A unitary (Fock-Tani) transformation of the second-quantized Hamiltonian breaks the interaction into its component parts, e.g., elastic scattering, inelastic scattering, rearrangement interaction, etc. The interaction for a particular process is ‘‘weaker’’ than the overall interaction; this is reflected in certain orthogonality corrections which appear in a perturbation expansion of the T-matrix element. As a result, the internuclear potential makes a negligible contribution of order $m_e$/$m_p$ to the first-order amplitude for charge transfer. We find very good agreement with experimental and the best available theoretical results for the total cross section for the reaction p+H(1s)→H(1s)+p for energies greater than 10 keV and for the differential cross section at 25, 60, and 125 keV in an angular range of ∼1 mrad about the forward direction.

The energy of any bound state of the hydrogen molecule ion ${\mathrm{H}}_2$${\mathrm{}}^{+}$ has an expansion in inverse powers of the internuclear distance R of the form Rayleigh-Schrödinger perturbation theory (RSPT) gives the coefficients $E^{\left(N\right)}$ but is otherwise unable to treat the exponentially small series, which in part are characteristic of the double-well aspect of ${\mathrm{H}}_2$${\mathrm{}}^{+}$. (Here n denotes the hydrogenic principal quantum number.) We develop a quasisemiclassical method for solving the Schrödinger equation that gives all the exponentially small subseries.

The RSPT series diverges: for the ground state $E^{\left(N\right)}$∼-(N+1)!/$e^2$ for large N. The $E^{\left(N\right)}$ asymptotics are governed via a dispersion relation by the imaginary $e^{\mathrm{-}2R/n}$ series, which itself is given by the square of the $e^{\mathrm{-}R/n}$ series times a ‘‘normalization integral.’’ That the expansion itself contains imaginary terms might seem inconsistent with the reality of the ${\mathrm{H}}_2$${\mathrm{}}^{+}$ eigenvalues. In fact, the RSPT series is Borel summable for R complex. The Borel sum has a cut on the real R axis, and its limit from above or below the positive R axis is complex. The imaginary $e^{\mathrm{-}2R/n}$ (and higher) series consist of just the counterterms to cancel the imaginary part of the Borel sum.

Extensive numerical examples are given. Of interest is a weak (down by a factor $N^{\mathrm{-}6}$) alternating-sign contribution to $E^{\left(N\right)}$, which is uncovered both theoretically and numerically. Also of interest is the identification of the Borel sum of the RSPT series with nonphysical boundary conditions. This too is illustrated both theoretically and numerically.

Dielectronic recombination via 3s-3p excitation has been measured for the Na-like ions ${\mathrm{P}}^{4+}$, ${\mathrm{S}}^{5+}$, and ${\mathrm{Cl}}^{6+}$. We observed the amount of electron capture attending the passage of MeV/amu ion beams through a collinear, magnetically confined space-charge-limited electron beam as a function of relative energy. The measured rates fall between limits calculated from limiting-case theoretically predicted cross sections.

We consider a general reaction process in which two entrance-channel particles, the beam and target particles, interact off-resonance and produce two exit-channel particles. In the c.m. frame we derive a general expression relating the probability density of the exit-channel particles to that of the entrance-channel particles. Furthermore, we show that whenever the coherence length, $w_B$, of the beam particle is much larger than the coherence length, $w_T$, of the target particle, the wave function of each exit-channel particle may be expressed explicitly in terms of the wave function of the beam particle. We also derive expressions for the coherence time and coherence length of each exit-channel particle. In addition, whenever the speed of the target particle is much less than the speed $v_i$ (i=1,2) of an exit-channel particle, we show that a simple relationship exists between the coherence length, $w_{\mathrm{ci}}$, of the exit-channel particle and the beam particle: $w_{\mathrm{ci}}$=$v_i$($w_B$/‖${\mathrm{v}}_B$${\mathrm{-}\mathrm{v}}_T$‖){1 ${\mathrm{-}\left[\right(\mathrm{v}}_{\mathrm{T}}$⋅e${\mathrm{^}}_3$)/ $v_i$](costheta’)}, where the velocity of the beam particle is ${\mathrm{v}}_B$ ${(\mathrm{v}}_B$=$v_B$e${^}_3$), and the velocity of the target particle is ${\mathrm{v}}_T$ ${(\mathrm{v}}_T$=$v_T$e${^}_3$). The angle theta’ is the spherical polar angular coordinate, measured with respect to the unit vector e${^}_3$, of the point at which the coherence length $w_{\mathrm{ci}}$ is to be determined. The above relationship is applied in the case of photoionization of the hydrogen atom at low energies to obtain realistic estimates for the coherence lengths of the ionized electron and proton. The coherence length of the electron is shown to be of nearly macroscopic dimensions.

Total depopulation cross sections of Rb(ns) and Rb(nd) levels by collisions with ${\mathrm{NH}}_3$ have been measured over a wide range of n values (24≤n≤49). The analysis of the n-dependent behavior of the cross sections reveals that ${\mathrm{NH}}_3$ inversion can produce a very efficient l-mixing process via a quasiresonant mechanism. This behavior appears qualitatively well described by theoretical calculations based on the impulse approximation (IA). A quantitative comparison between theory and experiment appears difficult, but it seems that the IA should provide reasonable estimates (within a factor of 4), though its use for large dipole moment (1.47 D for ${\mathrm{NH}}_3$) is questionable from a theoretical point of view.

The transfer of internal energy and angular momentum in the collision of a highly excited atom with the polar molecules HF and HCl has been examined with use of the classical Monte Carlo approach. The relative motion of the molecule and atomic nucleus is taken to be rectilinear; and the electron-molecule interaction is represented by a cut-off dipole form. Cross sections for transitions involving quantum numbers n, l, and m of the atom, and rotational quantum numbers j and $m_j$ of the molecule have been obtained for a range of collision energies and initial atomic and molecular states. Qualitative agreement is found with some, but not all, features of the experimental measurements. A significant finding of the calculation is the importance of multiple electron-molecule encounters during a single collision.

The problem of the relativistic scattering of a charged particle in an external electric field is considered and an approximation is derived which represents the transition amplitude in terms of the on-shell field-free scattering amplitude. The field is assumed to be a slowly varying function of time, falling to zero in the remote past and distant future. It is also assumed that the field is weak enough, and the collision time short enough, that the energy of the particle is not appreciably affected by the field during the collision; in practice this represents a mild restriction on the applicability of the method. The derivation, in many respects similar to earlier treatments of scattering in a low-frequency external plane-wave field, makes use of Schwinger’s proper-time representation of the external-field Green’s function. In addition to the field-free amplitude the approximation requires as input the modified plane waves describing the motion of the charged particle in the field before and after the collision; these asymptotic states are shown to be adequately represented in the WKB approximation.

Absolute total cross sections for electron detachment and charge transfer (including dissociative charge transfer) have been measured for collisions of ${\mathrm{Na}}^{\mathrm{-}}$ and ${\mathrm{K}}^{\mathrm{-}}$ with ${\mathrm{H}}_2$, ${\mathrm{D}}_2$, ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, CO, ${\mathrm{CO}}_2$, and ${\mathrm{CH}}_4$ targets. The collision energies of this investigation range from the energetic thresholds for detachment up to 300 eV (in the laboratory frame). In this energy range, electron detachment is observed to be the dominant process for all of the targets except ${\mathrm{O}}_2$. For several of these systems, a simple optical model can be used to reproduce the observed values of the cross sections for detachment. In the case of the ${\mathrm{CO}}_2$ target, some of the detached electrons appear to be due to charge transfer to metastable ${\mathrm{CO}}_2$${\mathrm{}}^{\mathrm{-}}$. Significant isotope effects are observed for the ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ targets.

The Keilson-Storer collision kernel has been used extensively to model how velocity-changing collisions affect spectral line shapes. None of the standard references use or refer to the eigenvectors or eigenvalues of the collision kernel. Here the eigenvectors and eigenvalues of the Keilson-Storer collision kernel are given for both one- and three-dimensional problems.

A particular least-squares method is presented for the calculation of inelastic scattering wave functions by an expansion technique. The variational procedure is based on a convenient error functional. The test-function space is spanned by a finite set of square-integrable (Hilbert-space) basis functions. The open-channel orbitals include the Kohn-Hulthén–type oscillatory terms of nonvanishing asymptotic amplitudes. The error functional involves only bound-bound and bound-free matrix elements. Criteria are given to select acceptable approximations. Two-channel calculations show that the zero-order results of this method have an accuracy comparable to the first-order results of earlier calculations. No anomalies are encountered.

Accurate, O(5%) measurements of total-atom differential coherent-scattering cross sections of Sn and Pb within the range of scattering angles 10?(de<ψ<60° have been performed using 279.2and Comparison, with the predictions of Kissel, Pratt, and Roy and the various form-factor formulations, reveals general agreement with the predictions of Kissel et al. A systematic departure from agreement is apparent, however, at the smallest angle of scattering. Critical examination of other recent measured data also indicates a trend towards poorer agreement at smaller angles.

A formalism is developed for studying electron-capture processes in ion-atom collisions in the presence of intense radiation fields that are obtainable with lasers. The method is based on expansion of the total state in terms of the product of the atomic eigenstates and the photon states. It is applied to study the process of electron capture into the ground state of hydrogen in ${\mathrm{H}}^{+}$-He collisions in the presence of radiation of wavelength between 2000 and 6000 Å and intensity between ${10}^{12}$ and ${10}^{14}$ W/${\mathrm{cm}}^2$ for incident-ion energy varying between 5 and 20 keV.

Accurate measurements of the 1000-eV noncoplanar symmetric (e,2e) reaction on xenon are reported. Cross-section calculations are carried out with the use of both the plane-wave and distorted-wave impulse approximations. The distorted-wave impulse approximation accurately describes both the 5$p^{\mathrm{-}1}$ and 5$s^{\mathrm{-}1}$ angular correlations and their relative cross sections. It also describes accurately the 5$p_{3/2}^{\mathrm{-}1}$:5$p_{1/2}^{\mathrm{-}1}$ branching ratios if Dirac-Fock target wave functions are used. The branching ratios show the inadequacy of Hartree-Fock wave functions for xenon. The plane-wave impulse-approximation overestimates the 5$s^{\mathrm{-}1}$ cross section relative to the 5$p^{\mathrm{-}1}$ and underestimates the cross section at large angles. The 5$s^{\mathrm{-}1}$ spectroscopic factors are assigned up to a separation energy of 45 eV, and the distorted-wave impulse-approximation calculation verifies that all the 5$s^{\mathrm{-}1}$ strength has been found. The spectroscopic factors for the 5$s^{\mathrm{-}1}$ manifold are obtained at 1000 and 1200 eV at a number of angles and are found to be independent of incident energy and ion recoil momentum. The spectroscopic factor for the lowest 5$s^{\mathrm{-}1}$ transition at 23.4 eV is 0.37±0.01, whereas that for the ground-state 5$p^{\mathrm{-}1}$ transition is greater than or equal to 0.98.

We present a novel scheme to calculate directly the complex resonance poles in electron-atom or electron-molecule scattering. The method is based on the many-body Green’s-function formalism and the use of separable expansions of the self-energy part. It is shown that the poles are given by the complex zeros of certain determinants, which can be straightforwardly calculated using analytically determined matrix elements of the free-particle Green’s function. We introduce a projection procedure which (i) leads to a simple and unified description of shape resonances as quasiparticles and (ii) is essential for the numerical feasibility of the calculations. Exploratory calculations are performed for the ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ shape resonance in electron-${\mathrm{H}}_2$ scattering in the static-exchange approximation. This resonance represents a difficult problem owing to its large width at short and intermediate internuclear distances. The fundamental difficulties which arise when using basis-set representations of the potential in the calculation of complex resonance poles are discussed.

We have calculated approximate hyperspherical adiabatic ${\mathrm{HD}}^{+}$ potential curves. In contrast to the Born-Oppenheimer adiabatic potential curves, the hyperspherical ones exhibit the correct dissociation limits. The lowest-order vibrational spectrum that we obtain compares favorably with conventional higher-order calculations. The implications of our results for continuum states of ${\mathrm{HD}}^{+}$ and for ion-atom scattering in general are discussed. We show that translation factors are not needed in the hyperspherical formulation.

We have used the stabilization method to perform calculations on autoionizing states of the ${\mathrm{LiHe}}^{3+}$ system which are involved in ${\mathrm{Li}}^{3+}$+He collisions. The molecular energies and radial couplings are calculated with use of programs developed at our laboratory. For both short and large internuclear distances, the stabilization treatment is complemented by block-diagonalization techniques. Our calculations allow us to draw conclusions on the conditions under which these methods can be used to calculate energy positions and radial couplings for states that lie in an ionization continuum.

We present a systematic study of composite population kernels for ${}_{}{}^{174}{}_{}{}^{}\mathrm{Yb}$ collisions with He, Ar, and Xe buffer gases, using laser-saturation spectroscopy. ${}_{}{}^{174}{}_{}{}^{}\mathrm{Yb}$ is chosen as the active species because of the simple structure of its ${}_{}{}^1{}_{}{}^{}\mathrm{S}_0^{}{}_{}{}^{}$${\mathrm{-}}^3$${\mathrm{P}}_1$ resonance transition (λ=556 nm). Elastic collisions are modeled by means of a composite collision kernel, an expression of which is explicitly derived based on arguments of a hard-sphere potential and two-category collisions. The corresponding coupled population-rate equations are solved by iteration to obtain an expression for the saturated-absorption line shape. This expression is fit to the data to obtain information about the composite kernel, along with reasonable values for other parameters. The results confirm that a composite kernel is more general and realistic than a single-component kernel, and the generality in principle and the practical necessity of the former are discussed.

Si(LVV) Auger spectra have been obtained for gas-phase ${\mathrm{SiF}}_4$ molecules with use of tunable photon energies from monochromatized synchrotron radiation. In addition to the normal Auger spectrum excited by photon energies well above the Si 2p photoionization threshold, resonance Auger spectra were measured by exciting the Si 2p electrons to different empty molecular and Rydberg orbitals. Our normal Auger spectrum shows more detailed structure than those previously reported using electron-beam excitation, and verifies the double structure corresponding to the case where the two final-state holes are either in the same or different Si—F bonding orbitals. In the resonance Auger spectra, the peaks shift by 7.5±0.5, 4.6±1.0, or 2.7±1.0 eV to higher energies when the Si 2p electron is excited to the ${\sigma }^{\mathrm{*}}$[3s($a_1$)], 4s, and 3d orbitals, respectively.

This paper presents for the first time an explicit calculation of the partial dielectronic-recombination-rate coefficients via the 3l3l’ manifold for 17 neonlike ions ranging from argon to tungsten, using relativistic multiconfiguration wave functions to calculate both the Auger and radiative matrix elements. The effect of electron collisions on the dielectronic-recombination-rate coefficient is also examined at several densities of interest for modeling laboratory plasmas.

The cross section for three-photon ionization of ground-state krypton at λ=193 nm (ArF laser) has been determined. In these experiments, a microwave-absorption technique provided real-time detection of electrons along with measurements of the absolute electron density. Due to a two-photon resonance with the 6p${\left[\mathrm{}\right(3/2\left)\mathrm{}\right]}_2$ level, the photoelectron number density was observed to vary quadratically with ArF laser intensity for $I_{\mathrm{ArF}}$ beyond 50–100 MW ${\mathrm{cm}}^{\mathrm{-}2}$ and Kr pressures below 50 Torr.