Electronic transitions in collinear H+ + D2 (ν = 0) → HD+ (ν = 0,1) + D via classical trajectories in complex time and complex phase space

A semiclassical treatment of electronic transitions in the collinear rearrangement H⁺ + D₂ (ν = 0) → HD⁺ (ν = 0,1) + D is presented. The treatment represents an extension of Stueckelberg's method for a single nuclear degree of freedom to collisions involving several nuclear degrees of freedom. The classical limit of scattering amplitudes (S-matrix elements) is calculated for the transition between the two adiabatic potential energy surfaces corresponding to the two lowest singlet states of HD⁺₂. S-matrix elements are constructed from trajectories propagating in complex time and complex phase space, which make localized transitions between the two surfaces by crossing their complex line of intersection. The action along each trajectory acquires an imaginary part, which contributes exponential damping to the corresponding amplitude for electronic transition.