Impact-parameter dependence of atomic CoulombK- shell ionization cross sections in a peaked- binary- encounter approximation

Abstract

Cross sections for the ionization of atoms by the impact of heavy, charged particles are expressed as a function of the impact parameter $b$ of the incident projectile. The ionization probability $P\left(b\right)\mathrm{}$, which is obtained in a peaked-binary-encounter approximation (BEA), is compared to several recent experiments and to the semiclassical Coulomb approximation (SCA). At high energies the BEA and plane-wave SCA models give the same result, the shape of which is proportional to a simple function of $\frac{2b}{a}$ ($a$ is the atomic radius). The functional form is independent of both projectile and target for isotropic target-electron distributions. At low energies the BEA and SCA models give similar but not identical results. The scaling properties at low energies are the same for both models. Comparison to experimental results at intermediate energies does not strongly favor either model at this time. Typically, the shape of $P\left(b\right)\mathrm{}$ is within ∼ 50% of experiment. A table of $P\left(b\right)\mathrm{}$ for the BEA model is given which, together with scaling laws, may be used to find $P\left(b\right)\mathrm{}$ for arbitrary projectiles and targets at various energies.