Electron scattering at high momentum transfer from methane: Analysis of line shapes

Abstract

The measurement of the energy distribution of keV electrons backscattered elastically from molecules reveals one or more peaks. These peaks are at nonzero energy loss and have an intrinsic width. The usual interpretation of these measurements is attractively simple and assumes billiard-ball-type collisions between the electron and a specific atom in the molecule, and the scattering atom is assumed to behave as a free particle. The peak position is then related to the mass of the scattering atom, and its width is a Compton profile of the momentum distribution of this atom in the molecule. Here we explore the limits of the validity of this picture for the case of electrons scattering from methane. The biggest discrepancy is found for electrons scattering from carbon. For electrons scattering from hydrogen the effects are substantial at relatively low incoming energies and appear to decrease with increasing momentum transfer. The discrepancy is analyzed in terms of the force the atom experiences near the equilibrium position.

Electron scattering as a tool to study zero-point kinetic energies of atoms in molecules

“…The results vs T are plotted in Fig. 4 together with one measured value at 295 K obtained [4,36] using the ECS technique, K e (H) = 151 ± 4 meV, revealing a good agreement with the calculations. This value is in fact an average over 6 measured values using different incident energies between 0.75 keV and 2.5 keV.…”

“…1 depicts the Doppler broadened shape of electrons scattered at 135°from the H-atom (of a solid ammonia (NH 3 ) sample) at 80 K using a 2.5 keV incident e-beam. It shows the energy separation between the peak intensities of the electrons scattered from N-and H-atoms in NH 3 , illustrating the type of resolution required in such measurements [4]. As the N peak is much narrower than the H peak, it is immediately clear that the width of the latter is dominated by Doppler broadening.…”

“…Few methods were reported in the literature in which a direct measurement of the atomic kinetic energies was carried out: (1) Nuclear resonance photon scattering (NRPS) [1], (2) neutron compton scattering (NCS) [2,3], and (3) electron compton scattering (ECS) [4][5][6]. Here we use the abbreviation ECS, to emphasize the similarities with the well-established NCS technique.…”

“…Thus, the scattering process operates as a mass analyzer causing the energy spectrum of the deflected electrons to split according to the masses of the scattering atoms of the molecule. In order for the energy separations between the scattering peaks to be resolved, a high resolution spectrometer had to be used [4]. The Doppler broadening D = (4K e E rec ) 1/2 of each electron line is related to the mean kinetic energy K e of the scattering atom and to the recoil energy E rec ; it provides information on K e in the same fashion as that of NCS [19].…”

Comparison between electron and neutron Compton scattering studies

“…Because of the high n-H scattering cross section, the NCS method is best suited for studying the kinetic energy of Hydrogen in H-containing systems such as H 2 O and CH 2 using incident neutron energies of 10 eV to 200 eV [3]. In spite of the small e-H scattering cross section (which follows the Rutherford Z 2 formula), the ECS method was used for studying several targets at energies between ~ 1 -6 keV such as H 2 O [4], CH 2 [5], NH 3 [6], CH 4 [7] as well as graphite and diamond [8] and SiO 2 at energies up to 40 keV. The measured atomic kinetic energies using the NCS and ECS techniques were found to be in fair agreement with each other and with calculated values as will be shown below.…”