E. Weigold

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.

Momentum distributions and ionization potentials for the valence orbitals of hydrogen fluoride and hydrogen chloride

Abstract The binding-energy spectra and momentum distributions for the valence orbitais of HF and HCI have been obtained at 1200 and 400 eV using (e, 2e) spectroscopy with symmetric kinematics For HC1, the strength of the innermost valence-orbital (4cr) is found to be significantly split among several ion~states in the range 20u41 eV The corresponding orbital (2G) in HF is, however, not significantly split among ion states The measured momentum-distributions are compared with the results of several calculations of at least double-zeta quality, as well as with a one-particle Greenaes function calculation of the generalized overlap amplitude (GOA) Agreement in shape is quite good for the innermost orbitais, but for the ii and outer a orbitais of HF, the momentum distributions calculated directly from the molecular orbitais are significantly more extended in momen- tum space than are the measured distributions The Greenaes function calculations give momentum distributions in reasonable agreement with the data, and pole-strengths for transitions which are in qualitative agreement with the observed cross-sections

(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.

High-energy (e, 2e) spectrometer for the study of the spectral momentum density of materials

A new spectrometer for the study of energy-resolved momentum densities is described. The (e, 2e) spectrometer uses a symmetric configuration and uses incoming energies up to 50 keV. Energy resolution and momentum resolution are 1.8 eV and 0.1 a.u., respectively. Compared to previous spectrometers this spectrometer has rather low levels of multiple scattering, and thus allows for more quantitative analysis of the data and/or the measurement of thicker samples.

Condensed matter electron momentum spectrometer with parallel detection in energy and momentum

An electron momentum spectrometer has been constructed which measures electron binding energies and momenta by fully determining the kinematics of the incident, scattered, and ejected electrons resulting from (e,2e) ionizing collisions in a thin solid foil. The spectrometer operates with incident beam energies of 20–30 keV in an asymmetric, non‐coplanar scattering geometry. Bethe ridge kinematics are used which for 20 keV incident energy has scattered electron energies of 18.8 keV at a polar angle of θs=14°and azimuthal angles φs in the range from −18° to +18° and ejected electrons of 1.2 keV and θe=76°with φe=π±6°. The technique uses transmission through the target foil, but it is most sensitive to the surface from which the 1.2 keV electrons emerge, to a depth of about 2 nm. Scattered and ejected electron energies and azimuthal angles are detected in parallel using position sensitive detection, yielding true coincidence count rates of 6 Hz from a 5.5 nm thick evaporated carbon target and an incident bea...

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.

Some reaction cross sections for copper and nickel from 13.9 to 14.9 MeV neutron energy

Abstract Absolute cross sections for the reactions Cu63(n, 2n) and Cu65(n, 2n) at 14.77 MeV neutron energy and ratios of these cross sections in the range 13.86–14.77 MeV are obtained and correlated with previous data. Cross sections for the reactions Ni58(n, p), Ni58(n, np) and Ni58(n, 2n) in the range 13.86–14.88 MeV are measured. It is shown that cross sections for proton emission derived from observation of the spectra of emitted protons are in agreement with activation measurements.

Some activation measurements and a comparison with theoretical (n, 2n) cross sections and isomeric cross section ratioss

Abstract Cross sections are measured for the reactions Co59(n, 2n), Zn64(n, 2n) and Zn64(n, p) in the energy range 13.8–14.8 MeV. At 14.7±0.3 MeV a value of 20±5 μb is obtained for the S32(n, t) cross section and an upper limit of 0.1 mb for Ca40(n, t). The Co58 isometric cross section ratio for the (n, 2n) reaction and ratios reported for other reactions leading to Co58 are compared with theory and shown to be consistent with a value of approximately 4 for the parameter σ which characterises the dependence of the nuclear level density on angular momentum. Using nuclear temperatures derived from spectrum measurements(n, 2n) cross sections calculated from the Weisskopf-Ewing formula are shown to be in good agreement with experimental results for cases in which the implicit theoretical assumption (that the second particle emitted is always a neutron) is valid. A simple criterion is derived to identify cases in which the assumption is invalid.

Direct measurement of the electron momentum probability distribution in atomic hydrogen

Abstract We report here the direct measurement of the momentum distribution of electrons in the ground state of atomic hydrogen using the noncoplanar symmetric (e, 2e) technique.