The electronic energy shifts due to the vacuum polarization are calculated to all orders $\alpha {\left(Z\alpha \right)}^n$, $n\ge 1$, and $100\le Z\le 174$. The calculations are carried through in momentum space and the results are generally in good agreement with coordinate-space results. The momentum-space method is discussed in detail.

We describe a three-dimensional model, based on the temporal invariance of the statistical properties, which allows us to calculate the spatial and energy probability densities of strongly confined ions in the presence of a buffer gas. This model is then applied to a population of ${\mathrm{Cs}}^{+}$ ions for which we compute these densities within the whole stability diagram and for various gases. In the case of helium, in particular, we show that these laws can be described by Gaussian functions, and we present the evolution of the temporal average of the spatial dispersions and ionic temperatures at the working point.

Excitation-autoionization contributions to electron-impact ionization are calculated for several atomic ions in the cadmium isoelectronic sequence. We calculate excitation cross sections in the distorted-wave approximation and compare them in one case to a calculation in the close-coupling approximation. We focus attention on the $4d^{10}5s^2\to 4d^{9}5s^2\mathrm{nf}$ innershell excitations in ${\mathrm{In}}^{+}$, ${\mathrm{Sb}}^{3+}$, and ${\mathrm{Xe}}^{6+}$. Hartree-Fock atomic structure calculations for the $4d^{9}5s^2\mathrm{nf}$ configurations are found to be highly term dependent. Thus our predictions for the total ionization cross section from the $5s$ subshell for these ions exhibit strong target term dependence. Our ${\mathrm{Xe}}^{6+}$ results are found to be in excellent agreement with the recent experimental crossed-beam measurements of Gregory and Crandall.

The absolute cross section for electron-impact ionization of ${\mathrm{Xe}}^{6+}$ has been measured from below threshold to 1500 eV with the Oak Ridge National Laboratory crossed-beams apparatus. Excitation of inner-shell electrons to autoionizing states is found to contribute up to a factor of 10 more than direct processes to the single-ionization cross section, and indirect effects dominate the measurement over the entire energy range studied. Good agreement is found with distorted-wave excitation calculations added to Lotz direct-ionization predictions.

Electron capture from a hydrogenlike ion of large nuclear charge $Z_{T}e$ by a bare ion of charge $Z_{P}e$ moving with speed $v$ has been studied using the strong-potential Born approximation to the amplitude. Under the conditions $Z_P\ll Z_T$ and $Z_P{e}^2\ll \hslash v$, it is shown that, in comparison with the impulse approximation, the correct weighting of the target spectrum of intermediate states in the strong-potential Born theory significantly alters the $1s\to 1s$ cross section and at the same time makes peaking approximations to the amplitude more realistic, even for low $v$. The specific cases of $Z_T=6, 10,\mathrm{and} 18$ are treated over the velocity range $\frac{Z_T}{3}\lesssim \frac{\hslash v}{e^2}\lesssim \frac{Z_T}{\mathrm{}\left(0.3\right)\mathrm{}}$. Instituting a one-electron model, $K$-shell capture cross sections and probabilities for protons on carbon, neon, and argon are calculated and compared with experiment. The strong-potential Born theory is seen to give a good representation of the data. Total cross sections for $1s\to 1s$ capture for $Z_P=Z_T=1\mathrm{}$ are also presented.

Relativistic plane-wave Born-approximation calculations of cross sections for $M$-shell ionization of ${}_{67}{}^{}{}_{}{}^{}\mathrm{Ho}$, ${}_{79}{}^{}{}_{}{}^{}\mathrm{Au}$, and ${}_{92}{}^{}{}_{}{}^{}\mathrm{U}$ by protons with incident energies from 0.05 to 1 MeV are reported. Dirac-Hartree-Slater wave functions were employed and binding-energy change and Coulomb deflection were taken into account. Associated x-ray production cross sections were also computed. Results are compared with previous theoretical predictions and with experimental data. Definite improvement in the theory has been attained by the use of realistic wave functions and consistent inclusion of the effects of relativity.

The charge transfer of doubly charged and trebly charged ions of C, N, O, and Ne with atomic hydrogen at thermal energies is studied. Adiabatic potential-energy curves and radial coupling matrix elements are presented. The collision cross sections are calculated after transforming to a diabatic basis. For the trebly charged ions, there exists at least one exit channel into which charge transfer is highly probable. Cross sections for doubly charged ions are sensitive to the energy-level structure of the ionic species.

It is known that the subshell contributions to the coefficient of the $O\left(\ln E\right)$ asymptotic term of the Bethe-Born stopping-number formula are not given correctly by partitioning the squared matrix element defining this coefficient into a simple sum of its subshell contributions. This interesting result is extended to the second, or $O\mathrm{}\left(1\right)\mathrm{}$, asymptotic term in the stopping number. In this case, the subshell decomposition results in a sum of two expressions. One is simply the subshell decomposition of the squared matrix element defining the $O\mathrm{}\left(1\right)\mathrm{}$ coefficient for the total system. The second term is more complex in form but sums to zero, as it must, when summed over all subshells in the target. It is pointed out that this second term and its summation requirement can be used to impose a useful restriction on the construction of theoretical subshell corrections for the Bethe-Born formula.

Doubly differential cross sections of secondary electrons ejected from ${\mathrm{N}}_2$ by electron impact have been measured by a crossed-beam method. The incident energies used were 50, 70, 100, 200, and 400 eV. The energy and angular range of secondary electrons measured were from 1.0 eV to one-half of the difference between the incident energy and ionization potential and 12° to 156°, respectively. The present results have been compared with two previous measurements and considerable discrepancies were found.

Electron capture in ${\mathrm{Ar}}^{2+}$ + Ar is studied at low keV energies. Using ${\mathrm{Ar}}^{2+}$ + He collisions as an energy reference we show that the dominant single-electron-capture process is endothermic and of the type ${\mathrm{Ar}}^{2+}{}_{}{}^3{}_{}{}^{}P+\mathrm{Ar}\to {\mathrm{Ar}}^{+}{}_{}{}^2{}_{}{}^{}P+{\mathrm{Ar}}^{+}3s^{2}3p^4\mathrm{nl}$. Detailed studies at 2.4 keV show $\mathrm{nl}$ to be predominantly $3d$ and $4p$. Weaker exothermic processes are found and due mainly to long-lived, highly excited states of ${\mathrm{Ar}}^{2+}$. The direct scattering and double-electron-capture channels are also studied. The direct scattering occurs with no Ar-target excitation. Differential cross sections are presented for the collision processes. The single-electron-capture results are interpreted with the use of a simple model in which a strongly attractive intermediate state couples the incident and outgoing channels.

A detailed and systematic analysis of the scope of the Firsov model as modified by Cheshire when no adjustable parameters are included in the calculations of the low-velocity electronic-stopping cross section is presented. For this purpose we summarize and extend our previously reported [Radiat. Eff. Lett. 43, 79 (1979);Nucl. Instrum. Methods 170, 205 (1980)] preliminary results on the role of all computational degrees of freedom that influence the outcome of the calculations, namely, (a) inclusion of trajectory, (b) accuracy of wave functions and speed of atomic electrons, (c) motion of Firsov's plane, and (d) consideration of experimental conditions. We find that the Firsov theory is accurate only within a factor of 2; therefore, at least a scale factor is necessary in order to get reasonable agreement with experiment.

For $20\le n\le 45$, two types of quasielastic state-changing-collisional (QESCC) processes, i.e., (i) $l$-changing and (ii) $n$-and $l$-changing processes, have been theoretically investigated based on the free-electron model in which an excited Rydberg electron behaves as if it were "free" and slow with its interaction with a rare-gas atom playing a decisive role. It is shown that a parameter $u_{min}[=\frac{\nu {\nu }^{\prime }\Delta E{a}_0}{\left(\hslash V\right)}]$ is quite useful for characterizing both of these QESCC processes in a unified way where $\nu \left(\simeq {\nu }^{\prime }\right)$ is an effective principal quantum number of the initial (final) state, $\Delta E$ is an energy defect, and $V$ is a relative velocity. It is theoretically found that higher-angular-momentum states are dominantly populated in the final channel of these QESCC processes with $1<\mathrm{}{u}_{min}\lesssim \nu$ such as in the $n$- and $l$-changing collision of ${\mathrm{Rb}}^{**}\mathrm{}\left(\mathrm{ns}\right)+\mathrm{He}$. This is in contrast with the uniform distribution over the final angular-momentum states for the usual $l$-changing processes, i.e., $u_{min}\lesssim 1$. The calculated cross sections of these QESCC processes with $1<\mathrm{}{u}_{min}\lesssim \nu$ are found to be in reasonable agreement with experimental findings available at present.

A detailed theoretical study of ${\mathrm{H}}^{+}$+${\mathrm{H}}^{-}$⇄${\mathrm{H}}^{*}$+H collisions in the $0.02<\mathrm{}{E}_{\mathrm{c}.\mathrm{m}.\mathrm{}}<10\mathrm{}$ keV energy range is reported. Calculations of the relevant states of the quasimolecular system are carried out at large internuclear distances ($5a_0<R<\mathrm{}100\mathrm{}{a}_0$) with a model involving only the loosely bound electron of the system. Our calculated adiabatic states agree well with the available accurate ab initio results. Diabatic states are found not only to differ from the conventionally invoked pure ionic and covalent states, but also to depend dramatically on the choice of the fixed electron coordinate origin. Such differences show up in the cross-section calculations when ${\mathrm{H}}^{*}\mathrm{}(n=3\mathrm{})+\mathrm{H}$ channels are taken into account and demonstrate the need for considering the problem of the electron translation factor. Cross-section calculations are finally calculated in a 12-state projected valence-bond diabatic basis incorporating a common translation factor of the Schneiderman-Russek type. The results demonstrate the important contribution of ${\mathrm{H}}^{*}\mathrm{}(n=3\mathrm{})+\mathrm{H}$ channels to the mutual neutralization process. Good agreement is obtained with the experimental data on neutralization and detachment in ${\mathrm{H}}^{+}$+${\mathrm{H}}^{-}$ and on ${\mathrm{H}}^{+}$ formation in ${\mathrm{H}}^{*}\mathrm{}\left(2s\right)+\mathrm{H}$, for collision energies $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}\gtrsim 200$ eV. At lower energies no explanation of the structures and magnitude of the experimental neutralization cross section is found.

We have formulated a generalized method for the evaluation of the cross sections for $1s$-$\mathrm{np}$ excitation of hydrogenlike ions by electron impact both in Coulomb-Born and Coulomb-Born-Oppenheimer (CBO) approximations. In this formulation we have replaced the associated Laguerre polynomial for the final-state wave function by an integral representation. The main advantage of our method is that the higher-order parametric differentiations usually adopted in order to obtain the amplitudes for the higher values of the principal quantum number $n$ are avoided by one-dimensional integration. To our knowledge, this is the first attempt to calculate the electron-ion excitation cross section in the CBO approximation for an arbitrary $p$ state without any recourse to partial-wave analysis. We have also calculated asymptotic scaled cross sections for the limit $n\to \infty$ at different energies. The direct-excitation results are in good agreement with the existing theoretical findings of Tully for different $n$ values in the intermediate- and high-energy regions.

Density-matrix equations of motion derived from Heisenberg picture source-field quantum electrodynamics contain damping constants and frequency shifts which are not associated with a single radiative transition but which instead couple two separate transitions together. In the absence of degeneracies in the atomic levels, these coupling terms are normally neglected when the rotating-wave approximation is invoked. These terms cannot be neglected when there are degeneracies or near degeneracies. In this paper, we interpret the generalized frequency shifts, show how they can be renormalized and included in shifts of atomic energy levels and altered damping constants, and discuss their experimental significance.

The triplet $4d$ states of ${\mathrm{H}}_2$ have been studied by using a tunable single-mode dye laser to excite metastable molecules in the $2p{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ state to the $4s$ and $4d$ triplet states. Ninety-three transitions were detected and their line positions measured. Some of these states decay primarily by predissociation. A simple model for the energies of the Rydberg states was developed; the model depends upon the polarizability and quadrupole interactions of the Rydberg electron with the ${\mathrm{H}}_2^{+}$ core. It provides a remarkably good description of the measured energy intervals.

Two-step laser-induced-fluorescence techniques are used to investigate $n$-changing collisional processes $\mathrm{Li}\mathrm{}(n=9\mathrm{})+\mathrm{Li}\left(2\mathrm{}{}_{}{}^2{}_{}{}^{}S\right)\to \mathrm{Li}\left(n^{\prime }\ne n\right) +\mathrm{Li}\left(2\mathrm{}{}_{}{}^2{}_{}{}^{}S\right)+\Delta E_{\mathrm{nn}}^{}{}_{}{}^{\prime }$ in a temperature-controlled lithium heat-pipe oven. Numerical identification of the resonance- and collision-induced fluorescences with the hydrogenic rate equations describing the time variation of the $n=7,8,9,10,11\mathrm{}$ populations allows the determination of collisional transfer and quenching rate coefficients. $n$-changing collisions with $\Delta n=|n-n^{\prime }|=1\mathrm{}$ predominate, and the quenching rate coefficients are found nearly independent of $n: k_n\sim 1.3\times {10}^{-9\mathrm{}}$ ${\mathrm{cm}}^3$${\mathrm{s}}^{-1\mathrm{}}$.

We report the study of a sharp perturbation of the $\mathrm{Ba}6sng{}_{}{}^1{}_{}{}^{}G_4^{}{}_{}{}^{}$ series at $n=24\mathrm{}$ by a $5d7d$ level converging to the excited ${\mathrm{Ba}}^{+}5d$ limit. We compare the traditional spectroscopic approach of determining the strength of the configuration interaction by energy-level perturbations to the values obtained by forced autoionization in an electric field. While the energy of the perturbing $5d7d$ level can be determined accurately by either approach we find a significant difference in the apparent strengths of the configuration interaction.

Bound-free transitions of ${\mathrm{Cs}}_2^{+}$ are studied in a fast-ion-beam photofragment spectrometer. Molecular cesium ions are produced by field ionization on a liquid cesium droplet and extracted as an ion beam. Their photodissociation is observed by monitoring the appearance and energy distribution of the charged photofragments ${\mathrm{Cs}}^{+}$. In the wavelength range between 4067 and 9500 Å, three photodissociation channels are identified of the type $\mathrm{Cs}_2^{}{}_{}{}^{+}\left(X{}_{}{}^2{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}\right)+h\nu \to \mathrm{Cs}_2^{}{}_{}{}^{+*}\to {\mathrm{Cs}}^{+}\left({}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\right)+\mathrm{Cs}\mathrm{}\left(\mathrm{nl}\right)+E_{\mathrm{kin}}$. At the longest wavelengths studied, photodissociation produces ground-state atoms $\mathrm{Cs}6s$. In the range between 5309 and 4545 Å, excited-state atoms $\mathrm{Cs}6p$ are produced. Beginning at 4579 Å, photodissociation leads to formation of both $\mathrm{Cs}6p$ and $\mathrm{Cs}5d$. The $\mathrm{Cs}5d$ channel dominates at wavelengths around 4100 Å. The angular distribution of photofragments is investigated to help identify the excited molecular states involved in the photodissociation processes. An approximate relative cross section for photodissociation of ${\mathrm{Cs}}_2^{+}$ over this wavelength range is obtained. At 7992.2 Å the absolute cross section for photodissociation of ${\mathrm{Cs}}_2^{+}$ is measured to be 2×${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$. Our measurements establish, for the first time, a lower limit for the bond energy of $\mathrm{Cs}_2^{}{}_{}{}^{+}\left(X{}_{}{}^2{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}\right)$ of 0.59±0.06 eV. This places an upper limit of 3.76±0.06 eV for the ionization potential of ${\mathrm{Cs}}_2\left(X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}\right)$.

Up to quadruply charged ions are induced in Xe atoms by a 50-psec laser pulse at 0.53 μm in the ${10}^{12}$ W ${\mathrm{cm}}^{-2\mathrm{}}$ range. The mechanism of the formation of ${\mathrm{Xe}}^{2+}$ ions is elucidated. In the lowest intensity range, ${\mathrm{Xe}}^{2+}$ ions are produced by direct 15-photon absorption from the ground state of the atoms, while at a higher intensity ${\mathrm{Xe}}^{2+}$ ions are produced by a stepwise process via ${\mathrm{Xe}}^{+}$ ions. These two processes take place at distinctly different intensities. A kinetic model using rate equations affords a good fit with experimental results. Moreover, for the first time it was possible to obtain the multiphoton ionization cross sections related to the two-electron removal from Xe atoms, as well as the one-electron removal from ${\mathrm{Xe}}^{+}$ ions.