Pseudo-adiabatic region

The interactions neglected in the adiabatic approximation should be considered in the region where the Massey parameter is not high, i.e. where the potential surfaces either cross or pseudo-cross. For these regions, the problem is formulated in terms of coupled equations for wave functions describing nuclear motions over several potential surfaces. If, however, the motion of nuclei can be considered as classical, these equations can be substantially simplified. The semiclassical version of an adiabatic function T (q, Q) (Eq. (9.3)) reads... 

Consider now the. case of pseudo-crossing. Here, the adiabatic terms look like hyperbolae in the region of mutual rapproachment. If we represent the asymptotes of these hyperbolae by straight lines, = —Fi(Q — Qq) and Ug == —F2(Q — Qo), and 2 a is the minimum splitting of the adiabatic terms, then in the vicinity of pseudo-crossing the adiabatic terms may be represented in the form... 

---