A numerical method for the evaluation of the Born-Floquet amplitude fo
r laser-assisted scattering is proposed for the case when a large basi
s set is required to achieve convergence. The method is applied to ana
lyze the elastic scattering of fast electrons by the H(2s) state in a
low-intensity laser field of varying frequency and to study the resona
nt scattering with increasing laser intensity. While the behavior of a
n atom in a resonant field of low intensity is determined by virtual t
ransitions between resonant levels, at high intensity a great number o
f nonresonant virtual transitions may significantly influence laser-as
sisted processes. As a consequence, the attenuation of resonant effect
s could appear, as well as the ''local'' stabilization of the atom aga
inst ionization. [S1050-2947(97)00411-3].