The paper presents the results of measurement of the total cross sections for reactions 4,6He + Si and 6,7,9Li + Si in the beam energy range 5−50 A∙MeV. The enhancements of the total cross sections for reaction 6He + Si compared with reaction 4He + Si, and 9Li + Si compared with reactions 6,7Li + Si have been observed. The performed microscopic analysis of total cross sections for reactions 6He + Si and 9Li + Si based on numerical solution of the time-dependent Schrödinger equation for external neutrons of projectile nuclei 6He and 9Li yielded good agreement with experimental data.