Ionization transition states of the hydrogen molecular ion in external electric fields

The transition state is fundamental to modem theories of reaction dynamics. While transition state theory (TST) has been used mainly in chemical physics, it can be applied to any problem that involves some form of transformation, including half-scattering events such as ionization of Rydberg atoms. In this paper, we construct the ionization transition states of H-2(+) in an external electric field. In the process, we encounter and eliminate small divisors in our perturbation expansion and monitor its convergence using a new error criterion. The procedure is readily applicable to multiple Coulomb centres at large separations characteristic of Rydberg plasmas.