Nonadiabatic transitions when there is pseudocrossing of a group of terms

A study is made of nonadiabatic transitions when there is simultaneous pseudocrossing of a group of molecular terms. The motion of the nuclei is taken to be classical. The problem is solved by means of asymptotic methods in which the relative velocity of the atoms is a small parameter. The system of Born-Fock equations describing the interaction of the terms reduces in the neighborhood of the point of crossing of the terms to a system of master differential equations, whose solutions can be expressed in terms of Meijer $G$-functions. This can be done under fairly general assumptions about the behavior of the electron Hamiltonian in the neighborhood of the point of crossing of the terms. As an example, the amplitude for the transition probability between the outside terms when there is pseudocrossing of three terms is given.