 2N-2$ in ${\mathrm{H}}^{-}$ and He. We investigate the structure of these intrashell spectra using a recent "supermultiplet" approach which orginates in the O(4) shell structure of one-electron atoms. We provide new interpretations of the electron correlation underlying the O(4) states and supermultiplets of two-electron atoms; this accounts qualitatively for approximate separability of rotationlike and vibrationlike progressions of levels found in the computed spectra. Certain diamond-shaped patterns of supermultiplet energies are found to contain near degeneracies of levels with $\Delta L=\pm 2$; this accounts in part for level clustering we find in the unresolved spectra. Our investigation of scaling of the apparent rotational and vibrational parts of the energy with higher $N$ shows consistency with a simple model of the atom which has electrons on the surface of a spherical shell, with radius $R\simeq N^2$. We investigate the model group theoretically, and find two different O(4) groups which describe angular electron correlation in limiting cases of large or small shell radius for each principal quantum number $N$. A third O(4) group is related to intrashell radiative transitions.

We investigate whether the intrashell portion of the double-excitation spectrum of the helium atom may be interpreted in terms of collective rotational and bending vibrational motion, analogous to the ro-vibrational motion of molecules. Earlier work by us had identified a few levels in each atomic shell as having a rotorlike spectrum cutoff at higher energies, analogous to the cutoff rotorlike spectra of some nuclei. In this paper we use the $I$ and $d$ supermultiplets of the preceding paper of this journal, to interpret the entire intrashell manifold for each principal quantum number $N$, as resembling cutoff rotational and bending vibrational levels of a highly nonrigid linear symmetric $\mathrm{XYX}$ "molecular" structure. We obtain a good qualitative fit of each intrashell spectrum using leadingorder ro-vibrational energy formulas from molecular spectroscopy including anharmonicity, centrifugal distortion, and rotation-vibration coupling. We interpret these effects for low-lying intrashell states of two-electron atoms, and find them to be consistent with an average equilibrium configuration ${\theta }_{12}=180\mathrm{}°$ for the interelectronic angle. Analysis of the time scales of the proposed rotational, bending, and other degrees of freedom suggests approximate separability. We also identify parts of the spectrum analogous to molecular $l$ doubling, and indicate a possible link between the related Coriolis force and a recently proposed mechanism for decay by autoionization. Certain aspects of our collective interpretation of the atomic supermultiplets are discussed which have close parallels in nuclear physics, including the Elliott model and the SU(6) interacting boson model for nuclear collective motion.

Many-body perturbation theory is applied to the process of $K$-shell photoionization of Ne with the $2p\to 3s$ excitation. Absolute cross section of the process as well as the conjugate shake-up probability, i.e., the ratio to the simple $K$-shell photoionization cross section, are calculated as functions of the photon energy. The latter agrees very well with the available experimental data. The calculated probability is large (about 5%) near the threshold. The angular distribution of the ejected electron with respect to the photon polarization axis is also obtained in the case of the linearly polarized photon.

Interference between magnetic-dipole and electric-dipole transition moments has been observed in the molecularbeam rf spectrum of methane. The transition studied is between two levels in the $J=2\mathrm{}$ rotational state and ground vibronic state. This transition is both magnetic-dipole allowed and electric-dipole allowed because a static electric field mixes states of opposite parity. The transition probability was observed to depend upon the amplitudes and relative phases of the applied rf magnetic and electric fields. A theoretical explanation of this effect is given.

We have measured the absolute wave numbers of the $2s{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-2p{}_{}{}^3{}_{}{}^{}P_J^{}{}_{}{}^{}$ transitions in ${}_{}{}^7{}_{}{}^{}\mathrm{Li}_{}^{+}{}_{}{}^{}$ by laser fluorescence spectroscopy on an ion beam. Using the hyperfine structure (hfs) theory of Jette, Lee, and Das, we have extracted the following hfs-free wave numbers: $\sigma (2s{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-2p{}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{})=18\mathrm{} 231.3030\left(12\right),\sigma (2s{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-2p{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{})=18\mathrm{} 226.1082\left(12\right)\mathrm{}$, and $\sigma (2s{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-2p{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{})=18\mathrm{} 228.1979\left(12\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. By subtracting the theoretical values of Accad, Pekeris, and Schiff, we obtain the differential Lamb shifts $\mathcal{S}(2s{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-2p{}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{})=1.2539\mathrm{}\left(16\right),\mathcal{S}(2s{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-2p{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{})=1.2543\mathrm{}\left(16\right)\mathrm{}$, and $\mathcal{S}(2s{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-2p{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{})=1.2545\mathrm{}\left(16\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. These results are in agreement with the calculations of Ermolaev and with earlier measurements by Bacis and Berry. The fine-structure intervals obtained from the absolute wave numbers are in agreement with the theory of Accad et al. and with the measurements of Bacis and Berry, but they exhibit a disagreement, which amounts in one case to two standard deviations, with the recent more precise results of zu Putlitz and co-workers.

A calculation of the ground-state hyperfine frequency in muonic helium is given. Perturbation theory is applied to the Schrödinger equation to obtain a series in $\frac{m_e}{m_{\mu }}$. The value obtained is 4462.6 ± 3 MHz, which is consistent with experiments at the Swiss Institute for Nuclear Research and the Los Alamos Meson Physics Facility. The theoretical value includes a — 46-MHz contribution from excited states of the effective ${\left(\alpha {\mu }^{-}\right)}^{+}$ nucleus.

Using the method of explicit summation over the intermediate states two-photon absorption cross sections in light and intermediate atoms based on the simplistic frozen-core approximation and $\mathrm{LS}$ coupling have been formulated. Formulas for the cross section in terms of integrals over radial wave functions are given. Two selection rules, one exact and one approximate, valid within the stated approximations are derived. The formulas are applied to two-photon absorptions in nitrogen, oxygen, and chlorine. In evaluating the radial integrals, for low-lying levels, the Hartree-Fock wave functions, and for high-lying levels, hydrogenic wave functions obtained by the quantum-defect method have been used. A relationship between the cross section and the oscillator strengths is derived.

Measurements of collisional $l$-mixing cross sections for Na $\mathrm{nd}$ states have been extended to C${\mathrm{H}}_4$ and ${\mathrm{C}}_3$${\mathrm{H}}_8$. The measurements, which have been made using a time-resolved laser induced fluorescence approach, show that the cross section for C${\mathrm{H}}_4$ rises sharply from $n=7\mathrm{} \mathrm{to} 10$, and then decreases. The ${\mathrm{C}}_3$${\mathrm{H}}_8$ cross section is much larger than for previously studied collision partners, and rises monotonically from $n=7\mathrm{} \mathrm{to} 17$ with the exception of an unexpected dip at about $n=15\mathrm{}$. The measurements are in qualitative agreement with expectations based on low-energy $e-\mathrm{C}{\mathrm{H}}_4$ and $e-{\mathrm{C}}_3{\mathrm{H}}_8$ scattering, and suggest that the effect of internal structure and molecular geometry on the collision dynamics is relatively small.

The alignment and orientation produced by the tilted-foil excitation of He was studied for a wide range of foil tilt angles and outgoing-atom velocities. In particular, two quantum states of different orbital angular momentum ($3p {}_{}{}^1{}_{}{}^{}P$ and $4d {}_{}{}^1{}_{}{}^{}D$) were investigated and the results were compared with a number of previously proposed models.

The experimental data on muonic x-ray intensities for the third-row atoms ($Z=11-17\mathrm{}$) are analyzed in a unified way. The deduced initial $l$ distributions are not very far from the statistical ones; they are, however, somewhat steeper near the closed atomic shells and somewhat flatter in the middle of the shell. The $K$-electron refilling rate is fast increasing with $Z$; it is considerably smaller than the refilling rate of normal neutral atoms. The calculation shows that in these light atoms the inner electron shells ($K$ and $L$) are strongly perturbed during the muonic cascade. Correct treatment of their depletion and refilling is essential. The two existing computer cascade programs are compared. It is stressed that a correct treatment of penetration effects as well as inclusion of quadrupoles in the Auger electron emission is necessary when one wants to utilize the full accuracy of the experimental data.

The first high-resolution $M_{4,5}{N}_{4,5}{N}_{4,5}$ and $M_{4,5}{N}_{4,5}{O}_1$ Auger electron spectra from silver vapor have been measured using electron-beam excitation. The spectra reveal fine structure not observable in solid-state measurements. The spectra have been analyzed in terms of the optically known energy levels of the $4d^{8}5s$ and $4d^9$ final-state configurations. The intensity anomaly of the high-energy components of the $M_5{N}_{4,5}{N}_{4,5}$ group found in the spectrum of solid silver does not exist in the present vapor-phase spectrum. The relative intensities of lines are found to correspond very well to the intensities of $4d^8$ parent Auger lines calculated in a mixed coupling scheme. For the binding energies of the $M_4$ and $M_5$ levels of free silver atoms 381.55 ± 0.10 and 375.55 ± 0.10 eV, respectively, have been obtained. A comparison with the published solid-state photoenergies and Auger energies shows that the free atom binding energies are 3.3 ± 0.5 eV higher and the kinetic energies of the $M_{4,5}{N}_{4,5}{N}_{4,5}$ Auger electrons 12.1 ± 0.5 eV lower than the corresponding solid-state values.

X-ray photoelectron spectroscopy (XPS) has been used to measure lifetime broadening of $L$, $M$, $N$, $O$, and $P$ core levels with binding energies less than 1500 eV in approximately 25 elements. The results show that the framework provided by previously accepted theoretical estimates of lifetime broadening is sometimes misleading. Lifetimes derived from theory and experiment often differ by a factor of 2 or more. In the transition metals of the first period plots of measured widths of the $L_1\mathrm{}\left(2s\right),L_2\left(2\mathrm{}{p}_{\frac{1}{2}}\right)$, and $L_3\left(2\mathrm{}{p}_{\frac{3}{2}}\right)$ levels as a function of atomic number show broad maxima which are not adequately described by theory. The origin of this broadening is extensively discussed, as is the overestimation of lifetimes by theory in other areas of the periodic table.