In the present paper we derive the new generalized energy sudden appro
ximation theory and the generalized adiabatic nuclei theory of atom-di
atomic molecule scattering through the transformation of the full Gree
n operator. The derivation is quite simple and it is different from pr
evious methods. The formulation has an obvious physical meaning and sh
ould lead to accurate numerical results. Numerical results for H(e)-H-
2 scattering are given and compared with previous results.