Tunneling ionization of atoms with excitation of the core

A general formula is obtained for the probability of tunneling ionization of an atom accompanied by excitation of the core. This formula is a generalization of the Carlson formula for the probability of a single-photon two-electron transition in atoms. The limiting case of this formula, just as that of the Carlson formula, is the well-known random-perturbations approximation. Numerical results are presented for Zn, Sr, and Cd atoms. For these atoms the contribution of the excited states of singly charged ions to the probability of the formation of doubly charged ions is a nonmonotonic function of the laser radiation intensity. Analysis of the tunneling ionization of molecules shows that with overwhelming probability an ion is formed in the ground vibrational state, while for the standard photoionization the distribution over vibrational states is determined by the Franck-Condon factors.