Schwinger Multichannel Research Articles

Photoemission in the molecular frame induced by soft X-ray elliptically polarized light

A new step for complete experiments in photoionization (PI) of linear molecules is achieved when the electron-ion vector correlation method, based on imaging and time-of-flight resolved electron-ion coincidence techniques, is combined with the use of elliptically polarized light. The molecular frame photoelectron angular distributions (MFPADs), as well as the s 1 and s 2 Stokes parameters characterizing the polarization state of the light, can be derived from a single experiment performed with undefined elliptically polarized light. Using this method, we report and discuss MFPADs for site selective K-shell ionization of the NO and N 2O linear molecules in the region of the N 1s and O 1s shape resonances. A large molecular frame circular dichroism is observed, well predicted by the multi-channel Schwinger configuration interaction calculations reported for PI of NO. We also present recent experimental results for PI of non-linear molecules like CH 3Cl measured above the Cl 2p and C 1s ionization thresholds: the recoil frame photoelectron angular distributions (RFPADs) obtained by the vector correlation method may be influenced both by the molecular frame photoemission pattern and the fragmentation process.

Similarities and differences in e ±–molecule scattering: Applications of the Schwinger multichannel method

In this paper, we present a comparative study of low energy electron and positron scattering by H 2 and N 2 molecules, using the Schwinger multichannel (SMC) method. We briefly discuss the elastic collision of electrons and positrons by H 2 below positronium formation threshold. The electronic excitation of N 2 by electron impact is then compared with available data in the literature and with previously published results by positron impact. Strategies to treat the nuclear dynamics in the collision process, specifically adiabatic approximation for direct scattering and boomerang model for resonant scattering, are introduced within the SMC context. Partial results for H 2 are shown.

Elastic electron scattering by fullerene,C60

We report cross sections for elastic scattering of low-energy electrons by fullerene, C60, calculated within the static-exchange approximation. The calculations are carried out via the Schwinger multichannel (SMC) method, equivalent in this case to the standard Schwinger variational principle. Combining the high parallel efficiency of the SMC method with a quadrature specially adapted to the high symmetry of C60 facilitates the most demanding step of the calculation and so permits the use of a large basis set. We analyze the structure of the cross section with reference to a simple spherical-shell model, and we compare our results to prior measurements and calculations.

Dissociative photoionization of N(2)O in the region of the N(2)O(+)(B (2)Pi) state studied by ion-electron velocity vector correlation.

Dissociative direct photoionization of the N2O(X 1Sigma+) linear molecule via the N2O+(B 2Pi) ionic state induced by linearly polarized synchrotron radiation P in the 18-22 eV photon energy range is investigated using the (VA+,Ve,P) vector correlation method, where VA+ is the nascent velocity vector of the NO+, N2+, or O+ ionic fragment and Ve that of the photoelectron. The DPI processes are identified by the ion-electron kinetic energy correlation, and the IchiA+(thetae,phie) molecular frame photoelectron angular distributions (MFPADs) are reported for the dominant reaction leading to NO+ (X 1Sigma+,v) + N(2D)+ e. The measured MFPADs are found in satisfactory agreement with the reported multichannel Schwinger configuration interaction calculations, when bending of the N2O+(B 2Pi) molecular ion prior to dissociation is taken into account. A significant evolution of the electron scattering anisotropies is observed, in particular in the azimuthal dependence of the MFPADs, characteristic of a photoionization transition between a neutral state of Sigma symmetry and an ionic state of Pi symmetry. This interpretation is supported by a simple model describing the photoionization transition by the coherent superposition of two ssigma and ddelta partial waves and the associated Coulomb phases.

Near threshold photoionization of the ground and first excited states of C(2).

Calculations using the multichannel Schwinger configuration-interaction method are presented for the photoionization from the ground and the first excited states of the C(2) molecule. Both single channel and multichannel calculations are presented in a photon energy range from the threshold to about 50 eV of photon energy. For the ground state, inclusion of both intrinsic and dynamical correlation effects is seen to strongly alter the picture of the photoionization process inferred from single-channel frozen-core Hartree-Fock calculations. Furthermore, the photoionization study of the first excited state of molecular carbon has revealed the presence of strong interchannel coupling between the 3sigma(g)-->ksigma(u) channel and the photoionization channels leading to the A (4)Pi(g) and f (2)Pi(g) ionic states in the near threshold region.

Low Energy Positron Scattering by SF6 and CO2

In this work we present theoretical integral (ICS) and differential (DCS) cross section calculations for low-energy positron scattering by SF6 and CO2 molecules. Our scattering wave functions were obtained with the Schwinger Multichannel Method (SMC) at the static and static-plus-polarization levels of approximation. The elastic DCS were calculated over an energy interval ranging from 4 eV up to 50 eV for SF6 and from 1 eV up to 20 eV for CO2. The results show, in general, good agreement with recent experimental data. We found a Ramsauer–Townsend minimum in e+ - CO2 calculations, even though no signature of virtual state formation was observed, contrasting with the well-known case of electron scattering.

Complete description of linear molecule photoionization achieved by vector correlations using the light of a single circular polarization

In this paper we demonstrate that the vector correlation approach for the study of dissociative photoionization (DPI) of linear molecules enables us to achieve a complete description of molecular photoionization by performing a single experiment using only one state of circularly, or elliptically, polarized light. This is illustrated by the derivation of the complex dipole matrix elements for the benchmark DPI reaction of the NO molecule, where (4σ)−1 inner-valence ionization is induced by left-handed circularly polarized synchrotron radiation at hν=23.65 eV. The importance of electronic correlation for this process is emphasized by comparing the experimental results with multichannel Schwinger configuration interaction calculations. The energy dependence of the transition matrix elements and that of the electronic correlation in the 25–40 eV energy range are illustrated by the calculations and compared with the present results and recent experimental studies at 40.8 eV.

Vector correlations in dissociative photoionization of O2 in the 20–28 eV range. II. Polar and azimuthal dependence of the molecular frame photoelectron angular distribution

A combined experimental and theoretical study of the polar and azimuthal dependence of the molecular frame photoelectron angular distributions (MFPADs) for inner-valence-shell photoionization of the O2 molecule into the O2+(B 2Σg−,3 2Πu,c 4Σu−) states is reported. The measured MFPADs, for each orientation of the molecular axis with respect to the linear polarization of the synchrotron radiation, are derived from the spatial analysis of the (VO+,Ve,P) vector correlation, where the nascent ion and electron velocity vectors VO+ and Ve are determined for each dissociative photoionization (DPI) event using imaging and time of flight resolved coincidence technique as described in the companion paper of this series [J. Chem. Phys. 114, 6605 (2001)]. Expressed in the general form of four FLN(θe) functions which contain all the dynamical information about the photoionization processes, they are compared with the MFPADs computed using the multichannel Schwinger configuration interaction method. A very satisfactory agreement is found. When the lifetime of the O2+ ionic states is a significant fraction of the rotational period, the rotational motion of the molecule is included in the quantal derivation of the MFPADs. Measured MFPADs are also reported for the additional DPI process identified in Paper I, and for DPI involving the excitation of the neutral (3 2Πu,4sσg) Rydberg state.

Theoretical studies of cross sections and photoelectron angular distributions in the valence photoionization of molecular oxygen

Photoionization from ground state of molecular oxygen leading to a number of 1πg−1, 1πu−1, 3σg−1, and 2σu−1 ion states have been investigated for photon energies up to 50 eV using the multichannel Schwinger method with configuration interaction. The use of a multichannel approach and correlated targets not only enables us to obtain results in good agreement with experimental data, but also leads to a better understanding of electron correlation effects in these photoionization processes. In addition to numerous Rydberg-type autoionization states that have been identified in the multichannel study, substantial effects of the open-channel coupling have also been found in almost every channel. These effects are evidences of the strong electron correlation in the photoionization dynamics of this system. The most significant interchannel coupling effect exists in the photoionization to the 3σg−1 channels, in which a complete failure of the single-channel photoionization description is found in the shape resonance process. In contrast to earlier theoretical studies, we found only one shape resonance in the photoionization to the 3σg−1 channels instead of two separated multiplet-specific shape resonances. A full description of the resonant state requires the inclusion of coupling to other valence photoionization channels. The photoelectron angular distributions have also been computed and compared to the existing experimental data. Good agreement between experiment and theory has been achieved. In this study, we also calculated molecular orientation parameters under the fixed-nuclei approximation, which contain symmetry information about the resonances and outgoing waves and which can be used to characterize the dynamics of the photoionization.

Applications of the Schwinger Multichannel method with pseudopotentials to electron scattering from polyatomic molecules II: rotational excitation cross sections

This paper reports results for rotational excitation of H2O and H2S molecules by electron impact. It is also a databasis including tables of previously published rotationally resolved cross sections for CH4, SiH4, GeH4, SnH4, PbH4, NH3, PH3, AsH3, SbH3, CF4, CCl4, SiCl4 SiBr4, and SiI4. Our scattering amplitudes were calculated using the Schwinger multichannel method with norm-conserving pseudopotentials and the rotational resolved cross sections were obtained with the help of the adiabatic nuclei rotation approximation. Our results are in good agreement with other theoretical data and experimental results when available.

Positronium formation in positron-hydrogen scattering using Schwinger’s principle

Accurate results are reported for ground-state positronium formation in positron-hydrogen collisions using 12 correlated basis functions in a multichannel Schwinger's principle in momentum space at intermediate energies 30--150 eV in an extension of our earlier work [Phys. Rev. A 59, 1913 (1999)]. The rich structure in the differential cross section is found to be present due to the existence of critical angles. Results for the total formation cross section are in excellent agreement with other variational and nonvariational calculations available in the literature. The observed data of Zhou et al. [Phys. Rev. A 55, 361 (1997)] are also in good accord with these predictions.

Effective configurations in electron-molecule scattering

We present a more efficient way of treating polarization effects in the scattering of low-energy electrons by molecules within the Schwinger multichannel (SMC) method. We propose to expand the scattering wave function in a set of functions of $N+1$ electrons that describe the scattering in an effective way, which allows the use of a small number of functions to describe the polarization effects. As a first test, we apply the method to the scattering of electrons by the ${\mathrm{H}}_{2}$ molecule. We calculate elastic integral and differential cross sections, and we obtain excellent results with a reduction in the number of configurations of up to 98% when compared to the traditional method used in the SMC method. This is a substantial size reduction of all matrices involved in the SMC method and, as a consequence, it represents a promising technique for treating more complex molecular systems.

Multichannel Schwinger’s principle for rearrangement collisions: Positronium formation in positron-hydrogen collisions

Post and prior forms of the multichannel Schwinger's principle for rearrangement collisions are presented using discrete basis sets. An application is made to positronium formation in positron-hydrogen collisions at low energies in the range 6.8--30.0 eV. A total number of eight terms of a type of correlated basis functions involving inverse powers of half-odd integers is required to predict accurate results in conformity with the available variational and nonvariational values in the literature. Our findings indicate that destructive interference between partial-wave contributions to the scattering amplitude is responsible for the appearance of critical angles in positronium formation. Surface plots of the differential cross section display immensely rich structure. The total positronium formation cross sections agree nicely with the observed data of Zhou et al. [Phys. Rev. A 55, 361 (1997)] in the entire energy range.

Electronic excitation of the a3 ∑ g+ and c3Πu states of H 2 by electron impact using the method of continued fractions

In the present work we use a multichannel extension of the method of continued fractions (MCF) to study the low-energy electron-impact excitation in linear molecules at the two-state close-coupling level. In particular we have calculated the excitation cross sections for the X 1 ∑ g + → a 3 ∑ g + and X 1 ∑ g + → c 3 Π u transitions in H 2 for incident energies from near threshold to 30 eV. In our work, in contrast with the early two-state studies of Chung and Lin, no orthogonality constraint between the bound and continuum orbitals is imposed and the one-electron exchange terms are explicitly considered. In general our calculated cross sections are in good agreement with the results of the two-state Schwinger multichannel method. Our results for the a 3 ∑ g + are also in quite good agreement with the available experimental data. However, the cross sections for excitation of the c 3 Π u state differ significantly from the measured values at 20 and 30 eV, where they are available. The disagreement is attributed to the multichannel effects, not accounted for in this study.

Low-energy electron scattering by N, P, As and Sb

We report elastic integral, momentum transfer and differential cross sections from 10-30 eV for electron scattering by (X = N, P, As, Sb). These results were obtained at the static-exchange approximation with the Schwinger Multichannel Method with Pseudopotentials [M H F Bettega, L G Ferreira and M A P Lima 1993 Phys. Rev. A 47 1111]. Our results for are in good agreement with experimental data. We also compare our results with previous calculations on (X = P, As, Sb) [M H F Bettega, M A P Lima and L G Ferreira 1996 J. Chem. Phys. 105 1029] and found, as expected, that the cross sections are larger than the corresponding cross sections.

Auger decay of theC1s→2π*excitation of CO

Calculations on the Auger decay of CO after the $\mathrm{C}1s\ensuremath{\rightarrow}2{\ensuremath{\pi}}^{*}$ excitation have been performed utilizing a multichannel Schwinger approach. The bound orbitals used to expand the multichannel configuration-interaction wave functions of the ion state were the natural orbitals of a single excitation and double excitation configuration-interaction (CI) calculation on the $\mathrm{C}{1s}^{\ensuremath{-}1}$ core-hole state of CO. Fixed-nuclei photoionization cross sections were then obtained with target states represented by complete active space CI wave functions. An analysis of the resulting cross sections using Fano's spectral line profile and the lifetime vibrational interference theory has lead to photoabsorption profiles in good agreement with experimental measurements. Additionally, we have found good agreement with experimental data for the resulting photoelectron and photoemission spectra.

Cross sections for rotational excitations of CH 4 , SiH 4 , GeH 4 , SnH 4 and PbH 4 by electron impact

We report differential and integral cross sections for rotational excitation of XH4 molecules (X: C, Si, Ge, Sn, Pb) from 7.5–30 eV by electron impact. These cross sections were derived from fixed-nuclei scattering amplitudes (Bettega et al. 1995) obtained using the Schwinger Multichannel Method with Pseudopotentials (SMCPP) (Bettega et al. 1993). Our results represent the first rotational excitation cross sections for molecules as large as GeH4, SnH4 and PbH4 using entirely ab initio procedures. The cross sections for CH4 and SiH4 obtained with pseudopotentials are in very good agreement with all-electron calculations and with other theoretical results. A comparison between our calculated cross sections and experimental data for CH4 is in general encouraging, but some discrepancies remain. We found inelastic rotational cross sections and momentum transfer cross sections to be larger for SiH4, GeH4, SnH4 and PbH4 than for CH4. We could explain this feature.

Calculation of elastic scattering cross sections of low-energy electrons by PbH4 and SnH4

We report elastic integral, differential, and momentum transfer cross sections from 10 to 30 eV for electron scattering by SnH4 and PbH4, obtained using the Schwinger Multichannel Method with Pseudopotentials [M. H. F. Bettega, L. G. Ferreira, and M. A. P. Lima, Phys. Rev. A 47, 1111 (1993)]. With these molecules we close the series of XH4 molecules, with X=C, Si, Ge, Sn, Pb. We compare the present results with those obtained previously for CH4, SiH4, and GeH4. We find similarities in the cross sections for SiH4, GeH4, SnH4, and PbH4 and a distinctive behavior of CH4. We discuss the role of the center atom size in the scattering process. To our knowledge this is the first ab initio calculation of the SnH4 and PbH4 electron scattering cross sections.

Elastic and vibrational excitation cross sections for electron collisions with propane

Absolute, elastic differential cross sections (DCS) for electron-propane collisions have been measured over a range of scattering angles from 10 degrees to 130 degrees and at incident kinetic energies from 2 to 100 eV. The angular distributions were extrapolated to 0 degrees and 180 degrees by a nonlinear phase shift fit and integrated numerically to obtain the integral elastic and momentum transfer cross sections. The observed DCS agree approximately with a continuum multiple scattering calculation that uses only local potentials and also with a multichannel Schwinger variational calculation. The vibrationally inelastic DCS reveal a shape resonance with a peak at 7.5 eV that is characteristic of trapping by valence orbitals with C-H antibonding character and is identical with peaks encountered in electron-methane and electron-ethane scattering.

Elastic scattering and some vibrational excitation cross sections for electron collisions with Si2H6

Absolute elastic cross sections for e-disilane collisions have been measured by using incident kinetic energies of 2, 3, 4, 5, 7.5, 10, 15, 20, 40, and 100 eV and recorded over a scattering angular range of 10-130 degrees . These cross sections have been integrated by employing a nonlinear phase shift fitting procedure to generate a list of integral elastic and momentum transfer cross sections for the same energy range. The angular distributions have been found to agree reasonably well with a continuum multiple scattering calculation using only local potentials and also with a multichannel Schwinger variational calculation. Limited experiments on vibrationally inelastic scattering reveal the existence of a shape resonance with a peak at approximately 2 eV that is characteristic of trapping by a valence orbital with Si-H antibonding character analogous to that encountered in e-monosilane scattering.