Impact-Parameter Dependence of Vacancy Production in Strongly Bound Quasimolecular States of Heavy Collision Systems

With a new method to determine the impact-parameter dependence, $P\left(\rho \right)$, of $K$-shell vacancy production, which utilizes a kinematic analysis of Doppler-broadened x-ray lines, we show that the $K$-shell excitation probability in heavy collision systems at Coulomb barrier energies is both large and narrowly peaked at small impact parameters. In particular, for $1s\sigma$ excitations, $P\left(\rho \simeq 0\right)$ can exceed a few percent with approximately half the total cross section contributed by collisions with $\rho \lesssim 40$ fm.