We present a two-channel model of the vibrational relaxation (VR) of H-2 molecule, nu=1, j=0-->nu=0, j=0, in collisions with a He atom over a broad energy range, bridging the gap between the Landau-Teller and Bethe-Wigner limits. The model is based on the generalized Landau approach for calculating the VR transition matrix element. The analytical expression for the VR cross section qualitatively reproduces the energy dependence of the numerically calculated cross section and identify the key parameters that determine this energy dependence: the steepness of the repulsive part of the potential, the depth of the potential well, and the s-wave elastic scattering length. On the basis of our findings and available data from the literature, we discuss the manifestation of the attractive interaction on the qualitative features of the VR cross sections and rate constants over a wide range of energies and temperatures. (C) 2003 American Institute of Physics.