We present in detail an alternative experimental set-up and data analysis, based on the electron-recoil ion and recoil ion-projectile coincidence techniques, that enable the measurement of partial pure ionization and partial charge exchange cross sections for an effusive gas jet set-up, where the absolute target density and recoil ion efficiency cannot be measured directly. The method is applied to the ionization of helium atoms due to collision with partially stripped C(3 +) projectiles. In order to check the method, the results are compared to data available in the literature where the target density and recoil ion detection efficiency were measured directly. The pure ionization channel is compared to the electron capture channel.