  We have implemented three variants of the exterior complex scaling procedure
in prolate spheroidal coordinates (PS-ECS) to study the dissociative electron
impact ionization-excitation of hydrogen molecule, where the emerging electrons
and one of the protons are detected in coincidence for the first time in a
recent experiment. In the first variant, designated PSECS-1B, the two target
electrons are treated ab initio while the interaction of the incident-scattered
electron is taken into account using the first term of the Born series. In the
second, PSECS-2BCD, the second Born term is introduced in the dipole
approximation. In the third approach, designated PSECS-SW, applied to the
ionization-excitation to the $2p\sigma_u$ level of H$_2^+$, the
multi-configurational single active electron approximation is used for the
target, while the interaction of the incident electron with the target is
described ab initio. Our results agree partially with those of a recent
experiment which is in progress.
