Search

The dielectric function is often known in the optical limit (zero momentum) but knowledge away from zero momentum is required for the calculation of many physical properties, such as ion stopping and inelastic mean free path. We review the several extension schemes and compare the results with the available literature and investigate in particular the effect of the extension scheme on the calculated proton stopping for the case of Li.

Many aspects of the interaction of charged particles with matter can be expressed in terms of the dielectric function e ( q , ω ) . The dielectric function is relatively well known in the optical limit ( q = 0 ) but, for example, stopping power calculations require the knowledge of the dielectric function for q ≠ 0 . Several approaches have been used to extend the dielectric function to q ≠ 0 for both the valence electrons, using variations of the Lindhard dielectric function and the core levels where an atomic description can be used. The intermediate case of shallow core levels is somewhat problematic. Here collective effects modify the atomic picture, and the hydrogenic approximation of the wave function is less accurate. In this paper we describe a new extension scheme of the contribution to the energy loss function of shallow core levels to q ≠ 0 and show that tor Al and Si it describes the experimental stopping data somewhat better than previous approaches. It also describes reasonably well the proton and electron induced ionization cross section of these shallow core levels. Lastly we investigate the dielectric function in the limit of high momentum, where it can be interpreted as a Compton profile. An approximation scheme in terms of Mermin dielectric function with an amplitude that depends on q works in all cases quite well.

The Drude dielectric function is a simple way of describing the dielectric function of free electron materials, which have an uniform electron density, in a classical way. The Mermin dielectric function describes a free electron gas, but is based on quantum physics. More complex metals have varying electron densities and are often described by a sum of Drude dielectric functions, the weight of each function being taken proportional to the volume with the corresponding density. Here we describe a slight variation on the Drude dielectric functions that describes insulators in a semi-classical way and a form of the Levine-Louie dielectric function including a relaxation time that does the same within the framework of quantum physics. In the optical limit the semi-classical description of an insulator and the quantum physics description coincide, in the same way as the Drude and Mermin dielectric function coincide in the optical limit for metals. There is a simple relation between the coefficients used in the classical and quantum approaches, a relation that ensures that the obtained dielectric function corresponds to the right static refractive index. For water we give a comparison of the model dielectric function at non-zero momentum with inelastic X-ray measurements, both at relative small momenta and in the Compton limit. The Levine-Louie dielectric function including a relaxation time describes the spectra at small momentum quite well, but in the Compton limit there are significant deviations.