We present a more efficient way of treating polarization effects in the sca
ttering of low-energy electrons by molecules within the Schwinger multichan
nel (SMC) method. We propose to expand the scattering wave function in a se
t of functions of N + 1 electrons that describe the scattering in an effect
ive way, which allows the use of a small number of functions to describe th
e polarization effects. As a first test, we apply the method to the scatter
ing of electrons by the H-2 molecule. We calculate elastic integral and dif
ferential cross sections, and we obtain excellent results with a reduction
in the number of configurations of up to 98% when compared to the tradition
al method used in the SMC method. This is a substantial size reduction of a
ll matrices involved in the SMC method and, as a consequence, it represents
a promising technique for treating more complex molecular systems.