Alex G. Harvey

An R-matrix approach to electron–photon–molecule collisions: photoelectron angular distributions from aligned molecules

We present a new extension of the UKRmol electron–molecule scattering code suite, which allows one to compute ab initio photoionization and photorecombination amplitudes for complex molecules, resolved both on the molecular alignment (orientation) and the emission angle and energy of the photoelectron. We illustrate our approach using CO2 as an example, and analyze the importance of multi-channel effects by performing our calculations at different, increasing levels of complexity. We benchmark our method by comparing the results of our calculations with experimental data and with theoretical calculations available in the literature.

Electron re-scattering from aligned linear molecules using the R-matrix method

Electron re-scattering in a strong laser field provides an important probe of molecular structure and processes. The laser field drives the ionization of the molecule, followed by acceleration and subsequent recollision of the electron with the parent molecular ion, the scattered electrons carry information about the nuclear geometry and electronic states of the molecular ion. It is advantageous in strong field experiments to work with aligned molecules, which introduces extra physics compared to the standard gas-phase, electron–molecule scattering problem. The formalism for scattering from oriented linear molecules is presented and applied to H2 and CO2. Differential cross sections are presented for (re-)scattering by these systems concentrating on the most common, linear alignment. In H2 these cross sections show significant angular structure which, particularly for a scattering angle of 90°, are predicted to vary significantly between re-collisions stimulated by an even or an odd number of photons. In CO2 these cross sections are zero indicating the necessity of using non-parallel alignment with this molecule.

The role of multichannel effects in the photoionization of the NO 2 molecule: an ab initio R- matrix study

We present the first ab initio photoionization calculations for the NO 2 molecule in its equilibrium geometry using the multichannel R- matrix method and a multiconfigurational description of the system. We focus on the role of correlation in NO 2 photoionization and find that it plays a key role, both at the level of partial cross sections and asymmetry parameters. For the most sophisticated model used here, we achieve excellent agreement with the experimental data of Baltzer et al (2009 Chem. Phys. 237 451–70 ) for the asymmetry parameters of angle-resolved photo-electron spectra. We also present and analyse the angle-resolved photoionization dipoles for photon energies up to 90 eV and for the two lowest-energy ionization channels. Our results should advance the analysis of experiments in the field of attosecond spectroscopy, especially high harmonic generation, where angle-resolved photorecombination dipoles become crucial for the interpretation of experiments, even for randomly oriented molecular ensembles, due to coherent addition of signals from different orientations.

Electron re-scattering from H2 and CO2 using R-matrix techniques

The R-matrix method is being used to investigate electron (re-)scattering for the H2 and CO2 systems. This is being done computationally using the UK molecular R-matrix package. The similarity of re-scattering to electron–molecule scattering off the associated cations at geometries near to those of the neutral molecules forms the basis of our initial model. Preliminary cross-sections and eigenphase sums have been calculated for molecular hydrogen and carbon dioxide. These show highly resonant behaviour in the energy range studied and this is particularly pronounced as channel thresholds are approached. The initial results suggest that inclusion of resonance phenomena could be vital for interpretation of electron re-scattering experiments. Elastic differential cross-sections for symmetries relevant to experiments performed using linear polarization are also presented and prospects for a more realistic model are discussed.

Calculated photoionization cross sections using Quantemol-N

Quantemol-N is an expert system designed to run the widely used UK Molecular R-matrix code (UKRMol). Originally designed to consider electron?molecule collision problems, here we present an extension to treat molecular photoionization. Sample results are given for the photoionization of molecular nitrogen and methane. Comparisons are made with experimental results showing good agreement.

The R-matrix Calculations of Orientation and Coulomb Phase Effects in Electron–Molecule (Re-)Collisions

Electron recollision in strong laser fields is usually studied with oriented molecules. This introduces orientation effects into the recollision problem which are generally not present in usual treatments of electron–molecule collisions. In addition this collision occurs with a molecular ion which means that the dominant electron– molecule interaction is the long-range Coulomb potential, which competes asymptotically with the strong laser field. Different workers have performed treatments varying between the complete inclusion of all asymptotic Coulomb effects to their complete neglect. Three possible treatments of the Coulomb problem are explored using H2 and CO2 as prototypical systems. Calculations based on R-matrix studies of the (re-)collision, which neglect the effects of the laser field, show that inclusion of the complete Coulomb interaction leads not only to the well-known singularity problems for forward scattering but also leads to the washing out of much of the detailed, angular structure in the differential cross section of the oriented molecules.

Rotational Cooling of HD+ by Superelastic Collisions with Electrons

Rotational cooling of HD+ by superelastic collisions (SEC) with electrons was observed at the Heidelberg test storage ring by merging a beam of rotationally hot HD+ ions with an electron beam at zero relative energy. Neutral fragments resulting from DR events were recorded at different electron densities using a high resolution imaging detector and a large-area, energy sensitive detector. The data allowed to deduce the time dependence of the population of three groups of rotational angular momentum states J built on the vibrational ground state of the ion together with the corresponding DR rate coefficients. The latter are found to be (statistical uncertainties only) α0,1,2 = 3.8(1), α3,4 = 4.0(2), and α5,6,7 = 9.0(1.3) in units of 10−8 cm3/s, in reasonable agreement with the average values derived within the MQDT approach. The time evolution of the population curves clearly reveals that rotational cooling by SEC takes place, which can be well described by using theoretical SEC rate coefficients obtained by combining the molecular R-matrix approach with the adiabatic nuclear rotation approximation. We verify the ΔJ = −2 coefficients, which are predicted to be dominant as opposed to the ΔJ = −1 coefficients and to amount to (1 − 2) 10−6 cm3/s, to within 30%.

Electron correlations and pre-collision in the re-collision picture of high harmonic generation

We discuss the seminal three-step model and the recollision picture in the context of high harmonic generation in molecules. In particular, we stress the importance of multi-electron correlation during the first and the third of the three steps of the process: (1) the strong field ionization and (3) the recombination. We point out how accurate account for multi-electron correlations during the third, recombination, step allows one to gauge the importance of pre-collision: the term coined by J. H. Eberly to describe unusual pathways during the first, ionization, step.

General theory of photoexcitation induced photoelectron circular dichroism

The photoionization of chiral molecules prepared in a coherent superposition of excited states can give access to the underlying chiral coherent dynamics in a procedure known as photoexcitation induced photoelectron circular dichroism (PXECD). As in photoelectron circular dichroism (PECD), chirality manifests as asymmetric photoelectron emission in the forward/backward direction (relative to the laser propagation direction). However, in PXECD, the asymmetric photoemission is additionally contingent on coherence. This exclusive dependence on coherence can also be seen in a different part of the photoelectron angular distribution (PAD), where it is not contingent on the chirality of the molecule, thus allowing extension of PXECDs sensitivity to tracking coherence to non-chiral molecules. Here we present a general theory of PXECD based on angular momentum algebra and derive explicit expressions for all pertinent asymmetry parameters which arise for the arbitrary polarization of pump (which prepares the superposition of excited states) and ionizing probe pulses. The theory is developed in a way that clearly and simply separates chiral and non-chiral contributions to the PAD and also demonstrates how PXECD and PECD-type contributions, which may be distinguished by whether the pump or ionizing probe pulse enables chiral response, are mixed when arbitrary polarization is used.

Recent developments in R-matrix applications to molecular processes

We report on recent developments of the UKRmol suite, an implementation of the molecular R- matrix method and present examples of the calculations (e.g. electron scattering, photoionization, high harmonic generation, etc.) it has enabled.