Electron collisional data are required for population kinetics modeling and spectral predictions of highly ionized ions in high-temperature plasmas. Nickel-like ions are especially interesting for their potential use in soft-x-ray laser schemes pumped by electron collisional excitation and recombination. For highly stripped ions of moderate to high Z, relativistic effects begin to play a role in the atomic-physics calculations. We have used a relativistic multiconfigurational distorted-wave model for the calculation of electron excitation cross sections and rate coefficients between the 3$s^2$3$p^6$3$d^{10}$ Ni-like Gd ground state and the singly excited states with an N-shell electron.

Collisional transfers induced in the n=6–13 Li Rydberg states by ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, and CO molecules have been experimentally studied in a heat-pipe oven. The l-mixing cross sections have been deduced from the fast component of the population relaxations following pulsed laser excitation. The order of magnitude of these cross sections (${10}^3$ A${̊}^2$) is well predicted by the existing theories. For large n, the cross sections stay approximately constant. This can be partly explained by the influence of inelastic processes such as n changing. In the particular case of ${\mathrm{H}}_2$, n-changing collisions have been identified by the fluorescence starting from the n’=n±1, n-2 levels. Cross sections of the order of 10 A${̊}^2$ have been measured. The systematic study of the n-changing cross sections as a function of the transferred energy shows some evidence of resonance phenomena corresponding to an energy exchange between the Rydberg electron and the molecular rotation. This effect is also observed when ${\mathrm{H}}_2$ is replaced by ${\mathrm{D}}_2$. These resonances are well described by the theory of Petitjean and Gounand based on the e-quadrupolar interaction.

Bethe’s expressions for the stopping cross section and the straggling parameter of a penetrating point charge have been evaluated for a spherical harmonic oscillator as a target. The results, which are rigorous except for the neglect of relativistic corrections and higher-order Born terms, are given in tabulated form as well as in the form of asymptotic shell-correction expansions to arbitrary order. Existing general expressions for the stopping cross section and straggling are confirmed as far as they go. The range of validity of various model theories of atomic stopping is tested. At velocities down to about the stopping maximum, the agreement is very good for the kinetic theory, while a Fermi gas with a properly chosen electron density yields a significantly different stopping maximum. The binary encounter theory underestimates the stopping power at all speeds. The dielectric or local-density approach does not reproduce the correct scaling behavior. None of the model theories reproduces the threshold behavior. For light projectiles, i.e., positrons and electrons, a Franck-Hertz-type structure is observed in the velocity dependence of the stopping cross section which is particularly pronounced near threshold. An equipartition rule is derived for contributions to the stopping cross section from low excitations, i.e., distant collisions, and close encounters. A straight extension of Bohr’s oscillator model of atomic stopping is proposed which is shown to reproduce leading shell corrections in both stopping power and straggling and which, when applied to hydrogen, accurately describes the stopping power at velocities around and above the stopping maximum.

In order to understand some of the systematic effects associated with conventional Mott-scattering electron polarization measurements, we analyzed asymmetry data obtained with 94-keV polarized electrons scattered at 120° from gold-foil targets ranging in thickness from 27 to 62 μg/${\mathrm{cm}}^2$. Based upon an examination of the influence of multiple and plural scattering, we conclude that the precision of such Mott measurements is fundamentally limited by an experimental uncertainty of greater than ±2.5% and an absolute uncertainty of approximately ±5%, considerably worse than is customarily assumed. We believe that similar conclusions can be drawn for measurements made with ‘‘compact’’ cylindrical and spherical Mott polarimeters.

Electron collisional excitation of the low-lying 1$s^2$2$s^2$2$p^5$ and 1$s^2$2s2$p^6$ states of F-like selenium to the singly excited M-shell states is studied using a relativistic distorted-wave model and multiconfigurational relativistic Hartree-Fock bound states. Results are presented for all 2-3 transitions from the low-lying 2$s^2$2$p^5$ ${}_{}{}^2{}_{}{}^{}\mathrm{P}_{3/2}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}\mathrm{P}_{1/2}^{}{}_{}{}^{}$ levels, and also the 2s2$p^6$ ${}_{}{}^2{}_{}{}^{}\mathrm{S}_{1/2}^{}{}_{}{}^{}$ level. We find a number of strong dipole-allowed 2p-3d cross sections with peak values near threshold in excess of ${10}^{\mathrm{-}20}$ ${\mathrm{cm}}^2$, and derive Gaunt factors which are in good agreement with values used in the literature (0.15–0.20) for most strong transitions.

Very strong monopole 2p-3p excitation cross sections have been important in soft-x-ray laser theory, and are found to be as strong as the largest dipole-allowed cross sections for F-like selenium. Theoretical output powers for the strong lines of the 2p-3s, 2p-3d, and 2s-3p transition arrays are computed and presented for plasma conditions of $N_e$=3×${10}^{20}$ ${\mathrm{cm}}^{\mathrm{-}3}$ and $T_e$=1.0 keV. These results are compared in detail for proportionality against gf values for each array separately, as a test of how well line intensities might be judged from gf values in the absence of detailed theoretical intensity results. We find that for the 2p-3s and 2p-3d arrays, the intensities are in fair agreement with gf values within the array, while the agreement is much poorer in the case of the 2s-3p array. The two weaker arrays 2p-3s and 2s-3p are found to radiate more per unit gf than the 2p-3d transition array, in agreement with earlier observations in the Ne-like sequence. Theoretical line positions are tabulated for all strong 2-3 lines, and found to be in good agreement with experimental results for most strong transitions. Gains on the 3-3 transitions in between 2 and 4 ${\mathrm{cm}}^{\mathrm{-}1}$ are predicted for four lines under the plasma conditions quoted. Such conditions are similar to those of the recent extreme-uv laser experiments at the Lawrence Livermore National Laboratory, yet no F-like 3-3 amplification has yet been observed for F-like transitions. The discrepancy is currently a mystery.

Threshold phase shifts (or equivalently, quantum defects at the series limit) are calculated within the framework of the Hartree-Slater (central-field) approximation for positive atomic ions with nuclear charge number Z≤37. The results are displayed in isoelectronic (the number of electrons, N, constant), isonuclear (Z constant), and isoionic (Z-N constant) pictures. The systematics of the threshold phase shifts are delineated, and the utility of each of the pictures is discussed. The possibilities and pitfalls of interpolation to generate new data are also discussed. This paper represents the initial report of a systematic investigation of ionic properties.

We report ab initio calculations for the electron-${\mathrm{CH}}_4$ elastic scattering around the Ramsauer-Townsend (RT) minimum region (0.1–1.0 eV). A model potential approach, in the fixed-nuclei and one-center-expansion formalism, is employed in which the total optical potential is composed of three interaction terms: an accurate static potential of the Hartree-Fock level, an exchange interaction in the Hara free-electron-gas-exchange approximation (plus the orthogonalization), and a semiempirical polarization of the form &) ${}_{}{}^6{}_{}{}^{}$, where $r_c$ is an adjustable parameter. The final results on the total and momentum-transfer cross sections compare reasonably well with experimental data. In particular, a shallow RT structure rather than a pronounced dip in the total cross section is reproduced, which is in good agreement with recent measurements. We also determine the scattering length to be a=-3.4 a.u. by extrapolating our very-low-energy eigenphases (E≃0.001 eV) to the limit of zero energy: From a simple s-wave analysis, this value gives the RT minimum position around 0.4 eV, which is in close agreement with the correct value.

Geometrical relationships illustrate the significance of the transformation between new and orbital quantum numbers. The semiclassical analysis of 6j coefficients by Ponzano and Regge clarifies the geometrical relationships and identifies a classically forbidden range, which can be singled out for its small contribution to the summation over the partial waves relevant to observable parameters (differential cross section and orientation).

The total cross section for electrons scattered by ground-state hydrogen atoms has been calculated for incident energies from 12 to 54 eV. The calculations are based primarily on an 11-state expansion including seven pseudostates. The cross section for all inelastic processes is also reported.

Two apparently distinct instances of quantum-mechanical scattering where the prevailing long-range potential permits application of the Jacobi-matrix method are unified by identifying the underlying SO(2,1) Lie algebra. The resulting three-term recursion is solved in its own right without any reference to the coordinate representation of the scattering wave function but in a manner which brings out the similarity between differential and difference equations. The normalized regular solution of the recursion is obtained, its asymptotic form is analyzed, and it is found to vary sinusoidally. The irregular solution is defined to have the same amplitude as the regular solution in the asymptotic limit and to lead it in phase by π/2. It is argued that this method is particularly suitable for computing the scattering wave function of the hydrogen atom in a magnetic field.

While the exact amplitude for scattering in the presence of an external electromagnetic field is invariant under a change of gauge, the invariance property will not necessarily be preserved in approximations, and this may lead to inaccuracies and ambiguities in the results of numerical calculations. A method for removing this undesirable feature through a reformulation of the scattering problem is proposed here. The equations which determine the time evolution of the system are rewritten in a form which involves not the (gauge-dependent) vector and scalar potentials associated with the external field but rather effective potentials which are gauge independent; this allows for the introduction of gauge-invariant approximations in a systematic way. To focus on the essential features the method is described in the context of the relatively simple problem of nonrelativistic potential scattering but greater generality is possible. As an illustration of the method the problem of scattering in a slowly varying external field is considered and an approximation of the ‘‘low-frequency’’ type is obtained. The result, whose gauge invariance is verified explicitly, represents an improvement over earlier versions, having been obtained through a more accurate treatment of the interaction of the projectile with the external field in intermediate states of the scattering process.

For excitation to very high levels or ionization of a complex ion there are sometimes several possible final states for the remaining core (next higher stage of ionization in the case of ionization). Then formulas, such as the widely used ionization formula of Lotz or other ionization and excitation formulas in which the cross section is expressed essentially as a product of the number of electrons in the initial subshell times a cross section having the form of a hydrogenic ion cross section, must be multiplied by an additional factor giving the relative probability or branching ratio for the particular final state of the core. This problem was considered previously by Bely and Schwartz [Astron. Astrophys. 1, 281 (1969)] for the case of ionization. They used LS coupling, exchange was neglected and the remaining core was assumed to contain one or two partially filled subshells. Here we have included exchange and we have obtained the branching ratios for jj coupling as well as LS coupling for the general situation that any number of filled and partially filled subshells are present. The results apply for both collisional and radiative transitions.

We discuss two sets of conditions that are necessary and sufficient for a function defined on phase space to be a Wigner distribution function (WDF). The first set is well known and involves the function itself; the second set is less familiar and involves the function’s ‘‘symplectic’’ Fourier transform. After explaining why these two sets are equivalent, we explore some properties and applications of the second one. Among other things, we show that that set includes the position-momentum uncertainty relations as a special case, and in doing so we give a new derivation of them. This derivation itself serves as the starting point for the discussion of a quantum-mechanical moment problem. It also enables us to exhibit a real-valued phase-space function that obeys the uncertainty relations but that is not a WDF.

Measurements of the double-differential cross sections (DDCS) as a function of the ejected energy, angle, and primary energy for electron-impact ionization of helium are reported at incident energies of 200, 500, 1000, and 2000 eV. The ejection angle is varied from 30° to 150° in steps of 15°. The cross sections were obtained by use of a crossed-beam apparatus with an effusive gas source and a pulsed electron beam. Scattered and ejected electrons were energy analyzed by time-of-flight analysis from 2 eV to the primary energy as a function of the ejection angle. The relative measurements were normalized by matching the experimental elastic differential cross sections to absolute measurements at selected angles. Comparisons of the DDCS with available literature values revealed significant differences. At 2000 eV impact energy, first-Born-approximation calculations of the DDCS were found to be in agreement with the present data for ejected energies between 2 and 40 eV. At large angles and lower incident energies the Born calculation results are lower than the present DDCS. The DDCS were fitted with a Legendre-polynomial expansion as a function of ejection angle for fixed ejected and primary energies. The energy distributions of ejected electrons derived from these fits are presented and used to calculate the total ionization cross section.

The relative yields per carbon atom of continuum electrons captured by 0.6–2.5-MeV/u ${\mathrm{H}}^{+}$ and 0.5–0.8-MeV/u ${\mathrm{He}}^{2+}$ projectiles from gaseous hydrocarbon targets are observed to decrease with increasing numbers of carbon atoms and with decreasing projectile velocity. For isotachic ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{2+}$, the relative yields are the same. Assuming intramolecular electron-outscattering processes, additivity failure in electron capture to the continuum and its dependence of the projectile energy and molecular size can be reproduced by incorporating electron-scattering cross sections into a geometrical outscattering model.

In this work we report resonance parameters in electron-hydrogen scattering converging on the N=4, 5, and 6 hydrogenic thresholds. Results are calculated by a method of complex coordinate rotation. Hylleraas-type wave functions are used for L=0 and L=1 resonances, and products of Slater orbitals for states with L≥2. Both states with parities ${\left(\mathrm{-}1\right)}^L$ and ${\left(\mathrm{-}1\right)}^{L+1\mathrm{}}$ are calculated. All the intrashell resonances (both electrons occupying the same shell) below the respective thresholds are included in this work with approximate quantum numbers K and T assigned to each state. Results are used to construct ‘‘supermultiplet’’ structures of the doubly excited resonances of hydrogen negative ions.

Using an electron-beam–molecular-beam apparatus and employing the relative flow technique, ratios of the differential elastic scattering cross sections (DCS’s) of ${\mathrm{H}}_2$ to He were measured at incident electron energies of 15–100 eV and angular range of 10°–125°. From these ratios, the absolute elastic DCS’s for ${\mathrm{H}}_2$ were determined by normalization to accurate, available elastic DCS’s of He. Since pure rotational structure was not resolved in this work, the DCS’s reported are the sum of elastic and rotational excitations of ${\mathrm{H}}_2$ at room temperature. The reliability of the relative flow normalization to He was checked at each energy and angle by performing similar elastic DCS measurements on Ne (for which the cross sections are known). The resulting absolute Ne DCS’s were found to be in good agreement (within 10%) with the Ne elastic DCS’s measured previously [D. F. Register and S. Trajmar, Phys. Rev. A 29, 1785 (1984)]. From the DCS’s, integral and momentum-transfer cross sections were calculated. The present results are compared with other recent measurements.

Normalized differential and integral cross sections for electron-impact excitation of the dipole-allowed B ${\mathrm{}}^1$${\Sigma }_u^{+}$,C ${\mathrm{}}^1$${\Pi }_u$ and dipole-forbidden a ${\mathrm{}}^3$${\Sigma }_g^{+}$,c ${\mathrm{}}^3$${\Pi }_u$ states of molecular hydrogen have been determined by analysis of energy-loss spectra obtained with a crossed-beam apparatus at electron-impact energies of 20, 30, 40, and 60 eV and scattering angles ranging from 10° to 120°. Normalization of the data was achieved by utilizing the elastic differential cross sections measured previously by us (preceding article). The cross sections are compared with other available theoretical and experimental data.

We consider two quasimolecular states, one discrete and one quasistationary, whose dynamical coupling becomes possible only by absorption or emission of laser-field photons. In the presence of the laser field the initially discrete state also becomes quasistationary, with an energy continuum shifted with respect to the continuum into which the initially quasistationary state decays. For such an interacting system, the corresponding system of coupled equations is derived and then solved within the Landau-Zener and Demkov nonadiabatic-coupling models, with various assumptions about the time variation of decay widths. Closed-form expressions for the transition probabilities of the half and full collision are obtained. The considered general physical problem is related to electron-capture processes in slow ion–excited-atom (or atom–excited-ion) collisions in a laser field or to laser-assisted excitation-transfer processes in atom–excited-atom slow collisions.

High Rydberg states in neon ions are formed in interactions of 85-MeV ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}_{}^{6+}{}_{}{}^{}$ ions with a thin carbon-foil target and with a helium-gas target. The effect of a weak, transverse, static electric field on the Rydberg states is investigated by measuring the electron yield due to field ionization in the strong electric field of an electron spectrometer. For both targets, marked oscillatory structure is observed in the dependence of the electron yield on the strength of the weak field. The Fourier analysis of the data reveals the dominance of a narrow band of fundamental frequencies in the oscillations and indicates the presence of second-harmonic contributions. The oscillations are interpreted in terms of quantum interferences among Stark states coherently developing in the weak electric field. The relevance of experiments of the present type to the understanding of the mechanisms of Rydberg state formation is discussed.