Probability of Atomic Displacement in Platinum

Exact relativistic calculations of the cross section for atomic displacement in platinum were compared with recent electron-irradiation data in an attempt to determine whether such data can reveal detailed features of the probability-of-displacement function. Eight different probability-of-displacement functions were studied: single-step, two-step, three-step, linear, parabolic, sine, sine-squared, and exponential. The parameters on which the analysis is based are the threshold energy $T_d$ for the onset of damage; the energy $T_{\frac{1}{2}}$ at which the probability equals ½; and the width $\Delta T$ of the probability function. Although the cross sections are rather insensitive to the probability function, it is possible to assign approximate limits for these parameters. In the case of platinum it appears that $\Delta T\lesssim 44$ eV, that $37 \mathrm{eV}\lesssim T_{\frac{1}{2}}\lesssim 46 \mathrm{eV}$, and that $T_d\lesssim 37$ eV. In addition it was found that the effective threshold of 37 eV, previously determined for platinum using a step function, is the energy at which the probability reaches ¼ to $\frac{1}{3}$.