A systematic study was done in order to relate the J-F characteristic variation with three emission mechanisms: tunneling, thermionic, and ballistic. All three are now effective during the field emission from cathodes with work function Phi less than 2 eV. The current density is computed using the transmission probability for an electron to cross the barrier between the electron sea of the cathode and the vacuum. The corresponding Schrodinger equation is solved by means of the self-consistent Lippmann-Schwinger equation, with values of the effective potential corrected with the image potential between the cathode and the anode and resolved by spatial discretization. This method allows computing the exact current within a zero emitted current approximation. It fills the gap leave by the former analytical resolution by Murphy and Good [Phys. Rev. 102, 1464 (1956)]. The ln(J/F-2) vs (1/F) plot shows three zones for the current variation. The first zone, corresponding to low applied electric fields, shows a nonlinear variation of the field emission current. It is followed by a second zone having a linear variation with a slope proportional to Phi(3/2). The third zone, concerning high field values, indicated saturation behavior specific to a field induced ballistic emission. (c) 2007 American Vacuum Society.