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Full quantum mechanical models are needed to describe the ionization process by electron impact. Some empirical approaches can provide rather accurate total cross sections but are not able to calculate fully differential cross sections. First Born models describe correctly the triple differential cross section at some specific kinematics but remain unable to reproduce total cross section data at low energy. More sophisticated non first order models provide differential cross section results in good agreement with experiments but can't be applied for total cross section calculation because they are computationally intensive. We use here a first order model, which is less computationally intense to evaluate ionization cross sections. In this model a full orthogonalization of the final state to all occupied initial states of the target is enforced, the method is applied to investigate the ionization process of some atoms and small molecules. It is observed that the model is capable of reproducing quite good results especially for total cross sections. In this case the amplitudes at low incident energy are rather well reproduced highlighting an overall good agreement with experiments.