Universal Cross Sections forK-Shell Ionization by Heavy Charged Particles. I. Low Particle Velocities

Experimental $K$-shell ionization cross sections are reported for low-velocity heavy projectiles of atomic number small compared to the target atomic number. For such projectile-target combinations, the Coulomb interaction between the projectile nucleus and the $K$-shell electrons dominates the $K$-shell ionization process at all projectile velocities. The data can disagree by orders of magnitude with the primary predictions of the nonrelativistic quantum theory in the plane-wave Born approximation. Important physical processes are shown to be at the root of the discrepancies. They derive from the finite charge of the moving projectile, and thus do not contribute in the plane-wave Born approximation. They are the Coulomb deflection of the projectile in the field of the target nucleus and the perturbation of the target atomic states by the projectile. A theory for these processes is developed in an approximate manner. When incorporated with the theory in the plane-wave Born approximation, it accounts quantitatively for the data. A method results for reducing cross-section data in a comprehensive way. A universal graph of cross sections emerges which, in effect, constitutes an extrapolation of the data to the conditions of zero projectile charge. It comprises cross sections ranging over six orders of magnitude measured on different targets for various projectiles with a wide range of velocities, mostly below the mean $K$-shell velocities. The locus of this universal graph coincides with the prediction of the plane-wave Born approximation.