Inner-shell excitation and ionization processes in relativistic collisions of very heavy ions are treated by a nonperturbative method for the first time. The time-dependent Dirac equation is solved by a finite-difference method for the scattering of ${\mathrm{U}}^{92+}$ on ${\mathrm{U}}^{91+}$ at a value of $E_{\mathrm{lab}}$ corresponding to 1 GeV/amu and zero impact parameter. The $K$-shell-ionization probabilities are compared with those resulting from first-order perturbation theory.

• Received 23 December 1985

DOI:https://doi.org/10.1103/PhysRevLett.56.2016