  The article discusses the correctness of the assumption about the similarity
of molecular continuum electron functions with wave functions in electron-atom
scattering. The elastic scattering of slow particles by pair of non-overlapping
short-range potentials has been studied. The continuum wave function of
particle is represented as a combination of a plane wave and two spherical
s-waves, generated by the scattering centers. The asymptotic of this function
determines in closed form the amplitude of elastic particle scattering. It is
shown that this amplitude of scattering on a nonspherical target cannot be
correctly represented as an expansion into a series of spherical functions , as
is the case for scattering on an atom. Therefore, methods of the scattering
phase calculation based on the assumption of spherical symmetry of the
molecular potential field beyond the molecular sphere cannot be considered as
justified and reliable. So is the representation outside this sphere of the
wave function as a linear combination of the regular and irregular solutions of
the Schr\"odinger equation. It has been shown that asymptotically at great
distances from the molecule the continuum wave functions can be presented as an
expansion in a set of other, than spherical, orthonormal functions . General
formulas for these functions are obtained. The coefficients of the scattering
amplitude expansion to a series of these functions determine the scattering
phases for the molecular system under consideration. The special features of
the S-matrix method for the case of arbitrary non-spherical potentials are
discussed.

Atomic Physics