Ionization Amplitudes Research Articles

Elliptic and Circular Dichroism Effects in Two-Photon Double Ionization of Atoms

An ab initio parametrization of the two-photon double ionization amplitude from an s2 subshell of an atom in a 1S state is presented and used to predict two light polarization effects on photoelectron angular distributions that do not exist in single-photon double ionization: (i) elliptic dichroism and (ii) circular dichroism at equal energy sharing. Estimates for He show large magnitudes for these effects, which provide a means for polarization control of double ionization by vacuum ultraviolet light.

Young-Type Interference in(e,2e)Ionization ofH2

We have investigated the electron impact single ionization of the hydrogen molecule, with fully determined kinematics. The experimental and theoretical results are compared with He ionization under the same conditions. The results indicate that the ejected electron angular distribution for H(2) is modified due to Young-type interference between ionization amplitudes for scattering from the two centers in the hydrogen molecule. The observable result is a suppression of the backward scattering (recoil) peak compared with the binary peak.

Gauge-invariant relativistic strong-field approximation

The problem of the choice of gauge in the relativistic strong-field approximation (SFA) is analyzed. The main motivation is to obtain a relativistic ionization amplitude in the SFA which in the nonrelativistic limit coincides with the conventional well-accepted results of the SFA in the length gauge. A gauge-invariant formulation of the SFA is derived which is applicable both in the nonrelativistic as well as in the relativistic regime of laser-induced strong-field ionization phenomena. The gauge invariance is achieved by means of employment of an eigenstate of the physical energy operator for the initial atomic state. As an example, a comparison of predictions of the gauge-invariant theory with conventional SFA results in the radiation gauge is given for above-threshold ionization in the relativistic regime.

Coulomb—Born—Oppenheimer approximation in Ps—H scattering

To improve the Coulomb-Born approximation (CBA) theory of ionization in positronium (Ps) and atom scattering, the effect of exchange is introduced. The nine-dimensional exchange amplitude for ionization of Ps in Ps—H scattering is reduced to a two-dimensional integral using the present Coulomb-Born-Oppenheimer approximation (CBOA). The methodology is extremely useful to evaluate ionization parameters for different target systems and for different types of ionization processes. It is then applied to evaluate the Ps-ionization cross-section and to estimate the effect of exchange on Psionization in Ps-H system. We establish the importance of exchange at lower energy region.

Strong-field ionization of laser-irradiated light homonuclear diatomic molecules: A generalized strong-field approximation–linear combination of atomic orbitals model

The strong-field ionization in a number of light homonuclear diatomic molecules (${\mathrm{N}}_{2}$, ${\mathrm{O}}_{2}$, and ${\mathrm{H}}_{2}$) irradiated by an intense laser field of low fundamental frequency $\ensuremath{\omega}⪡{I}_{p}$ is considered theoretically and studied numerically compared to their ``companion'' atoms, having nearly identical ionization potential ${I}_{p}$. The background applied strong-field approach is based on using the $S$-matrix formalism of conventional strong-field approximation supplemented by the standard linear combination of atomic orbitals and molecular orbitals method utilized for approximate analytical reproduction of the two-centered wave function of an initial molecular bound state. Accordingly, the ionization of a diatomic molecule is described as a quantum-mechanical superposition (intramolecular interference) of contributions from ionization amplitudes corresponding to photoelectron emission from two atomic centers separated by equilibrium internuclear distance. Besides the bonding (or antibonding) symmetry of the highest occupied molecular orbitals (HOMO) corresponding to the outermost molecular valence shell, its spatial configuration and predominant orientation with respect to the internuclear axis and polarization of incident laser field also proved to be of substantial importance and, thus, are taken into equally detailed consideration. Moreover, wherever appropriate, the comparable contributions from other (inner) molecular valence shells of a larger binding energy (closest to that of HOMO, but of different bonding symmetry and spatial configuration) are additionally taken into account. The related results for calculated differential and/or integral molecular ionization rates, molecular photoelectron spectra, and angular distributions are fairly well consistent with available experimental data and, in particular, provide one with a transparent physical interpretation of the nature and origin of high suppression in ionization of the ${\mathrm{O}}_{2}$ molecule (as compared to its companion Xe atom) as well as no suppression in ionization of ${\mathrm{N}}_{2}$ molecules (as compared to its companion Ar atom).

Electron-helium scattering in theS-wave model using exterior complex scaling

Electron-impact excitation and ionization of helium is studied in the $S$-wave model. The problem is treated in full dimensionality using a time-dependent formulation of the exterior complex scaling method that does not involve the solution of large linear systems of equations. We discuss the steps that must be taken to compute stable ionization amplitudes. We present total excitation, total ionization, and single differential cross sections from the ground and $n=2$ excited states and compare our results with those obtained by others using a frozen-core model.

Theory of electron-impact ionization of atoms

The existing formulations of electron-impact ionization of a hydrogenic target suffer from a number of formal problems including an ambiguous and phase-divergent definition of the ionization amplitude. An alternative formulation of the theory is given. An integral representation for the ionization amplitude which is free of ambiguity and divergence problems is derived and is shown to have four alternative, but equivalent, forms well suited for practical calculations. The extension to amplitudes of all possible scattering processes taking place in an arbitrary three-body system follows. A well-defined conventional post form of the breakup amplitude valid for arbitrary potentials including the long-range Coulomb interaction is given. Practical approaches are based on partial-wave expansions, so the formulation is also recast in terms of partial waves and partial-wave expansions of the asymptotic wave functions are presented. In particular, expansions of the asymptotic forms of the total scattering wave function, developed from both the initial and the final state, for electron-impact ionization of hydrogen are given. Finally, the utility of the present formulation is demonstrated on some well-known model problems.

Double photoionization of polyatomic molecules by arbitrarily polarized light: theory

This paper develops a theoretical framework suitable for studying simultaneous ejection of two electrons following the absorption of a single photon by a molecule belonging to one of the 32 point groups. The ionizing electromagnetic radiation is assumed to have any arbitrary polarization. Both photoelectrons are analysed in terms of their energies as well as directions of propagation. The transformation properties of the molecular point symmetry group are used to their full advantage to reduce the various expressions obtained herein to their simplest possible forms. The ionization amplitude is thus shown to decompose into a sum of transitions each involving a final state wavefunction belonging to the irreducible representations of the point group of the molecular target. Molecules with both a random or a fixed orientation in space have been considered. The results obtained herein can therefore be used to study double photoionization of any point symmetry molecule in either its gaseous phase or oriented on liquid and solid surfaces. The analysis is general in that it is independent of any particular dynamical models for the description of photoionization. The present results show that such double photoionization experiments are richer sources of information, specifically on interaction between adsorbed molecules and surfaces and on the geometry of the adsorbate–substrate system, in addition to the electron–electron correlation, than their counterpart experiments on single photoionization. Various possible cases and several observables are discussed.

Complete direct method for electron-hydrogen scattering: Application to the collinear and Temkin-Poet models

We present an efficient generalization of the exterior complex scaling (ECS) method to extract discrete inelastic and ionization amplitudes for electron-impact scattering of atomic hydrogen. This fully quantal method is demonstrated over a range of energies for the collinear and Temkin-Poet models and near-threshold ionization is examined in detail for singlet and triplet scattering. Our numerical calculations for total ionization cross sections near threshold strongly support the classical threshold law of Wannier [Phys. Rev. 90, 817 (1953)] (σ∝E1.128±0.004) for the L=0 singlet collinear model and the semiclassical threshold law of Peterkop [J. Phys. B 16, L587 (1983)] (σ∝E3.37±0.02) for the L=0 triplet collinear model, and are consistent with the semiclassical threshold law of Macek and Ihra [Phys. Rev. A 55, 2024 (1997)] (σ∝exp[(-6.87±0.01)E-1/6]) for the singlet Temkin-Poet model.

Integral representation for the electron-atom ionization amplitude which is free of ambiguity and divergence problems.

It is shown that existing problems with the formal theory of ionization can be effectively resolved. An integral representation for the ionization amplitude free of ambiguity and divergence problems is given. Moreover, the ionization amplitude in the new formulation is shown directly to have an ideal form for practical calculations.

Energy and cusp-conditions study for the He isoelectronic sequence

We present variational wave functions for He-like atoms with nuclear charge Z=1,…,10. We propose modifications of some usual simple correlated wave functions to account for the integration factor required in the evaluation of atomic ionization and excitation amplitudes with distorted wave methods. We determine the parameters of the trial functions and the resulting energies. We introduce new procedures to test the cusp conditions at the singularities of the Coulomb field.

Resolution of phase ambiguities in electron-impact ionization amplitudes

The formal theory of atomic ionization by electron impact relates the breakup amplitude to an integral expression involving the exact wave function and an unperturbed final state that contains two Coulomb functions with effective, noninteger charges. This integral expression has an associated phase factor that diverges logarithmically on an infinite volume unless the effective charges are chosen to satisfy a kinematic relationship, the so-called ``Peterkop condition.'' We derive the explicit form of the Peterkop phase for two commonly used models of electron-hydrogen ionization, the Temkin-Poet model and the collinear model. We show that the formal theory can be used to identify and remove this physically insignificant, volume-dependent phase from amplitudes computed using numerically stable integral expressions that do not satisfy the Peterkop condition.

Unambiguous ionization amplitudes for electron-hydrogen scattering

According to quantum collision theory, scattering amplitudes are complex numbers, which are completely defined by their magnitude and phase. Although the phase information is generally not determined entirely in collision experiments, the phases are well defined and can be used to check computational models. We use four state-of-the-art approaches to calculate the magnitude and phase of the electron-hydrogen ionization amplitude in the Temkin-Poet S-wave model. We demonstrate that the correct phase can be extracted for each method by using the appropriate final-state continuum functions.

Optimal Truncation in Ionization of hydrogen by Electron Impact

An analytic expression for the ionization amplitude of hydrogen byelectron impact is found to contain a polynomial by an optimaltruncation in an asymptotic series and a convergent series. Theionization amplitude, i.e., the transition matrix element on the energyshell, is decomposed into two parts: the structure-scattering factor andcorrelation factor, based on an approximation of the projectile plane wavein coplanar asymmetric geometries. The contribution of these factors tothe triple differential cross section is evaluated using the method ofoptional truncation of asymptotic and convergent series.

Investigation of complex ionization amplitudes in xenon by(e,2e)spectroscopy

We have carried out an $(e,2e)$ experiment that investigates ionization in Xe over the autoionizing region between the ${}^{2}{P}_{3/2}$ and ${}^{2}{P}_{1/2}$ ionic thresholds. Manipulation of $(e,2e)$ energy spectra reveals interference effects between odd- and even-parity multipole ionization amplitudes. The data is analyzed in terms of a simple model that demonstrates that the data contains both magnitude and phase information about these complex ionization amplitudes.

Calculation of electron-impact total-ionization cross sections

A computationally efficient analytic form of the Born-approximation electron-impact ionization amplitude is derived for general neutral-atom targets. High-quality Hartree-Fock Slater orbitals are used to model the target wave function. Full orthogonalization of the continuum Coulomb wave to all occupied orbitals of the target atom is enforced. Results are presented for noble gases (Ne, Ar, Kr, and Xe), selected transition metals (Fe, Cu, and Ag), and elements from the fourth, fifth, and sixth columns of the periodic table (Si, Ge, Sn, P, As, Sb, S, Se, and Te), where theoretical comparisons are lacking. Full orthogonalization significantly improves agreement with experimental data for the noble-gas series compared to previous Born models. Overall agreement with all elements is uniformly good and variations within each series are systematic.

Symmetrized amplitudes of the helium-atom double photoionization

The symmetrized gerade and ungerade amplitudes of the helium atom double photoionization are extracted from the convergent close-coupling calculations at fixed excess energies of 9, 20, 40, and 60 eV above the double-ionization threshold, and varying energy-sharing ratios. The amplitudes are fitted with a simple Gaussian ansatz. Although some deviations from this ansatz are clearly visible, especially at small mutual angles, the fully resolved triple differential cross sections generated from the calculated and fitted amplitudes are very close. This observation lends support to the practical parametrization suggested by Cvejanovi\ifmmode \acute{c}\else \'{c}\fi{} and Reddish [J. Phys. B 33, 4691 (2000)]. A more thorough testing of the ionization amplitudes can be achieved by performing a complete double-photoionization experiment and by making a comparison with other highly accurate and computationally intensive theories.

Accurate amplitudes for electron-impact ionization

We show that the ``two-potential'' formalism of conventional distorted-wave rearrangement theory, which is formally valid only for short-range interactions, can be used to evaluate amplitudes for the ionization of atomic hydrogen by electron impact. The triply differential cross sections calculated using this method validate earlier results obtained by extrapolating the quantum mechanical flux. Although it uses the same time-independent wave functions, this method offers significant advantages over flux extrapolation. It is more accurate, can be applied in practical calculations over a broader range of collision energies, and unlike the flux-extrapolation method, can be applied for arbitrary values of energy sharing between the ejected electrons. Since this rearrangement formalism provides the complete scattering amplitude for ionization, it can be used to calculate any differential cross section.

Practical calculation of amplitudes for electron-impact ionization

An integral expression that is formally valid only for short-range potentials is applied to the problem of calculating the amplitude for electron-impact ionization. It is found that this expression provides a practical and accurate path to the calculation of singly differential cross sections for electron-impact ionization. Calculations are presented for the Temkin-Poet and collinear models for ionization of hydrogen by electron impact. An extension of the finite-element approach using the discrete-variable representation, appropriate for potentials with discontinuous derivatives like the Temkin-Poet interaction, is also presented.

A calculation of ionization amplitudes for e--H scattering

A simple procedure that takes account of dynamical screening in the final state and in which the two electrons are treated in an equivalent fashion, is used to calculate ionization amplitudes for e--H collisions in the near-threshold region. Results for angular distributions and total cross sections are presented and compared with experimental values. Some results that illustrate spin dependence are also displayed.