Use of the momentum approximation in classical scattering calculations

Abstract

The validity range of the momentum approximation in binary collisions : s investigated. It is shown that at high energies, E ≳ 10 · Z ₁ Z ₂ e ²/a _TF, the approximation is even applicable to scattering angles ϑ as large as 60 degrees. An empirical formula for the evaluation of the momentum approximation employing the Thomas-Fermi-Moliére potential is given. It reduces the computer time to calculate ϑ to ∼⊥₁₀ of the time consumed in using the standard algebraic functions appearing in the momentum approximation.