[en] As previously shown [B. Arezki, Y. Boudouma, P. Benoit-Cattin, A.C. Chami, C. Benazeth, K. Khalal, M. Boudjema, J. Phys.: Condens. Mat. 10 (1998) 741, K. Khalal-Kouache, A.C. Chami, M. Boudjema, P. Benoit-Cattin, C. Benazeth, Y. Boudouma, Nucl. Instr. and Meth. B 183 (2001) 279], energy spectra of scattered particles from amorphous solid surface can be deduced from angular distributions of the total path length of the projectiles. In preceding papers [K. Khalal-Kouache, A.C. Chami, M. Boudjema, P. Benoit-Cattin, C. Benazeth, Y. Boudouma, Nucl. Instr. and Meth. B 183 (2001) 279, K. Khalal-Kouache, A. Mekhtiche, A.C. Chami, M. Boudjema, Surf. Coat. Technol. 201 (2007) 8420], a model based on the transport theory was used to simulate the scattering of slow ions by a solid target. Angular distributions of the total path length were computed and compared, in absolute value, to those simulated using a Monte Carlo code. A good agreement was obtained except for the highest values of the total path length L. In the transport theory, the variation of the scattering cross section versus energy during the slowing down of the particle was not taken into account. The purpose of this contribution is to take into account this effect within the model. The obtained results are found to be in agreement with Monte Carlo computation for angular distributions of the total path length and for energy spectra of the scattered ions