Inner-shell corrections to proton stopping power for low-$Z$ atoms are often taken from hydrogenic calculations. To check the relevance of the hydrogenic correction, I have analyzed explicit Born-approximation stopping-power calculations for Al ions (${\mathrm{Al}}^{n+}$, $1\le n\le 11$) to extract the inner-shell corrections. I find a significant variation in inner-shell corrections with degree of ionization. For the $K$ shell of Al ions the hydrogenic correction is within a factor of 2 of the corrections from the explicit ion results between 1 and 10 MeV. In the analysis of the explicit calculations, a remarkable constancy is found in the inner-subshell $I_{\mathrm{nl}}$ values, as the degree of ionization is varied.

An optical-pumping state-selection technique for the study of collisions of ${}_{}{}^3{}_{}{}^{}P$ atoms in individual spin-orbit states is described. This technique is used to determine state-to-state intramultipletmixing cross sections for collisions of $\mathrm{Ca}{}_{}{}^3{}_{}{}^{}P_{}^o{}_{}{}^{}$ with helium in a beam—static-gas arrangement. The derived cross sections are as follows: for $J=2\mathrm{}\to J^{\prime }=1, 31.9\pm 4.2$ ${\mathrm{\AA }}^2$; for $J=2\mathrm{}\to J^{\prime }=0, 5.5\pm 1.6$ ${\mathrm{\AA }}^2$; and for $J=1\mathrm{}\to J^{\prime }=0, 2.0\pm 5.0$ ${\mathrm{\AA }}^2$. These quantities represent averages over the translational-energy distribution (average energy 0.0556 eV). In the following paper Alexander, Orlikowski, and Straub present quantum close-coupling cross sections as a function of translational energy, using the pseudopotential Ca-He interaction curves of Malvern [J. Phys. B 11, 831 (1978)]. The experimental 2→1 and 2→0 cross sections are found to be 3 to 4 times larger than the calculated theoretical values. In contrast to the theoretical prediction for the ratio of the smaller cross sections, the 2→0 cross section is found to be larger than the 1→0 cross section.

Classical trajectories and semiclassical energy eigenvalues are calculated for an atomic electron in a high Rydberg state in an external magnetic field. With the use of perturbation theory, a classical trajectory is described as a Kepler ellipse with orbital parameters evolving slowly with time. As they evolve, the ellipse rocks, tilts, and flips in space, but the length of its major axis remains approximately constant. Exact numerical calculations verify that perturbation theory is quite accurate for the cases considered (principal quantum number ≃ 30, magnetic field ≲ 6 T). Action variables are calculated from perturbation theory and from exact trajectories, and semiclassical eigenvalues are obtained by quantization of action. Excellent agreement is found with observations.

The quantum close-coupling (CC) treatment of collisions of an atom in a ${}_{}{}^3{}_{}{}^{}P$ electronic state with a structureless target is developed, based on earlier work of Mies [Phys. Rev. A 7, 942 (1973)] and a $j_z$-conserving [coupled-states (CS)] simplification presented. There is no direct coupling between the $J=0\mathrm{}$ and $J=1\mathrm{}$ levels; transitions between these levels will occur only as a result of Coriolis coupling involving the $J=2\mathrm{}$ state. Actual CC and CS calculations are reported for collisions of $\mathrm{Ca} 4{}_{}{}^3{}_{}{}^{}P_{}^o{}_{}{}^{}$ with He, based on the potential curves of Malvern [J. Phys. B 11, 831 (1978)]. In the CC results, of the three independent cross sections, $J=2\mathrm{}\to 1$ is predicted to be largest, and $J=2\mathrm{}\to 0$ smallest, over the entire range of collision energies sampled. By contrast, the CS approximation predicts the 1→0 transition to be forbidden, and yields only fair accuracy for the CC 2→1 and 2→0 transitions. The coupling between spin-orbit states is also interpreted within an adiabatic model. A comparison with the experimental results of Yuh and Dagdigian (preceding paper) is made by averaging the CC cross sections over the experimental translational energy distribution. The experimental cross sections for the 2→1 and 2→0 transitions are 3-4 times larger than the theoretical values, and the 2→0 cross section is found experimentally to be ∼3 times larger than the 1→0 cross section, in direct contrast with the theoretical prediction for this ratio.

The threshold laws for electron-atom scattering processes in a magnetic field are shown not to contain singularities in general. Observed modulations of photodetachment cross sections are due to the presence of true resonances rather than divergence of phase space. These resonances may be associated with thresholds, or they may be analogous to the quasi-Landau resonances observed in photoionization.

Electron-impact-ionization cross sections have been measured from threshold to about 20 times threshold for Be-like ions ${\mathrm{B}}^{+}$, ${\mathrm{C}}^{2+}$, ${\mathrm{N}}^{3+}$, and ${\mathrm{O}}^{4+}$ with the use of the crossed-beams technique. The ion beams consist of mixtures of ions in the $2s^2{}_{}{}^1{}_{}{}^{}S$ ground state and the $2s2p{}_{}{}^3{}_{}{}^{}P_{0,1,2}^{}{}_{}{}^{}$ metastable states. For ${\mathrm{B}}^{+}$ and ${\mathrm{C}}^{2+}$ the metastable fractions could be changed, allowing estimates of ground-state cross sections, while for ${\mathrm{N}}^{3+}$ and ${\mathrm{O}}^{4+}$ the metastables appear to dominate the beams and the fractions could not be changed. The measured cross sections are compared with a variety of predictions. Distorted-wave calculations compare most favorably, but discrepancies up to 40% are found. The metastable-state—ground-state mixture complicates the comparisons for these beam experiments and is probably an issue for all environments where light ($Z\le 15$) Be-like ions occur.

The systematics of single and double $K$-shell-vacancy production in titanium has been investigated in the limit of zero target thickness (∼ 1 μg/${\mathrm{cm}}^2$) for incident C, N, O, F, Mg, Al, Si, S, and Cl ions over a maximum energy range of 0.5 to 6.5 MeV/amu. This corresponds to collision systems with $0.27\le \frac{Z_1}{Z_2}\le 0.77$ and $0.24\le \frac{v_1}{v_{2 K}}\le 0.85$, where $v_1$ is the projectile nuclear velocity and $v_{2 K}$ is the mean velocity of an electron in the target $K$ shell. The present work is divided into four major sections. (1) Single $K$-shell-vacancy production has been investigated by measuring $K\alpha$ and $K\beta$ satellite x-ray-production cross sections for projectiles incident with no $K$-shell vacancies. For incident ions with $Z_1\ge 9$, the contribution due to electron-transfer processes from the target $K$ shell to outer shells of the projectile has also been noted. (2) Single $K$—shell-to-$K$-shell electron-transfer cross sections have been obtained indirectly by the measuring of the enhancement in the $\mathrm{Ti}K$ x-ray production cross section for bare incident projectiles over ions incident with no initial $K$-shell vacancies. (3) Double $K$-vacancy production has been investigated by measuring the $K\alpha$ hypersatellite intensity in ratio to the total $K\alpha$ intensity. (4) Double $K$—shell-to-$K$-shell electron-transfer cross sections have been obtained indirectly with the use of a procedure similar to that used for single $K$ to $K$ transfer. The measured cross sections have been compared to theoretical models for direct Coulomb ionization and inner-shell electron transfer and have been used to investigate the relative importance of these mechanisms for $K$-vacancy production in heavy-ion—atom collisions.

We present the simple generalization to complex energies of the normal global real scaling used for bound-state calculations to produce a variational energy which satisfies the virial theorem. We show that in two limiting cases, one or the other of which is almost always satisfied in all calculations, the virially stabilized complex energy is sensitive to only the real part or the imaginary part of the complex virial expression. We then compute the virial expression for a number of wave functions for the $1s2s^2{}_{}{}^2{}_{}{}^{}S {\mathrm{He}}^{-}$, $1s2s2p{}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{} {\mathrm{He}}^{-}$, and $1s^{2}2s^2\mathrm{kp}{}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{} {\mathrm{Be}}^{-}$ resonances and the corresponding virially stabilized resonance energies. In all calculations one of the limiting cases was applicable.

Relativistic many-body perturbation theory has been used to investigate the hyperfine structure of the singly ionized magnesium ion. These investigations were carried out to explain the recent experimental data in the ground state $3{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ of ${\mathrm{Mg}}^{+}$ as well as to compare the hyperfine interaction results, both experimental and theoretical, in alkali-metal atoms with those in the corresponding isoelectronic alkaline-earth positive-ion series. The one-electron contribution to the hyperfine constant in ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}_{}^{+}{}_{}{}^{}$ was found to be -553 MHz composed of the direct and exchange core-polarization contribution of -466 and -87 MHz, respectively, the many-electron correlation contribution being -48 MHz. The net theoretical hyperfine constant comes out to be -(602±8) MHz, which agrees very well with the recent experimental value of -596.25 MHz obtained with the use of ion-storage techniques.

The static quadrupole polarizability of Ne is calculated through the use of the many-body perturbation-theory scheme limited to single and double substitutions in the reference Hartree-Fock (HF) determinant (SD-MBPT). All calculations are performed within the finite-field numerical perturbation scheme. The fourth-order MBPT treatment based on the coupled HF solution for the perturbed system leads to the quadrupole polarizability value equal to 7.48 a.u. The convergence of the SD-MBPT series for properties and the role of the renormalization terms are discussed.

Quantum nondemolition measurements on an harmonic-oscillator detector are discussed for two detector-meter coupling schemes: parametric amplification and parametric frequency conversion. A time-dependent solution for the density operator of the coupled detector-meter system, including damping, is obtained. A sequence of measurements via meter state reduction is analyzed.

We report the results of a battery of experiments to determine the origin of ${\mathrm{Na}}_2^{+}$ produced by crossed sodium beams in the presence of intense optical radiation. The principal mechanism appears to be atomic collision combined with photon absorption. The characteristics of long-range optical collisions are compared with those expected from collisional resonances.

The interaction potentials of the quasimolecular $\Sigma$ and $\Pi$ states formed by the approach of a proton and the positive ion ${\mathrm{Fe}}^{13+}$ are calculated in an approximation which reproduces the long-range quadrupole and polarization terms and which accounts properly for short-range penetration effects. The interaction potentials are used in quantal calculations of the cross sections for proton-impact excitation of fine-structure transitions of ${\mathrm{Fe}}^{13+}$. Solutions of the close-coupled scattering equations are obtained and the resulting cross sections are compared with those given by the Coulomb-Born and elastic approximations. The sensitivity of the cross sections to features of the interaction potentials is explored. The Coulomb-Born and elastic approximations do not always reflect faithfully the physical characteristics of the potentials.

Absolute total cross sections for electron detachment and the production of slow product ions have been measured for collisons of ${\mathrm{H}}^{-}$ and ${\mathrm{D}}^{-}$ ions with ${\mathrm{H}}_2$, ${\mathrm{D}}_2$, and HD. The threshold behavior of the detachment cross section for the above reactants has been determined in experiments in which the relative collision energies range from about 1 eV up to several hundred. The thresholds for detachment for both ${\mathrm{H}}^{-}$ and ${\mathrm{D}}^{-}$ ions are found to be larger than the electron affinity. Isotopic substitution reveals that the detachment cross sections scale with relative collision energy at low collision energies and with relative collision velocity at high collision energies. Upper and lower bounds on detachment-rate constants which are based upon the measurements are presented.

A simplified model of electron-hydrogen scattering is considered in which all terms involving nonzero angular momenta are neglected. Elastic scattering and excitation cross sections for the $2s$ and $3s$ states are calculated for this model with the use of close-coupling expansion with four different pseudostate bases. Pseudothreshold structure is observed and removed. It is found that, after removal of this structure, the results agree quite well with each other and with exact results for this model which were given previously by Poet.

We propose a method for constructing an effective optical potential through which correlation effects can be introduced into the electron-molecule scattering formulation. The optical potential is based on a nonperturbative, Feshbach projection-operator procedure and is evaluated on an $L^2$ basis. The optical potential is incorporated into the scattering equations by means of a separable expansion, and the resulting scattering equations are solved by a linear-algebraic method based on the integral-equation formulation. We report the results of scattering calculations, which include polarization effects, for low-energy $e-{\mathrm{H}}_2$ and $e-{\mathrm{N}}_2$ collisions. The agreement with other theoretical and with experimental results is quite good.

The effects of the form of the distribution in energy of the electrons produced by ionization on electron-energy distributions and transport coefficients are investigated theoretically at high values of the ratio of the electric field to gas density, $\frac{E}{n}$. The calculations are carried out for ${\mathrm{N}}_2$ at $\frac{E}{n}$ from 100×${10}^{-21\mathrm{}}$ to 3000×${10}^{-21\mathrm{}}$ V ${\mathrm{m}}^2$ using previously determined electron-collision cross sections and secondary-electron energy distributions. As the energy of the secondary electrons and the energy lost by the higher-energy, scattered electrons is increased, the relative numbers of electrons at very low energies and at high energies in the calculated steady-state distributions decreases. These changes are accompanied by decreases in the calculated ionization coefficients, drift velocities, and mean energies and by an increase in the characteristic energy. A simplified secondary-electron energy distribution is proposed which gives distribution functions and transport coefficients in satisfactory agreement with the those obtained using the published experimental distributions.

It is demonstrated that the total F $K$ x-ray production cross section for ${\mathrm{F}}^{7+}$ + He collisions comes predominantly from three types of processes. These processes are $1s$-electron excitation of the $1s^2{}_{}{}^1{}_{}{}^{}S$ ground state of ${\mathrm{F}}^{7+}$, $2s$ electron excitation of the $1s2s{}_{}{}^3{}_{}{}^{}S$ metastable state of ${\mathrm{F}}^{7+}$, and $\mathrm{nl}$ electron capture by the $1s2s{}_{}{}^3{}_{}{}^{}S$ metastable state of ${\mathrm{F}}^{7+}$. All three of these processes have one thing in common, namely, they result in F $K$ x rays. By using a high-resolution x-ray spectrometer, the cross sections for the three processes are measured separately as a function of projectile energy in the range of 6 to 40 MeV. The assignment of the three different processes of $1s$ electron excitation, $2s$ electron excitation, and $\mathrm{nl}$ electron capture is corroborated by comparing the measured energy dependences of the various $K$ x-ray transitions with theory and other experimental measurements with ${\mathrm{F}}^{8+}$ and ${\mathrm{F}}^{9+}$ beams.

The cross section for the elastic scattering of electrons by hydrogen atoms in the excited $2S$ state has been calculated in the energy range of 10 to 1000 eV. In this calculation the method of Das, proposed for electron-atom collision problems, has been followed. Some of our results are compared with a few other theoretical results existing at present. Results for higher energies, for example, 200 eV and above, compare favorably with those of a few better-known methods, such as the optical-model calculation. For energies below 100 eV, the present results are the only results of moderate accuracy available at present. The low-energy results show valleys at small angles which disappear as the energy increases. Effects of exchange are observed to be insignificant down to such low energies as 10 eV.

The impact-parameter dependence of the inner-shell excitation was measured for 1.4-MeV/u Ni ions on Zr, Ag, Te, and Au. All the measured vacancy-production probabilities have impact-parameter dependences typical for direct excitation. Scaling the impact parameter with the adiabatic radius, calculated using united-atom binding energies, all Ni $K$ data can be brought to one common curve. The impact-parameter region contributing most to the vacancy-production cross section, as well as the plateau value of the vacancy-production probability attained at the lowest impact parameters could be explained by extending the semiclassical-approximation method to these collision systems.