Observation of strong relativistic and distorted-wave effects in $(e,2e)$ electron-momentum spectroscopy of mercury

We report a measurement of the valence orbital-momentum profiles of mercury (Hg) using a high-sensitivity binary $(e,2e)$ electron-momentum spectrometer at incident energies of 600 and 1200 eV plus the binding energy. The $6s_{1/2}$ orbital and the spin-orbit components of $5d_{5/2}$ and $5d_{3/2}$ orbitals are well separated in the measured binding-energy spectra. The experimental momentum distributions for the individual orbitals and the branching ratio of $5d_{5/2}$ to $5d_{3/2}$ are obtained and compared with predictions from a plane-wave impulse approximation (PWIA) in which the orbital wave functions are calculated using the nonrelativistic (NR) and spin-orbital (SO) relativistic theories. The SO relativistic calculations are in better agreement with experiment than the NR, indicating clearly the importance of relativistic effects in the electronic structure of Hg. We also observe some discrepancies between experiment and PWIA calculations in the high-momentum region of $6s_{1/2}$ and the low-momentum region of $5d$ orbitals which display a dynamic dependence on the impact energy. These discrepancies become smaller at a higher energy of about 1200 eV and thus can be qualitatively assigned to the distorted-wave effect in the $(e,2e)$ reaction of Hg.

Figure 1

Measured binding-energy spectrum summed over all azimuthal angles $\varphi$, obtained at an impact energy of about 1200 eV. The lines represent Gaussian fits to the data.

Figure 2

Comparison of momentum profiles between experiment and theory for the $6s_{1/2}$ orbital of Hg in the linear plots of (a) and the logarithmic plots of (b). The solid circles and opened diamonds with error bars are the experimental data at impact energies of about 600 and 1200 eV, respectively. Solid lines: Spin-orbital (SO) relativistic calculation. Dashed lines: Nonrelativistic (NR) calculation. The short dashed curves are a renormalization of the NR calculation.

Figure 3

Comparison of one-electron-momentum profiles between experiment and theory for $5d_{5/2}$ in (a), and $5d_{3/2}$ in (b); the total $5d$ cross sections are shown in (c). The solid circles and open diamonds with error bars are the experimental data at impact energies of about 600 and 1200 eV, respectively. Solid lines: Spin-orbital (SO) relativistic calculation. Dashed lines: Nonrelativistic (NR) calculation.

Figure 4

The branching ratio of $5d_{5/2}:5d_{3/2}$ cross sections as a function of the momentum for Hg. Solid lines: Spin-orbital (SO) relativistic calculation. Dashed lines: Nonrelativistic (NR) calculation. The open diamonds with error bars represent the experimental data at an impact energy of about 1200 eV.