We measured and calculated the energy dependence of the ${4p}^4{nd(}^2{S}_{1/2})$ $(n=4\mathrm{}–7)$ correlation satellites in Kr from 38.5 to 250 eV. Our high-resolution measurements used a photoelectron spectroscopy technique to determine the relative cross sections and angular distribution parameters β. We find that, as in the case of Xe, the absolute cross sections of these satellites lines follow very closely the shifted and scaled cross section of the $4s$ main line. However, in the case of β, we find that the ${nd(}^2{S}_{1/2})$ $\mathrm{}(n=4,5,6\mathrm{})\mathrm{}$ follow the β value of the $4s$ main line below 150 eV only, and that β of the ${7d(}^2{S}_{1/2})$ satellite does not. We find that the β of the ${nd(}^2{S}_{1/2})$ ($n=4,$ 5, and 6) satellites reach $\beta =2\mathrm{}$ below 150 eV, but this value drops significantly between photon energies of 200 and 250 eV. While the comparison of our measurements with our calculation is good overall, some effects are not reproduced by the calculation. Our results are compared with a previous measurement at 68.5 eV, and the agreement is fair. We also measured the $4s$ and $4p$ main line cross sections and angular distributions and these results are compared to previous measurements and calculations.

The $K{\alpha }_{1,2}$ and $K{\beta }_{1,3}$ emission spectra of the $3d$ transition metals Cr, Mn, Fe, Co, Ni, and Cu were measured, employing a single-crystal diffractometer optimized for minimal instrumental broadening. The high-accuracy diffractometer, and the interferometrically calibrated silicon crystal employed ensure absolute wavelengths in the metric scale to a sub-part-per-million accuracy. An accurate analytic representation of each line, obtained by a fit to a minimal set of Lorentzians, is presented. The absolute energies, linewidths, and indices of asymmetry, derived from the data, agree well with previous measurements. So do also the intensity ratios $K{\alpha }_2/K{\alpha }_1$ and $K{\beta }_{1,3}/K{\alpha }_{1,2},$ which are, however, slightly, but consistently, higher than previous values. Possible origins for the observed $Z$-dependent trends are discussed.

We studied the line shape of Rb $D_1$ and $D_2$ resonance lines in the presence of 1–10 amg of several gases: ${}^3$He, ${}^4$He, N${}_2$, and Xe. We found that the line cores are well described by the asymmetric line shape expected for a van der Waals interatomic potential. The width and shift of the lines is proportional to the density of the foreign gas with high degree of accuracy, while the asymmetry is independent of the density. The constants of proportionality for pressure broadening and shift were measured with much higher accuracy than in previous experiments. We also studied the density dependence of the oscillator strength of the transitions.

Darwin-Foldy nuclear-size corrections in electronic atoms and nuclear radii are discussed from the nuclear-physics perspective. The interpretation of precise isotope-shift measurements is formalism dependent, and care must be exercised in interpreting these results and those obtained from relativistic electron scattering from nuclei. We strongly advocate that the entire nuclear-charge operator be used in calculating nuclear-size corrections in atoms rather than relegating portions of it to the nonradiative recoil corrections. A preliminary examination of the intrinsic deuteron radius obtained from isotope-shift measurements suggests the presence of small meson-exchange currents (exotic binding contributions of relativistic order) in the nuclear charge operator, which contribute approximately $\frac{1}{2}$%.

The rates of Auger transitions of antiprotonic helium ${}^4$He${}^{+}\overline{p}$ and ${}^3$He${}^{+}\overline{p}$ are calculated by using a variational scattering method with an elaborate three-body trial function. The shift of the energy levels of these systems due to the coupling with the Auger-decay channels is also obtained from this calculation. Thus an improvement is made over the previously calculated nonrelativistic energies. Together with the relativistic corrections calculated elsewhere, the theoretical transition wavelength between the states $\mathrm{}(n,l)=(37,34)\mathrm{}$ and $\mathrm{}(38,33)\mathrm{}$ of ${}^4$He${}^{+}\overline{p}$, for example, is significantly improved to be 713.593 nm, which compares well with the experimental value 713.578$\pm$0.006 nm. The calculated Auger lifetime of the level (38,33) is 3.2 ps, as compared with the value 4.1$\pm$0.2 ps deduced from the measured line broadening. Auger rates are calculated also using Fermi’s golden-rule formula with a regular Coulomb function with no phase shift for the Auger electron. The results agree fairly well with the accurate variational results.

The equation of motion for the first-order density matrix (1DM) is constructed for interacting electrons moving under the influence of given external scalar and vector potentials. The 1DM is coupled there to the 2DM by means of the electron-electron interaction. This equation is then employed to obtain the differential virial equation for interacting electrons moving in a magnetic field of arbitrary strength. Suitable integration leads back to the virial theorem derived recently by Erhard and Gross. The exchange-correlation scalar potential of the current-density functional theory of Vignale and Rasolt is derived in two forms, in terms of 1DMs and 2DMs and their noninteracting-system counterparts, involving also (in a linear way) the vector potentials: external and exchange-correlation (xc) ones in the first form, and the xc one in the second form. An equation is obtained also for determining the corresponding xc vector potential in terms of the same DMs and the external vector potential. Approximate exchange-only scalar and vector potentials are proposed in terms of noninteracting 1DM. Finally the Hartree-Fock 1DM for atoms and molecules in magnetic fields is shown to satisfy the same equation of motion as the fully interacting 1DM.

We present convergent close-coupling (CCC) calculations and measurements of 26.5 eV electron-impact excitation of the ground state of helium. The present measurements extend the experimental information at this energy to include $3^{3}D$ excitation. The CCC theory is compared with all of the available $2^1{P,3\mathrm{}}^1{P,3\mathrm{}}^1{D,3\mathrm{}}^{3}D$ measurements, the agreement with which is very satisfactory and comparable to that at higher impact energies.

We have developed an experimental method for determining the initial density matrix of the foil-excited atoms. The excited hydrogen $\mathrm{}(n=2\mathrm{})\mathrm{}$ atoms pass through a region of a variable electric field ($-200\mathrm{k}\mathrm{V}/\mathrm{m}$ to $+200\mathrm{}\mathrm{k}\mathrm{V}/\mathrm{m}$), and the intensity of the Lyman-α line (121.6 nm) emitted in a free space downstream is observed. By using a vacuum ultraviolet polarizer, the dependence of the intensities of the polarized components on the electric field, including the field-dependent quantum beats, was measured and it was numerically fitted to a calculation. Thus all the initial density matrix elements were determined in a single measurement. It was found that, in the energy range 100–180 keV, just after the excitation, the electron cloud has higher density in the front side of the ion and the electron probability current is backwards.

We report measurements of absolute cross sections for single- and multiple-electron capture in slow collisions $(v\sim 0.1–0.2\mathrm{a}.\mathrm{u}.\mathrm{}).\mathrm{}$ Partial cross sections for simultaneous $r$-electron removal from the target and $p$- electron retainment by the projectile ${\sigma }_{q,q-p}^r$ are presented for the systems ${\mathrm{Xe}}^{q+}-B,$ $B=\mathrm{He},$ Ar, and Xe $(15\mathrm{}<~q<~43).$ The results are also described in terms of electron-retainment $\left({\sigma }_{q,q-p}\right),$ electron-removal $\left({\sigma }_q^r\right),$ and total-reaction $\left({\sigma }_q\right)$ cross sections. Further, we deduce experimental single-electron-capture cross sections ${\sigma }_{q-1,q-2}^1$ for ${\mathrm{Xe}}^{\left(q-1\right)+}-B$ collisions from measurements on the ${\mathrm{Xe}}^{q+}-B$ system. The data are compared with earlier and more recent scaling laws and the extended classical over-the-barrier model.

Effects of the fine structure of atomic oxygen on collisions of O with ${\mathrm{O}}^{+}$ have been investigated theoretically. The starting point of the analysis was a set of potential curves for ${\mathrm{O}}_2^{+}$ calculated in $\mathrm{LS}$ coupling. Potential curves and matrix elements were derived that include spin-orbit effects and properly dissociate to the three asymptotic limits ${\mathrm{O}}^{+}-\mathrm{O}{(}^3{P}_J)$ $\mathrm{}(J=2,1,0\mathrm{}).$ Quantum-mechanical, coupled-channel scattering calculations were performed to determine inelastic, charge-exchange and momentum-transfer (diffusion) cross sections in the energy range 0.002–1.9 eV. The results exhibit a strong dependence on the initial fine-structure level. For example, the momentum-transfer cross sections are typically about 50% larger for the initial level $J=2\mathrm{}$ than for $J=1\mathrm{}$ or 0. A weighted average of the present cross sections, appropriate for a statistical distribution of fine-structure levels, can be compared with previous results based on performing uncoupled, single-channel calculations. The comparison confirms the accuracy of the single-channel model as long as the collision energy is greater than about 0.03 eV. For lower energies, the single-channel model overestimates the cross sections. The problem arises because angular momentum coupling effects lead to considerable cancellation of the charge-quadrupole terms in the asymptotic interaction potentials. As the collision energy decreases, these terms become increasingly important.

The triple-differential cross sections for the ionization of $\mathrm{Kr}\mathrm{}\left(4p\right)\mathrm{}$ and $\mathrm{Xe}\mathrm{}\left(5p\right)\mathrm{}$ by a fast electron where the exiting electrons have energies of 20 eV and 1 keV have been measured and compared with distorted-wave Born calculations. Difficulties were encountered when trying to place the relative data on an absolute scale by extrapolation to the optical limit: an extensive study of this normalization process is presented and it is argued that it is not applicable to the heavier atoms considered here, but can be used effectively for helium targets.

Charge-transfer collisions between ${\mathrm{He}}^{+}$ ions at $v=0.1\mathrm{}\mathrm{a}.\mathrm{u}.\mathrm{}$ and excited states of Rb with $n_t=7\mathrm{}–14$ have been studied, using a laser-based method of analyzing the final-state distribution. A Doppler-tuned ${\mathrm{CO}}_2$ laser is used to selectively detect one particular final state $\mathrm{}(n,L)\mathrm{}$ and directly measure the fraction of the total charge transfer product contained in that one level. The fractional population shows clear resonant behavior as a function of target excitation level ${(n}_t).\mathrm{}$ Measurements were made for $n=10\mathrm{}$ levels of helium with $L=4,$ 5, and 7–9, and for the $9G$ level. The results are compared with predictions of classical trajectory Monte Carlo calculations.

High-resolution measurements of the x-ray resonant photoemission of CO near the C$1s\to {\pi }^{*}$ transition are presented. The branching ratios for the valence shell ionization close to the resonance show a strong dependence on the photon energy with a clear asymmetry around the resonance energy. It is shown that this energy dependence is due to the presence of the direct photoionization channel in addition to the resonant channel and that it can be theoretically described in the framework of resonant multichannel ionization by a Fano approach. From this general formulation two models, including or excluding the interference between the direct and resonant processes, are derived and numerically evaluated. The no-interference model can explain only the gross features of the measured branching ratios, while inclusion of interference terms in the model can reproduce, almost quantitatively, the experimental results and justifies the observed asymmetry of the branching ratios. It is also proved that the lifetime vibrational interference is absent in the cross section integrated over the photoelectron energy.

High-resolution $K\alpha$ x-ray spectra of Ca, Cr, and Fe induced by (0.7–1.5)-MeV protons and of Ti induced by (0.7–4)-MeV protons were measured by a flat crystal spectrometer. From the relative yields of the ${\mathrm{KL}}^1$ satellites, which are the result of multiple inner-shell ionization, the average $L$-shell ionization probabilities in near-central collisions were determined. The effects of the rearrangement of the inner-shell holes prior to the $K$ x-ray emission and the changes of the fluorescence yields due to the multiple ionization were taken into account in the evaluation of the ionization probabilities. The direct Coulomb ionization probabilities in the near-central collisions were determined from the relative yields of the ${\mathrm{KL}}^1$ satellites after subtracting the shake contribution. The values obtained were compared with semiclassical approximation calculations exploiting relativistic hydrogenic and Hartree-Fock wave functions. The importance of a realistic atomic description using Hartree-Fock wave functions was demonstrated.

Double-electron capture by ${\mathrm{Ar}}^{8+}$ from He is analyzed. Since the incident ion beam contains a metastable fraction of the order 5%, two distinctly behaving systems are considered: (1) ${\mathrm{Ar}}^{8+}{(2p}^6{)}^1{S}_0+{\mathrm{He}\to \mathrm{Ar}}^{6+}{(2p}^6{\mathrm{nln}}^{\prime }{l}^{\prime }{)}^{2S+1}{L}_J+{\mathrm{He}}^{2+}$ and (2) ${\mathrm{Ar}}^{8+}{(2p}^5{3s)}^3{P}_J+{\mathrm{He}\to \mathrm{Ar}}^{6+}{(2p}^5{3snln}^{\prime }{l}^{\prime }{)}^{2S+1}{L}_J$$+{\mathrm{He}}^{2+}.$ For process (1), the comparison of translational energy gain and Auger spectra, with an extensive set of calculated data, supports the conclusion of an asymmetric double-electron transfer peaking at ${\mathrm{Ar}}^{6+}{(2p}^{6}3d4f)$ with a Rydberg tail getting to ${(3\mathrm{lnl}}^{\prime })$ with $n\cong 20$ $\mathrm{}(l=1,2\mathrm{}).$ For process (2), the double capture points dominantly into triply excited states ${\mathrm{Ar}}^{6+}{(2p}^5{3s3l4l}^{\prime }{)}^{2S+1}{L}_J.$ These are above the second ionization limit of the ground state ${\mathrm{Ar}}^{6+}{(2p}^6{3s}^2{)}^1{S}_0.$ Their decay takes place via two successive Auger steps: the first ending in the intermediate levels, ${\mathrm{Ar}}^{7+}{(2p}^5{3l3l}^{\prime }{)}^{2,4}{L}_J.$ These, in turn, autoionize to the ${\mathrm{Ar}}^{8+}{(2p}^6{)}^1{S}_0$ continuum. Both are identified in the Auger spectrum. These observations raise the question of the meaning of the auto transfer to Rydberg states and of correlated double capture processes.

We have measured the radiative stabilization probabilities after double-electron-transfer processes in slow $\left(1.5q\mathrm{keV}\right)$ ${\mathrm{I}}^{q+}+\mathrm{CO}$ collisions in the charge-state regime $8<~q<~26$ by using the charge-selected-projectile–recoil-ion-coincidence method. It was found that the radiative stabilization probabilities $P_{\mathrm{rad}},$ defined as $P_{\mathrm{rad}}{=T}_{\mathrm{DC}}{/(T}_{\mathrm{DC}}{+A}_{\mathrm{DC}})$ ($T_{\mathrm{DC}}$ is true double capture, and $A_{\mathrm{DC}}$ autoionizing double capture), increases from about 1% at the lowest charge up to about 10% at the highest charge as the charge state of the projectile increases. A model is proposed which can explain such a feature, by incorporating a slight modification of the initial population of the transferred levels in the projectile predicted in the extended classical over-barrier model. Based upon the present model, theoretical radiative and autoionization decay rates have been calculated, using the Cowan code. Fairly good agreement between the measured and calculated results has been obtained.

Experimental relative cross sections for electron capture by singly charged ions $\left({\mathrm{Na}}^{+}\right)$ from coherent elliptic states of principal quantum number $n=25\mathrm{}$ are presented. An interval of reduced impact velocities from about 1–2 is covered. Absolute reaction cross sections could not be determined precisely, but the eccentricity of the coherent elliptic states and their orientation relative to the ion-impact velocity were varied to expose the dependence of the electron-capture process on the initial motion of the electron. The dependencies on eccentricity and orientation are generally strong and they vary sharply with impact velocity. Qualitatively, the observations agree fairly well with classical trajectory Monte Carlo (CTMC) calculations, as expected for the large quantum numbers involved, but significant deviations of a systematic nature do remain, showing that some aspects of the capture reactions studied are described poorly by classical physics as represented by the CTMC model.

This paper presents systematic calculations of the dielectronic recombination (DR) rate coefficient for all energy levels in the ground configuration of each $L$-shell argon ion, Li-like Ar${}^{15+}$ to Ne-like Ar${}^{8+}$. The DR rate coefficients from H-like Ar${}^{17+}$ and He-like Ar${}^{16+}$ are also calculated. The rate coefficients are calculated ab initio using the fully relativistic, parametric potential atomic structure code RELAC. Autoionization rates are computed in the distorted wave approximation using RELAC’s wave functions. Configuration interaction (CI) in the levels of the initial and recombined ion is taken into account; CI strongly affects the energies of levels close to the continuum and strongly enhances the rates of weak autoionizing transitions. The contributions to recombination from the promotion of an $n$=1 $(K$ shell) or an $n$=2 $(L$ shell) electron are calculated. Capture of a free electron into levels with principal quantum numbers as high as $n$=14 is allowed, and is extended to $n$=18 in the case of Li- and Be-like ions. The contribution to recombination through high angular momentum orbitals $(l<~6)$ is included in the calculations.

$S$-wave $e^{+}+{\mathrm{He}}^{+}$ scattering is calculated using the hyperspherical close-coupling method. The two resonances found at about $-$0.73 Ry and $-$0.39 Ry by Bhatia and Drachman [Phys. Rev. A 42, 5117 (1990)] and reproduced by Ho [Phys. Rev. A 53, 3165 (1996)] do not occur in the present results. An argument against these proposed resonances is presented on the basis of the adiabatic hyperspherical potentials. Instead of these resonances, we have found narrow Feshbach resonances just below the thresholds $(-$0.25 a.u. and $-$0.0625 a.u.) of the formation of $\mathrm{Ps}\mathrm{}(n=1\mathrm{})\mathrm{}$ and $\mathrm{Ps}\mathrm{}(n=2\mathrm{})\mathrm{}$ and an extremely narrow shape resonance just above the threshold $-$0.08 a.u. of He${}^{+}$$(n$=5). They would be hardly detected since (i) the resonance widths are of the order of ${10}^{-4}$–${10}^{-5}$ a.u. or less, (ii) the resonance is weak in the elastic cross section, (iii) the magnitudes of the inelastic and Ps-formation cross sections are small, and (iv) the smooth cross sections due to higher partial waves should still be added to the $S$-wave cross section.

The direct-product states of the dissociative recombination (DR) of ${\mathrm{N}}_2^{+}$ have been studied using time-of-flight spectroscopy. The DR reaction occurred in a glow discharge maintained by electrons from a hot cathode. In addition to products from the $X{}^2{\Sigma }_g^{+}$ ground state of the molecular ion, the DR products from the $A{}^2{\Pi }_u$ $v=1\mathrm{}$ short lived (13.9 μsec) excited state were observed. The experimental energy resolution was sufficient to separate the rotational energy levels built on the $v=1\mathrm{}$ vibrational level.