Ian E. McCarthy

Electron momentum spectroscopy of atoms and molecules

Unique information about the motion and correlation of valence electrons in atoms, molecules and their ions is obtained from electron-impact ionization reactions near the Bethe ridge at total energies of the order of 1000 eV or higher. This is electron momentum spectroscopy. The history, theory and practice of the field are discussed and its value is shown by numerous examples.

(e, 2e) spectroscopy

Abstract We present a detailed treatment of the theoretical and experimental aspects of the symmetric (e, 2e) reaction in atoms, molecules and solids. Two experimental arrangements are described for measuring angular correlations and separation energy spectra. the one arrangement employing coplanar and the other noncoplanar symmetric kinematics. The latter arrangement is shown to be particularly suitable for extracting structure information. The basic approximation, the factorized distorted-wave off-shell impulse approximation with fully distorted waves, is shown to correctly describe the reaction in some test cases, as does the phase distortion approximation. At energies of the order of 1200 eV the simple eikonal and plane wave approximations adequately describe the valence shell cross sections for light atoms and molecules containing first row elements. Energy independent structure information is obtained on: (a) shapes and magnitudes of the square of the momentum space wave functions for individual electron orbitals; (b) separation energies for individual ion eigenstates; (c) the characteristic orbital of each state; and (d) spectroscopic factors describing the probability that an eigenstate contains the principal configuration of a hole in the characteristic orbital for each eigenstate. Comparison is made with photoelectron spectroscopy and Compton scattering, since they separately yield some of the information obtained by the (e, 2e) method. A brief summary is given of other electron-electron coincidence experiments.

Semiphenomenological optical model for electron scattering on atoms

It is shown that it is possible to derive from first principles a form for a local, central, complex potential that fits elastic electron scattering on hydrogen at various energies with two free parameters. The energy-dependence of the parameters is discussed. Understanding of the optical model based on hydrogen enables the authors to use published Hartree-Fock calculations to construct a potential that gives excellent fits to argon at several energies with no free parameters. In all cases, the total reaction cross section, obtained from independent experimental information, is used to determine the strength of the imaginary part of the potential.

(E, 2E) Collisions

Publisher Summary The study of (e, 2e) collisions has expanded rapidly since the first coincidence measurements of the two emitted electrons in the electron impact ionization of helium. This chapter focuses on the symmetric (e, 2e) reaction at high and intermediate energies—that is, the regime of (e, 2e) collisions that can yield reliable information on the momentum distribution of the struck electrons for transitions to definite final ion states. This chapter deals with only those experiments designed to yield detailed information on the electronic structure of atoms and molecules. This is the regime of symmetric kinematics at intermediate and high electron energies. The chapter outlines some of the experimental techniques employed in these investigations. The basic theory necessary for describing the reaction mechanism and for extracting all the structure information is developed. The theory for atoms is extended to cover the case of molecular targets. The reaction mechanism at intermediate to high energies is investigated in the chapter for atomic targets in both the coplanar and noncoplanar symmetric geometry. Some of the structure information that has been obtained on atoms and molecules that include electron–electron correlation effects in both the target and final ion states are also discussed in the chapter.

Non-coplanar symmetric (e, 2e) momentum profile measurements for helium: an accurate test of helium wavefunctions

The 1200 eV non-coplanar symmetric (e, 2e) cross sections for helium leading to the n=1, 2 and 3 ion states were measured with a modified coincidence spectrometer using position-sensitive microchannel plate detectors. The ground-state momentum profiles (cross sections) are compared with the momentum distribution given by the Hartree-Fock wavefunction, the accurate correlated wavefunction of Joachain and Vanderpoorten (1970), and the momentum distribution derived from accurate Compton profile measurements by Lee (1977). Good agreement is obtained between theory and the (e, 2e) measurements, but the Compton momentum distribution is seriously in error at low momentum. The small discrepancy at high momenta between the present measurements and the plane-wave impulse approximation is completely explained by allowing for distortion of the continuum electron waves by the helium and ion potentials. The n=2 and 3 cross sections cannot be explained using the helium HF wavefunctions, but are well described by the accurate correlated JV wavefunction. The measured n=2 to n=1 cross section ratio discriminates between several accurate correlated helium ground-state wavefunctions.

Distorted-wave effects at low momentum in binary (e, 2e) cross sections for d-orbital ionization

Unexpected and previously unexplained behaviour showing appreciable intensity at low momenta in previously published binary (e, 2e) cross sections for ionization from atomic orbitals including Xe 4d, Zn 3d and Cd 4d is investigated. Similar effects have also been observed recently in binary (e, 2e) studies of metal hexacarbonyls for the least tightly bound molecular orbitals which are dominated by metal character. The finite cross sections at low momenta (i.e. non-nodal behaviour) are not predicted by plane-wave calculations for atomic targets, but can be accounted for using distorted-wave theory. These distortion effects at low momenta appear to be due to a high- effect and the even-parity nature of atomic orbitals.

(e,2e) Spectroscopy of ethane

Abstract The 400-eV and 1200-eV non-coplanar symmetric (e, 2e) reaction has been used to measure the momentum distributions of electrons in the individual valence orbitals of ethane as well as to measure the complete separation energy spectra in the valence region. The shapes and relative magnitudes of the momentum distributions agree well with those calculated using the plane wave off-shell impulse approximation and double zeta basis molecular orbital wave functions. The ground state of C 2 H 6 + is shown to be 1e g −1 , with the vertical ionization potential being 12.25 ± 0.1 eV. Considerable structure due to configuration interaction is observed in the separation energy region 29–55 eV. Much of this structure can be assigned to the 2a 1g orbital.

Investigation of generalized overlap amplitudes via (e,2e) spectroscopy

Abstract The (e,2e) reaction has previously been shown to be an extremely direct and accurate measure of the overlap of the wavefunction of a target molecule with that of resolved electronic states of the posotive ion resulting from electron knockout. The present paper discusses the reaction in relation to the direct computation of the structure overlaps for different ion states as the generalized overlap amplitudes appearing in the spectral resolution of the one-particle Geens function. The case of water is used to illustrate the effectiveness of the Greens function technique for calculating (e2e) cross sections for the principal ion states and the use of the reaction as a very sensitive measure of the long-range charge density.

Imaging of the HOMO electron density in Cr(CO)6, Mo(CO)6 and W(CO)6 by electron momentum spectroscopy: a comparison with Hartree-Fock and DFT calculations

Abstract Studies of the electron density distributions in the t2g HOMO orbitals (essentially metal valence d character) of the transition metal carbonyls Cr(CO)6, Mo(CO)6 and W(CO)6 have been made using electron momentum spectroscopy (EMS). The EMS measurements provide a test of basis set effects and the quality of theoretical methods in the description of these large systems. The experimental momentum profiles are compared with theoretical spherically averaged momentum profiles calculated using the plane wave impulse approximation (PWIA) at the level of the target Hartree-Fock approximation (THFA) with a range of basis sets. Electron density maps for the HOMO orbitals in both momentum and position space have also been calculated for the oriented molecules at the Hartree-Fock level. Further comparisons of the measured momentum profiles to PWIA calculations are made in the target Kohn-Sham approximation (TKSA) using density functional theory (DFT) with the local density approximation and also with gradient corrected exchange correlation potentials. In addition to momentum profiles, other electronic properties have also been calculated by the various theoretical methods and compared to experimental values. The experimental momentum profiles for the HOMO orbitals of all three hexacarbonyls show significant cross-section at momenta below ∼0.5 au including a large contribution near p = 0 which is not expected from symmetry considerations or predicted by either the Target Hartree-Fock or the DFT target Kohn-Sham PWIA calculations. The discrepancies may be due to the significant vibrational excitation of the initial state metal carbonyl molecules expected at room temperature. However, theoretical studies of the Cr 3d and Mo 4d atomic systems show that significant low momentum components are introduced into the EMS cross-section when the PWIA treatment is replaced with the distorted wave impulse approximation (DWIA). While DWIA calculations are not possible for molecules the results for atomic Cr 3d and Mo 4d strongly suggest that the unusual effects observed experimentally in the M(CO)6 HOMO (essentially Cr 3d, Mo 4d and W 5d in character) cross-sections are due to distortion of the electron waves in the collision process.

Calculation of electron scattering on the He+ ion

We apply the convergent close-coupling method to the calculation of electron scattering on the ground state of He+ It is shown that the inclusion of the treatment of the continuum, even below the ionization threshold, significantly reduces the calculated 2S cross section. We generally find good agreement with the measurements of the 2S excitation cross section, though in the vicinity of a few eV near threshold our results are characteristically higher than the experiment Complete quantitative agreement is obtained with the measurement of the total ionization cross section from threshold to 700 eV.