Moliere potential

In Fig. 7 the purely repulsive Moliere potential is compared with the (partly) attractive Morse potential. It is to be noted from this comparison that the Morse (like the Lennard-Jones) potential, while providing a realistic description of the attractive part of the interaction, becomes insufficient at low intemuclear separations where the purely repulsive potentials are more adequate. While more sophisticated potentials calculated, for example, by employing the Dirac-Fock-Slater (DFS) method (Eckstein etai, 1992), have recently become available, such potentials are generally more complicated and are available only in numerical form, and are thus not very handy for the calculations of interest here. For Si-Si collisions, the interaction potential, being repulsive for small and attractive for... 

Figure 8 compares the Dirac-Fock-Slater potential for Si-Si collisions with the corresponding Moliere potential. While for low intemuclear separations the two potentials are almost indistinguishable from each other, significant differences occur for medium and large intemuclear separations, where both potentials are weak. Nevertheless, trajectories calculated with these two potentials differ significantly at large impact parameters, where the DFS potential becomes attractive (Fig. 9). 

The 4>(r) can be expressed in various fomis [30], e.g. the Bolir, Bom-Mayer, Thomas-Femii-Firsov and Moliere models, as well as the universal potential of Ziegler, Biersack and Littmark known as the ZBL potential [31]. The ZBL potential fiinction is expressed as... 

In conclusion, the repulsive interactions arise from both a screened coulomb repulsion between nuclei, and from the overlap of closed inner shells. The former interaction can be effectively described by a bare coulomb repulsion multiplied by a screening function. The Moliere function, Eq. (5), with an adjustable screening length provides an adequate representation for most situations. The latter interaction is well described by an exponential decay of the form of a Bom-Mayer function. Furthermore, due to the spherical nature of the closed atomic orbitals and the coulomb interaction, the repulsive forces can often be well described by pair-additive potentials. Both interactions may be combined either by using functions which reduce to each interaction in the correct limits, or by splining the two forms at an appropriate interatomic distance . 

Moliere central potential — an analytical expression to approximate the repulsive potential between two atoms at short range. The universal pairwise potential requires only two parameters — the atomic numbers of the interacting atoms. 

In a previous study [39] various ion models were tested and a new model was proposed, which was called the Moliere-ion potential . Due to its simplicity and good comparison with other models (including Dedkov s model for ions [43] and Moliere and Thomas-Fermi models for neutral atoms [44]) we have used this model throughout this study. 

Fig. 2. Comparison of the Coulomb potential and the screened Thomas-Fermi-Moliere (TFM) potential for the scattering of He ions off Ni. The typical impact parameter range of Rutherford back scattering (RBS) and low energy ion scattering (ISS or LEIS) are indicated by arrows [8]. Reprinted with permission from E. Taglauer and John Wiley Sons Ltd., 1997.

---