Depencences of the results of the first Born approximation on the choice of the approximate wave functions of helium are examined in collision processes of electron with helium. So far the wave function Ψ∼exp {-(27/16a0)(r1+r2)} has been used almost exclusively as the analytical wave function of the ground state of helium. In this paper Ψ∼exp {-(ζ/a0)r1-(ζ'/a0)r2} + exp {-(ζ'/a0)r1-(ζ/a0)r2} is used. It is found that the theoretical results are quite sensitive to the values of the parameters ζ and ζ' and with suitable choices of ζ and ζ' we obtain considerable improvements within the first Born approximation.