Deviations from Rutherford-scattering cross sections

Abstract

Recent experiments have demonstrated the utility of high-energy backscattering for thin-film analysis, often exploiting elastic-scattering resonances to increase sensitivity to low- Z elements. However, higher- Z elements may also exhibit deviations from Rutherford scattering, and it is desirable to examine the problem theoretically so that such deviations can be predicted and corrected for. We have used the optical-model computer code SCAT86 to calculate the projectile energy E nr at which the scattering cross section begins to deviate from its Rutherford value. The results agree well with data for both alpha particle and proton projectiles, but the interaction potentials are complicated, and the program does not provide an analytical predictive formula. We have therefore developed a simple classical model which treats the interaction as a sum of Coulomb and Yukawa-like potentials. For small deviations from Coulomb scattering, the problem can be solved analytically, providing a simple expression for E nr which agrees well with both experimental data and SCAT86. The classical approach is valid for all but small-angle forward scattering and can easily be extended to heavier projectiles such as Li.