Dependence of theK-shell ionization probability on small impact parameters with 1- and 2-MeV protons

The absolute impact-parameter dependence of $K$-shell ionization probability $I\left(p\right)\mathrm{}$ has been measured in the range ${10}^{-12\mathrm{}}$-${10}^{-11\mathrm{}}$ cm at incident proton energies of 1 and 2 MeV with Al, Cu, and Ti targets. In the first part we give a condensed survey of previous results showing that a detailed investigation of $I\left(p\right)\mathrm{}$ behavior at very small impact parameters is required for a better understanding of this problem. Such a study provides a useful check on the accuracy of classical and semiclassical ionization theories in a region where they are more likely to fail. Our results, obtained by a coincidence method, are compared with the presently available theories: the binary-encounter approximation and the semi-classical approximation. A systematic deviation is found between experimental and theoretical data which is not accounted for when relativistic effects and the actual projectile trajectory are included in the binary-encounter-approximation model.