In radiation damage simulations, atoms can come much closer together than in any other application. Interatomic force models are often parameterized on data that ignore very short-ranged interactions, and the physics of core wavefunction overlap is seldom well described by extarpolation.

In radiation damage, we are normally dealing with a case where two atoms come very close together, but the density of the material does not change. By anal­ogy with a free electron gas, we see that the energy cost of compressing the valence wavefunctions is important for high-pressure isotropic compression but absent in the collision scenario. In the first case, the ‘short range’ repulsion is a many-body effect, while in the second case, it is primarily pair­wise. Thus, we should not expect that fitting to the high-pressure equation of state will give a good representation of the forces in the initial stages of a cascade, or even for interstitial defects. Indeed, when there was no accurate measurement of interstitial

formation energies, older potentials gave a huge range of values based on extrapolation of near-equilibrium data and uncertain partition of energy between pairwise and many-body terms. Accurate values for these forma­tion energies are now available from first principles calculations and are incorporated in the fitting; there­fore, a symptom of the problem is resolved.

At very short range, the ionic repulsive interaction can be regarded as a screened-Coulombic interac­tion, and described by multiplying the Coulombic repulsion between nuclei with a screening function W(r/a):

Z1 Z2e2 4ne0r where w(r) ! 1 when r! 0 and Z1 and Z2 are the nuclear charges, and a is the screening length. The most popular parameterization of w is the Biersack — Ziegler potential, which was constructed by fitting a universal screening function to repulsions calculated for many different atom pairs (Ziegler 1985). The Biersack-Ziegler potential has the form

W(x) = 0.1818e~32x + 0.5099e~09423x

+ 0.2802e~0:4029x + 0.02817e~0:2016x

where

0. 8854a0

a = zpTzp

and x = r/a and a0 = 0.529 A is the Bohr radius.

This potential must then be joined to the longer ranged fitted potential. There are many ways to do this, with no guiding physical principle except that the potential should be as smooth as possible. Typical implementations ensure that the potential and its first few derivatives are continuous.

The short-range interactions arising from high pressure come mainly from isotropic compression, and should be fitted to the many-body part. To achieve this division in glue models, the function F(p) should become repulsive at large p, but f(r) should not become very large at small Rj.