Reflection Spectra of Liquid Hg, In, and Bi from 2-20 eV

Abstract

The reflection spectra of liquids Hg, In, and Bi have been measured from 2 to 20 eV and the real and imaginary parts of the dielectric constant of Hg obtained from a Kramers-Kronig inversion of the data. For the case of liquid Hg it is found that: (a) The imaginary part of the dielectric constant has a Drude-like contribution and three absorption peaks in the range 2-20 eV. (b) To account for the imaginary part of the dielectric constant in the energy range below 7 eV it is necessary to extend the Drude theory to include more realistically the effects of electron-ion interaction. When this is carried through in the pseudopotential approximation, excellent agreement between theory and experiment is obtained. (c) Both the shape and positions of two absorptions, centered at 8.3 and 10.0 eV, are consistent with the interpretation that the $5d$ levels of Hg are not appreciably broadened in the liquid. The experimental splitting of 1.7 eV is in good agreement with the observed spin-orbit splitting of the $5d^9$ $6s^2$ configuration of HgII, which is 1.87 eV. (d) There is a broad absorption centered at about 6.5 eV which at present cannot be unambiguously assigned. The possibility exists that this is an exciton state. Since the real part of the dielectric constant is zero at 7 eV, and thereby $\mathrm{Im}\left(\frac{1}{\epsilon }\right)$ has a maximum at 6.95 eV, the position of this absorption is consistent with the extra absorption recently predicted by Hopfield to arise from dynamical screening effects. (e) The data support the conclusion that liquid Hg may be described with the free-electron approximation over a wide range of energies and that the only interband excitations which occur are from the core states to the conduction state. There appear to be no analogs of the interband transitions from the conduction band to higher bands which occur in solids. For the case of liquid In and Bi it was not possible to make a Kramers-Kronig inversion of the data obtained. Nevertheless, it appears that: (a) Liquid In and Bi depart markedly from the free-electron model. (b) The reflectivity of In shows a peak centered at ∼20 eV which, by analogy with the interpretation given of the spectrum of liquid Hg, we believe to be an excitation of a $4d$ core electron. (c) As for Hg, there appear to be no interband transitions of conduction electrons to higher bands, such as occur in the solid on account of the zone structure.