This year we celebrate the 80th anniversary of the Landau-Teller model for energy exchange in a collinear collision of an atom with a harmonic diatomic molecule. Even after 80 years though, the analytic theory to date has not included in it the back-influence of the oscillator's motion on the energy transfer between the approaching particle and the molecule. This is the topic of the present paper. The back-influence can be obtained by employing classical second-order perturbation theory. The second-order theory is used in both a classical and semiclassical context. Classically, analytic expressions are derived for the final phase and action of the diatom, after the collision. The energy loss of the atom is shown to decrease linearly with the increasing energy of the oscillator. The magnitude of this decrease is a direct consequence of the back-reaction of the oscillator on the translational motion. The qualitative result is universal, in the sense that it is not dependent on the details of the interaction of the atom with the oscillator. A numerical application to a model collision of an Ar atom with a Br2 diatom demonstrates the importance and accuracy of the second-order perturbation theory. The same results are then used to derive a second-order perturbation theory semiclassical expression for the quantum transition probability from initial vibrational state ni to final vibrational state nf of the oscillator. A comparison of the theory with exact quantum data is presented for a model collision of Br2 with a hydrogen molecule, where the hydrogen molecule is considered as a single approaching particle.