Abstrakt
The energy-dependent frame transformation theory of Gao and Greene [H. Gao and C.
H. Greene, Phys.
Rev. A 42, 6946 (1990)] is extended to yield a quantitatively accurate description of the dissociative recombination process.
Evidence is presented to show that direct application of the original theory leads to inaccurate cross sections. A major revision, based on an interaction-free backpropagation of the Born-Oppenheimer solutions, markedly improves the frame transformation theory, reducing its average error by orders of magnitude.
The original theory and its extension are tested on the previously explored two-dimensional (2D) model that is tailored to describe the singlet ungerade states of molecular hydrogen. The 2D model can be solved exactly (within the numerical accuracy) without implementing the Born-Oppenheimer approximation.
These exact results then serve as a benchmark for the frame transformation theory developed in this paper.