Search

Author(s): Bello, RY; Lucchese, RR; Rescigno, TN; McCurdy, CW | Abstract: We demonstrate a theoretical treatment of dissociative single ionization of the LiH molecule using two-color UV-UV pulse sequences that makes use of a highly correlated description of both the ionization continuum and target molecular ion and neutral states to which it is coupled. The present results emphasize how the details of the ionization process at various internuclear distances combine to form a lens through which such experiments image the dynamics of intermediate electronic states populated by the pump pulse. While ionization yields (dissociative and nondissociative) provide information about the amplitudes and phases that build up the molecular wave packet in the neutral states, molecular frame photoelectron angular distributions exhibit the changing character of those states, i.e., from ionic to covalent. In addition, the time-dependent mean kinetic energy of the wave packet on neutral states is clearly mapped onto the kinetic energy release of the atomic fragments produced by the probe ionization pulse.

We present an experimental and theoretical energy- and angle-resolved study on the photoionization dynamics of nonresonant one-color two-photon single-valence ionization of neutral ${\mathrm{N}}_{2}$ molecules. Using 9.3-eV photons produced via high-order harmonic generation and a three-dimensional momentum imaging spectrometer, we detect the photoelectrons and ions produced from one-color two-photon ionization in coincidence. Photoionization of ${\mathrm{N}}_{2}$ populates the $X$ $^{2}\mathrm{\ensuremath{\Sigma}}_{g}^{+}, A$ $^{2}\mathrm{\ensuremath{\Pi}}_{u}$, and $B$ $^{2}\mathrm{\ensuremath{\Sigma}}_{u}^{+}$ ionic states of ${\mathrm{N}}_{2}{}^{+}$, where the photoelectron angular distributions associated with the $X$ $^{2}\mathrm{\ensuremath{\Sigma}}_{g}^{+}$ and $A$ $^{2}\mathrm{\ensuremath{\Pi}}_{u}$ states both vary with changes in photoelectron kinetic energy of only a few hundred meV. We attribute the rapid evolution in the photoelectron angular distributions to the excitation and decay of dipole-forbidden autoionizing resonances that belong to series of different symmetries, all of which are members of the Hopfield series, and compete with the direct two-photon single ionization.

We investigate the two-photon double ionization of atomic magnesium induced by ultrashort pulses. Though the initial and final state symmetries are comparable to the same process in helium, in stark contrast the range of photon energies for which nonsequential ionization is the only open pathway is narrow (less than 1 eV) in magnesium. Thus several sequential ionization pathways feature heavily in these processes. Nonetheless, it is found that for pulse durations between 0.25 and 2.0 fs, the joint angular dependence of the ejected electrons can depend sensitively on pulse length, varying between the strictly back-to-back ejection characteristic of nonsequential ionization to other distributions. The significance of excited-state correlating configurations in representing the initial state of magnesium is discussed in the light of their consequences for the resulting angular distributions at photon energies where sequential ionization can access intermediate states that lie nearby in energy, particularly for longer pulses.

Author(s): Larsen, KA; Rescigno, TN; Severt, T; Streeter, ZL; Iskandar, W; Heck, S; Gatton, A; Champenois, EG; Strom, R; Jochim, B; Reedy, D; Call, D; Moshammer, R; Dorner, R; Landers, AL; Williams, JB; McCurdy, CW; Lucchese, RR; Ben-Itzhak, I; Slaughter, DS; Weber, T | Abstract: We report measurements on the H++H+ fragmentation channel following direct single-photon double ionization of neutral NH3 at 61.5 eV, where the two photoelectrons and two protons are measured in coincidence using three-dimensional (3D) momentum imaging. We identify four dication electronic states that contribute to H++H+ dissociation, based on our multireference configuration-interaction calculations of the dication potential energy surfaces. The extracted branching ratios between these four dication electronic states are presented. Of the four dication electronic states, three dissociate in a concerted process, while the fourth undergoes a sequential fragmentation mechanism. We find evidence that the neutral NH fragment or intermediate NH+ ion is markedly rovibrationally excited. We also identify differences in the relative emission angle between the two photoelectrons as a function of their energy sharing for the four different dication states, which bare some similarities to previous observations made on atomic targets.

Author(s): Marante, CA; Greenman, L; Trevisan, CS; Rescigno, TN; McCurdy, CW; Lucchese, RR | Abstract: The simple single-channel static-exchange approximation completely ignores correlation between the continuum and molecular ion electrons. In molecular systems with symmetry equivalent atoms, the single-channel approximation can seriously fail in core ionization when using delocalized orbitals to represent the core hole states. We present cross sections and molecular frame photoelectron angular distributions with both localized and delocalized core orbitals in CF4 F (1s) ionization. We show that only a full coupled-channel calculation can recover an accurate description of the physics of inner-shell photoionization when using delocalized orbitals, whereas nearly the same result can be obtained from independent single-channel static-exchange calculations when localized core orbitals are used. A grid-based variational method described here makes such single-channel calculations possible on larger systems without local-exchange approximations. Illustrative calculations on the core ionization of SF6 are presented to illustrate the power of the grid-based method.

A hybrid method that combines Gaussian basis functions typically used in bound-state molecular electronic structure calculations with a grid-based discrete-variable representation with finite elements suitable for a general electronic continuum representation is used to fully describe the double ionization of molecular ${\mathrm{H}}_{2}$ by a single photoabsorption. This work expands the hybrid method, previously applied to single-ionization events, to double photoionization. Constructing the full two-electron operator encoding the electron correlation necessary to doubly ionize the target via the action of a single photon requires all classes of mixed integrals between combinations of the different basis-function types. Comparison of the present results with benchmark theoretical calculations and experimental results shows excellent agreement for both molecular ${\mathrm{H}}_{2}$ and its united-atom limit, atomic helium; the triply differential cross sections that relate the angular distribution and energy sharing of all of the particles in the frame of the molecule are compared. The two-electron results computed using this hybrid basis hint at application of this general descriptive scheme beyond this simplest molecular target towards describing double ionization in more complicated and experimentally relevant molecules.

We present a theoretical study of $K$-shell photodetachment of ${\mathrm{C}}_{2}{}^{\ensuremath{-}}$ and ${\mathrm{C}}_{3}{}^{\ensuremath{-}}$ ions. The calculations were carried out using the complex Kohn variational method. Our study addresses the recent observation that what appears as a single, narrow shape resonance close to threshold in the $K$-shell photodetachment of ${\mathrm{C}}^{\ensuremath{-}}$ splits into several peaks in the longer ${\mathrm{C}}_{n}{}^{\ensuremath{-}}$ carbon anion chains, with the number of peaks increasing with increasing $n$ values. We argue that the number of expected peaks is related to the number of symmetry-equivalent carbon atoms.

We present state-selective measurements on the NH$_2^{+}$ + H$^{+}$ and NH$^{+}$ + H$^{+}$ + H dissociation channels following single-photon double ionization at 61.5 eV of neutral NH$_{3}$, where the two photoelectrons and two cations are measured in coincidence using 3-D momentum imaging. Three dication electronic states are identified to contribute to the NH$_2^{+}$ + H$^{+}$ dissociation channel, where the excitation in one of the three states undergoes intersystem crossing prior to dissociation, producing a cold NH$_2^+$ fragment. In contrast, the other two states directly dissociate, producing a ro-vibrationally excited NH$_2^+$ fragment with roughly 1 eV of internal energy. The NH$^{+}$ + H$^{+}$ + H channel is fed by direct dissociation from three intermediate dication states, one of which is shared with the NH$_2^{+}$ + H$^{+}$ channel. We find evidence of autoionization contributing to each of the double ionization channels. The distributions of the relative emission angle between the two photoelectrons, as well as the relative angle between the recoil axis of the molecular breakup and the polarization vector of the ionizing field, are also presented to provide insight on both the photoionization and photodissociation mechanisms for the different dication states., Comment: 18 pages, 21 figures, 3 tables

We report experimental results on three-dimensional momentum imaging measurements of anions generated via dissociative electron attachment to gaseous formamide. From the momentum images, we analyze the angular and kinetic energy distributions for NH$_2^{-}$, O$^{-}$, and H$^{-}$ fragments and discuss the possible electron attachment and dissociation mechanisms for multiple resonances for two ranges of incident electron energies, from 5.3~eV to 6.8~eV, and from 10.0~eV to 11.5~eV. {\it Ab initio} theoretical results for the angular distributions of the NH$_2^{-}$ anion for $\sim$6~eV incident electrons, when compared with the experimental results, strongly suggest that one of the two resonances producing this fragment is a $^2$A$''$ Feshbach resonance., Comment: 10 pages, 6 figures

We present a combined experimental and theoretical investigation of the electron dynamics and body-frame angular dependence of valence photo-single ionization of CF4 and subsequent dissociation into CF3+ and F. Ionization from a valence t2 orbital shows overlapping shape resonances close to threshold that couple to the same total symmetry, leading to striking changes in the photoelectron angular distributions when viewed in the body-frame.

Author(s): Bello, RY; Yip, FL; Rescigno, TN; Lucchese, RR; McCurdy, CW | Abstract: By decomposing the initial-state wave function into its unique natural orbital expansion, as defined in the 1950s by Lowdin and used in modern studies of entanglement, we analyze the role of electron correlation in the initial state of an atom or molecule in determining the angular distribution of one-photon double ionization. Final-state correlation of the two ejected electrons is treated completely in numerically accurate calculations as the initial states of He, H-, and H2 are built up from correlating configurations in strict order of decreasing natural orbital occupations. In the two-electron atoms it is found that the initial-state correlation plays a sometimes modest but generally measurable role. In striking contrast, for H2 a large number of correlating configurations in the ground state is often necessary to produce angular distributions even approximately resembling the correct ones. One-photon double photoionization of oriented H2 is found to be particularly sensitive to left-right correlation along the bond.

The connection between resonant metastable states and bound states with changing potential strength in the presence of a Coulomb potential is fundamentally different from the case of short-range potentials. This phenomenon is central to the physics of dissociative recombination of electrons with molecular cations. Here, it is verified computationally that there is no direct connection between the resonance pole of the S-matrix and any pole in the bound state spectrum. A detailed analysis is presented of the analytic structure of the scattering matrix, in which the resonance pole remains distinct in the complex k-plane while a new state appears in the bound state spectrum. A formulation of quantum-defect theory is developed based on the scattering matrix, which nonetheless exposes a close analytic relation between the resonant and bound state poles and thereby reveals the connection between quantum-defect theory and analytic S-matrix theory in the complex energy and momentum planes. One-channel and multichannel versions of the expressions with numerical examples for simple models are given, and the formalism is applied to give a unified picture of ab initio electronic structure and scattering calculations for e-O2+ and e-H2+ scattering.

We report recent results of mass-resolved anion fragment momentum imaging experiments to investigate dissociative electron attachment to formic acid, for incident energies between 5 eV and 9 eV. A remarkable site-selectivity is found for a resonance at 8.5 eV by comparing anion fragment yields for two deuterated isotopologues of formic acid. This results in an H− fragment from the O-H bond of the transient anion, with negligible contribution from C-H break. In contrast, a lower-energy resonance at 7.1 eV dissociates by C–H or O–H break to produce H− and the neutral radicals HOCO or HCOO.

Author(s): Streeter, ZL; Yip, FL; Lucchese, RR; Gervais, B; Rescigno, TN; McCurdy, CW | Abstract: The measurement of the triple differential cross section in the body frame for double photoionization of a molecule can be made in principle by detecting the ionic fragments and the two photoelectrons in coincidence - but only if the dynamics and geometry of dissociation of the doubly charged molecular ion are known. A classical trajectory study of the nine lowest states of the water dication is presented using high quality ab initio potential-energy surfaces. Sampling from a semiclassical initial distribution of positions and momenta is used to approximate ionization from the Frank-Condon region of the ground vibrational state of neutral H2O. Excellent agreement in comparison with preliminary experimental momentum imaging measurements of double photoionization of water show that eight dication states can be unambiguously identified in the experiment with the aid of theory. The theoretical trajectory results allow body frame measurements of double photoionization to yield all eight states even though the usual assumption of direct dissociation, the "axial recoil" approximation, breaks down for three of the dication electronic states seen in the experiment.

The electronic and nuclear dynamics in methanol, following 156~nm photoexcitation, are investigated by combining a detailed analysis of time-resolved photoelectron spectroscopy experiments with electronic structure calculations. The photoexcitation pump pulse is followed by a delayed 260~nm photoionization probe pulse, to produce photoelectrons that are analyzed by velocity map imaging. The yield of mass-resolved ions, measured with similar experimental conditions, are found to exhibit the same time-dependence as specific photoelectron spectral features. Energy-resolved signal onset and decay times are extracted from the measured photoelectron spectra to achieve high temporal resolution, beyond the 20~fs pump and probe pulse durations. When combined with {\it ab initio} calculations of selected cuts through the excited state potential energy surfaces, this information allows the dynamics of the transient excited molecule, which exhibits multiple nuclear and electronic degrees of freedom, to be tracked on its intrinsic few-femtosecond timescale. Within 15~fs of photoexcitation, we observe nuclear motion on the initially bound photoexcited 2$^{1}$A$''$ (S$_2$) electronic state, through a conical intersection with the 1$^{1}$A$'$ (S$_3$) state, which reveals paths to photodissociation following C--O stretch and C--O--H angle opening., 8 pages, 5 figures + Supporting Info

Author(s): Hvizdos, D; Vaňa, M; Houfek, K; Greene, CH; Rescigno, TN; McCurdy, CW; Curik, R | Abstract: We present a simple two-dimensional model of the indirect dissociative recombination process. The model has one electronic and one nuclear degree of freedom and it can be solved to high precision, without making any physically motivated approximations, by employing the exterior complex scaling method together with the finite-elements method and discrete variable representation. The approach is applied to solve a model for dissociative recombination of H2+ in the singlet ungerade channels, and the results serve as a benchmark to test validity of several physical approximations commonly used in the computational modeling of dissociative recombination for real molecular targets. The second, approximate, set of calculations employs a combination of multichannel quantum defect theory and frame transformation into a basis of Siegert pseudostates. The cross sections computed with the two methods are compared in detail for collision energies from 0 to 2 eV.

The dynamics of autoionizing Rydberg states of oxygen are studied using attosecond transient absorption technique, where extreme ultraviolet (XUV) initiates molecular polarization and near infrared (NIR) pulse perturbs its evolution. Transient absorption spectra show positive optical density (OD) change in the case of $ns\sigma_g$ and $nd\pi_g$ autoionizing states of oxygen and negative OD change for $nd\sigma_g$ states. Multiconfiguration time-dependent Hartree-Fock (MCTDHF) calculation are used to simulate the transient absorption spectra and their results agree with experimental observations. The time evolution of superexcited states is probed in electronically and vibrationally resolved fashion and we observe the dependence of decay lifetimes on effective quantum number of the Rydberg series. We model the effect of near-infrared (NIR) perturbation on molecular polarization and find that the laser induced phase shift model agrees with the experimental and MCTDHF results, while the laser induced attenuation model does not. We relate the electron state symmetry dependent sign of the OD change to the Fano parameters of the static absorption lineshapes., Comment: 15 pages, 8 figures

Citation: McCurdy, C. W., Rescigno, T. N., Trevisan, C. S., Lucchese, R. R., Gaire, B., Menssen, A., . . . Weber, T. (2017). Unambiguous observation of F-atom core-hole localization in CF4 through body-frame photoelectron angular distributions. Physical Review A, 95(1). doi:10.1103/PhysRevA.95.011401

The valence-shell double ionization of atomic magnesium is calculated using a grid-based representation of the $3{s}^{2}$ electron configuration in the presence of a fully occupied frozen-core configuration of the remaining ten electrons. Atomic orbitals are constructed from an underlying finite-element discrete variable representation that facilitates accurate representation of the interaction between the inner-shell electrons with those entering the continuum. Length and velocity gauge results are compared with recent theoretical calculations and experimental measurements for the total double-, single-, and triple-differential cross sections, particularly at the photon energy of 55.49 eV for the last one. Comparison between the similar processes of double ionization of the $n{s}^{2}$ atoms helium, beryllium, and magnesium further illuminates the role of valence-shell electron correlation in atomic targets with heliumlike electronic configurations and symmetry.

The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules. It uses a basis set of product sinc functions arrayed on a Cartesian grid, and yields 1 kcal/mol precision for valence transition energies with a grid resolution of approximately 0.1 bohr. The Coulomb matrix elements are replaced with matrix elements obtained from the kinetic energy operator. A resolution-of-the-identity approximation renders the primitive one- and two-electron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices. The calculation of contracted two-electron matrix elements among orbitals requires only O(N log(N)) multiplication operations, not O(N^4), where N is the number of basis functions; N = n^3 on cubic grids. The representation not only is numerically expedient, but also produces energies and properties superior to those calculated variationally. Absolute energies, absorption cross sections, transition energies, and ionization potentials are reported for one- (He^+, H_2^+ ), two- (H_2, He), ten- (CH_4) and 56-electron (C_8H_8) systems., Comment: Submitted to JCP

© 2016 American Physical Society. Ab initio theoretical studies and momentum-imaging experiments are combined to provide a consistent picture of the dynamics of dissociative electron attachment to ammonia through its 5.5- and 10.5-eV resonance channels. The present study clarifies the character and symmetry of the anion states involved and the dynamics that leads to the observed fragment-ion channels, their branching ratios, and angular distributions.

We investigate the photodouble ionization of H2 molecules with 400 eV photons. We find that the emitted electrons do not show any sign of two-center interference fringes in their angular emission distributions if considered separately. In contrast, the quasiparticle consisting of both electrons (i.e., the "dielectron") does. The work highlights the fact that nonlocal effects are embedded everywhere in nature where many-particle processes are involved, This work was funded by the Deutsche Forschungsgemeinschaft (DFG), the BMBF, the European COST Action Grant No. XLIC CM1204, the European Research Council Advanced XCHEM Grant No. 290853, and the MINECO Project Grant No. FIS2013-42002-R. J. L. thanks the DFG for support. We are grateful to the staff of PETRA III for excellent support during the beam time. Raw data are archived at the Goethe-University Frankfurt am Main and are available on request

Dissociating hydrogen gas seems like it should be as easy as pulling apart two identical atoms. But resonant electron-impact experiments reveal that quantum interference induces a fundamental asymmetry in the process.

A review is given of recent theoretical studies of partial-channel photoionization cross sections in diatomic and polyatomic molecules. Results obtained from separated-channel static-exchange calculations and Stieltjes-Tchebycheff moment-theory techniques are compared with recent photoabsorption, electron-impact excitation, fluorescence production, photoelectron spectroscopy, and dipole (e, 2e) measurements. Various structures in the calculated and measured cross sections as functions of incident photon energy are attributed to final-state wavefunctions of either atomiclike or molecularlike composition. Specifically, σ-orbital cross sections in light diatomic and polyatomic molecules are found to be generally dominated by strong σ → σ^* photoionization resonances of molecularlike origin, whereas π-orbital cross sections in such molecules exhibit strong distinctly 2p → kd atomiclike features. These aspects of molecular photoionization are illustrated with the results of detailed theoretical and experimental studies of partial-channel cross sections in CO, CO_2, and H_2CO.

Although valence electrons are clearly delocalized in molecular bonding frameworks, chemists and physicists have long debated the question of whether the core vacancy created in a homonuclear diatomic molecule by absorption of a single x-ray photon is localized on one atom or delocalized over both. We have been able to clarify this question with an experiment that uses Auger electron angular emission patterns from molecular nitrogen after inner-shell ionization as an ultrafast probe of hole localization. The experiment, along with the accompanying theory, shows that observation of symmetry breaking (localization) or preservation (delocalization) depends on how the quantum entangled Bell state created by Auger decay is detected by the measurement.

Exterior complex scaling provides a practical path forfirst-principles studies of atomic and molecular ionizationproblemssince it avoids explicit enforcement of asymptotic boundary conditionsfor 3-body Coulomb breakup. We have used the method of exterior complexscaling, implemented with both the discrete variable representation andB-splines, to obtain the first-order wave function for molecular hydrogencorresponding to a single photon having been absorbed by a correlatedinitial state. These wave functions are used to construct convergedtriple differential cross sections for double photoionization of alignedH2 molecules.

We investigate the two-photon double ionization of beryllium atom induced by ultrashort pulses. We use a time-dependent formalism to evaluate the ionization amplitudes and generalized cross sections for the ejection of the 2s2 valence shell electrons in the presence of a fully occupied 1s2 frozen core shell. The relative contributions of the two-photon direct and sequential process are systematically explored by varying both pulse duration and central frequency. The energy and angular differential ionization yields reveal the signatures of both mechanisms, as well as the role of electron correlation in both the single and double ionization continua. In contrast with previous results on the helium atom, the presence of an electronic core strongly affects the final state leading to back-to-back electron emission even in the a priori less correlated two-photon sequential mechanism. In particular, a dominant pathway via excitation ionization through the Be+(2p) determines the profiles and pulse-duration dependencies of the energy and angle differential yields, This material contains work performed at Lawrence Berkeley National Laboratory supported by the US Department of Energy Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences Contract DE-AC02-05CH11231, and work at the University of California Davis supported by US Department of Energy Grant No. DESC0007182. Work at Cal Maritime is supported by the National Science Foundation, Grant No. PHY-1509971. Work at the Autónoma de Madrid was supported by the Advanced Grant of the European Research Council XCHEM 290853, the European grants MC-ITN CORINF and MC-RG ATTOTREND FP7-PEOPLE-268284, the European COST Action XLIC CM1204, the MINECO Project No. FIS2013-42002-R and the ERA-Chemistry Project PIM2010EEC-00751. We acknowledge computer time at the Centro de Computación Científica CCC-UAM and MareNostrum from Barcelona Supercomputing Center

We present a combined experimental and theoretical investigation of the dynamics and angular dependence of dissociative electron attachment to methane. We show that a triply degenerate (T2) Feshbach resonance is responsible for the broad 10 eV dissociation peak in methane. This resonance alone is shown to correlate asymptotically to the various dissociation channels observed experimentally. The molecular-frame entrance amplitude for electron attachment is calculated for each component of the threefold degenerate resonance. By investigating the topology of the anion potential energy surfaces, we deduce the main pathways to two- and three-body breakup channels involving both bond scission and bond formation. The computed fragment angular distributions reproduce the main trends of the experimental measurements.

Asymmetry in the molecular-frame photoelectron angular distributions from core-hole- or core-valence-excited polyatomic targets with symmetry-equivalent atoms can provide direct evidence for core-hole localization. Using acetylene as an example, we contrast the small asymmetry that can be seen in direct core-level ionization, due to the competition between two competing pathways to the continuum, with ionization from core-valence-excited HCCH, which offers the prospect of observing markedly greater asymmetry.

We consider the effect of substituting atomic ligands $X$ with different electronic properties in the carbon-$K$-shell photoionization of the linear $X\mathrm{CC}X$ molecules. We study the cases of lithium, hydrogen, and fluorine as ligands bonded to the carbon atoms. The molecular frame photoelectron angular distributions are computed using the variational complex Kohn technique. The electronic properties of the ligands have direct observable effects on the angular distribution of the emitted carbon core-hole photoelectron. These effects have already been observed experimentally using the cold target recoil ion momentum spectroscopy technique. We propose a simple classical explanation based on the intramolecular electrostatic potential to qualitatively explain the preferred directions of electron emission.

A combined basis of analytic Gaussian functions and grid-based finite element-discrete variable representation spherical harmonic expansion is specialized for the description of continuum electron dynamics in the presence of electrons held fixed in core molecular orbitals. The applicability of this hybrid representation designed for general problems involving accurate determination of molecular continua wave functions is illustrated for photoionization of second-row diatomic molecules. Accurate descriptions of such electron continuum dynamics are a necessary step towards analyzing correlated double continua photoejections. Examination of this hybrid method in comparison to a more computationally expensive pure grid-based single-center expansion reveals several key advantages that by design make it attractive for describing processes involving one or more electrons moved to the continuum.

Electron-impact ionization of the hydrogen atom is the prototypical three-body Coulomb breakup problem in quantum mechanics. The combination of subtle correlation effects and the difficult boundary conditions required to describe two electrons in the continuum have made this one of the outstanding challenges of atomic physics. A complete solution of this problem in the form of a 'reduction to computation' of all aspects of the physics is given by the application of exterior complex scaling, a modern variant of the mathematical tool of analytic continuation of the electronic coordinates into the complex plane that was used historically to establish the formal analytic properties of the scattering matrix. This review first discusses the essential difficulties of the three-body Coulomb breakup problem in quantum mechanics. It then describes the formal basis of exterior complex scaling of electronic coordinates as well as the details of its numerical implementation using a variety of methods including finite difference, finite elements, discrete variable representations and B-splines. Given these numerical implementations of exterior complex scaling, the scattering wavefunction can be generated with arbitrary accuracy on any finite volume in the space of electronic coordinates, but there remains the fundamental problem of extracting the breakup amplitudes from it. Methods are described for evaluating these amplitudes. The question of the volume-dependent overall phase that appears in the formal theory of ionization is resolved. A summary is presented of accurate results that have been obtained for the case of electron-impact ionization of hydrogen as well as a discussion of applications to the double photoionization of helium.

We present experimental results for dissociative electron attachment to acetylene near the 3 eV ${}^{2}{\ensuremath{\Pi}}_{g}$ resonance. In particular, we use an ion-momentum imaging technique to investigate the dissociation channel leading to ${\mathrm{C}}_{2}{\mathrm{H}}^{\ensuremath{-}}$ fragments. From our measured ion-momentum results we extract fragment kinetic energy and angular distributions. We directly observe a significant dissociation bending dynamic associated with the formation of the transitory negative ion. In modeling this bending dynamic with ab initio electronic structure and fixed-nuclei scattering calculations we obtain good agreement with the experiment.

Triply differential cross sections for electron-impact ionization of the $1{t}_{2}$ and $2{a}_{1}$ orbitals of methane are calculated using the complex Kohn variational method. The calculations are carried out for scattered electron energies of 500 eV and coplanar asymmetric kinematics far from the Bethe ridge, where previous experiment and theory are available for comparison. The present results are in reasonably good agreement with experiment for $1{t}_{2}$ ionization and in excellent agreement for $2{a}_{1}$ ionization, in contrast with previous theory.

The complex Kohn variational method, which has been extensively applied to low-energy molecule scattering, is extended to treat molecular ionization by fast electrons under the assumption that the incident and scattered electrons can be described by plane waves. The formulation reduces to the computation of the continuum generalized oscillation strength, which amounts to a generalization of the molecular photoionization problem to which the Kohn method has been successfully applied. To illustrate the approach, we present fully differential cross sections for the case of water, where good experimental data is available for comparison.

Since the invention of quantum mechanics, even the simplest example of the collisional breakup of a system of charged particles, e − + H → H + + e − + e − (where e − is an electron and H is hydrogen), has resisted solution and is now one of the last unsolved fundamental problems in atomic physics. A complete solution requires calculation of the energies and directions for a final state in which all three particles are moving away from each other. Even with supercomputers, the correct mathematical description of this state has proved difficult to apply. A framework for solving ionization problems in many areas of chemistry and physics is finally provided by a mathematical transformation of the Schrödinger equation that makes the final state tractable, providing the key to a numerical solution of this problem that reveals its full dynamics.

We analyze the consequences of discretizing one of the two continua in three-body breakup to reduce it to a two-body close-coupling problem. We identify the origin of oscillations in the singly differential cross section in those {open_quotes}convergent close-coupling{close_quotes} calculations as lying only in the way the cross section is calculated from the wave function and not in the wave function itself. The anomalous {open_quotes}step-function{close_quotes} behavior of those calculations is derived from a stationary-phase argument. Calculations are presented on the Temkin-Poet model for electron-impact ionization of hydrogen, a breakup problem with exponential potentials, and an analytically solvable model. The anomalies associated with two-body close-coupling calculations are demonstrated using wave functions from complex exterior scaling calculations that otherwise give converged results without any anomalies. {copyright} {ital 1999} {ital The American Physical Society}

We report the results of a theoretical study of electron scattering by CO[sub 2] at incident electron energies ranging from 0.25 to 10 eV using the complex Kohn variational method. These are the first fully [ital ab initio] calculations to accurately reproduce the two dominant features observed in experiment, namely, the dramatic rise in the integral cross sections below 2.0 eV and the resonance enhancement near 3.8 eV. Both of these effects are sensitive to the inclusion of electronic correlation effects involving long-range target polarization and short-range distortion. We have also carried out a preliminary study of effects of target vibrational motion in [sup 2][Pi][sub u] symmetry with an adiabatic nuclei treatment of the symmetric stretch mode. We find that this has a substantial effect on the width of the 3.8 eV resonance feature and gives results for both the integral elastic and total cross sections in excellent agreement with experiment. Our calculated differential elastic cross sections are also in good accord with recent experimental results. [copyright] [ital 1999] [ital The American Physical Society]

Exterior complex scaling enables one to compute the outgoing wave portion of the wave function for three charged particles without explicitly imposing the asymptotic boundary condition for three-body breakup. This technique is used in connection with a high-order finite difference scheme to provide numerically accurate single-differential ionization cross sections for the Temkin-Poet (s-wave) model of $e\ensuremath{-}\mathrm{H}$ scattering. These benchmark values are compared with results obtained from several recent close-coupling approaches that employ pseudostates to discretize the ionization continuum, but use a strictly two-body scattering formalism.

We comment on the accuracy of the results of Taioli and Tennyson in their paper 'A wave packet method for treating nuclear dynamics on complex potentials' (2006 J. Phys. B: At. Mol. Opt. Phys. 39 4379).

Despite the importance of BCl{sub 3} in plasmas used for commercial etching processes, no calculations or measurements of elastic low-energy electron scattering from BCl{sub 3} have previously appeared in the literature. We therefore present calculations based on the complex Kohn method for elastic electron-BCl{sub 3} scattering at incident electron energies below 8 eV. We find a near-zero-energy virtual state and a sharp temporary negative-ion resonance at 0.25 eV, which likely contributes to the large electron attachment cross sections observed in swarm studies. {copyright} {ital 1998} {ital The American Physical Society}

We describe complex Kohn calculations for elastic e{sup {minus}}-CF{sub 4} scattering at incident electron energies of 0.04{endash}20 eV. An accurate representation of the electronic correlation effects involving target polarization is critical in the explicit demonstration of a Ramsauer-Townsend minimum. We use a set of polarized virtual orbitals to form a compact representation of closed channels in the trial scattering function to include these effects. These are the first {ital ab initio} calculations to verify the Ramsauer-Townsend minimum in CF{sub 4}. We find excellent comparison between the complex Kohn results and measured differential and integral cross sections. {copyright} {ital 1998} {ital The American Physical Society}

An extension of the Kohn variational method for computing scattering amplitudes is demonstrated that requires only matrix elements of the resolvent of the Hamiltonian between energy-independent test functions. Scattering boundary conditions are imposed by expanding the resolvent in a basis of square-integrable functions and outgoing-wave continuum functions. By employing several continuum basis functions with overlaps defined by suitable analytic continuation, the scattering amplitude can be expressed efficiently over a continuous range of energies. The method described here differs from previous approaches using time-independent wave packets in that the wave packets which generate the initial and final states in this approach can lie within the interaction region. {copyright} {ital 1998} {ital The American Physical Society}

The complex Kohn variational method is used to study low-energy electron collision processes involving CH{sub 3}Cl. The elastic differential and momentum transfer cross sections are studied from low electron energy (0.5 eV) through the resonance region (3.5 eV) to 10 eV. The effects of target correlation and polarization are studied. A comparison is made between the results of this study and experimental results available for this system. {copyright} {ital 1997} {ital The American Physical Society}

We propose a general approach to the electron-impact ionization problem that involves two distinct steps. First, using exterior complex scaling, we calculate the outgoing portion of the scattering wave function without explicit use of boundary conditions for ionization or any other channel. Once that wave function is known for a finite region of space, we make use of a general formula for extracting the integral cross section for the breakup process from any wave function. That formula is a projected form of the optical theorem and has no relation to complex coordinates or other methods of computing the scattering wave function. A preliminary calculation on the s-wave radial limit form of electron{endash}hydrogen-atom ionization is presented in excellent agreement with calculations by other approaches. {copyright} {ital 1997} {ital The American Physical Society}

We examine finite basis set implementations of complex scaling procedures for computing scattering amplitudes and cross sections. While ordinary complex scaling, i.e., the technique of multiplying all interparticle distances in the Hamiltonian by a complex phase factor, is known to provide convergent cross-section expressions only for exponentially bounded potentials, we propose a generalization, based on Simon's exterior complex scaling technique, that works for long-range potentials as well. We establish an equivalence between a class of complex scaling transformations carried out on the time-independent Schr\"odinger equation and a procedure commonly referred to as the method of complex basis functions. The procedure is illustrated with a numerical example.