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The direct solution of the many-particle Schr\"odinger equation iscomputationally inaccessible for more than very few electrons. In order tosurpass this limitation, one of the authors [X. Oriols, Phys. Rev. Lett. 2007,98 (066803)] has recently proposed a new model to study electron-electroncorrelations from Bohm trajectories associated to time-dependent wave-packetssolutions of pseudo single-particle Schr\"odinger equations. In theaforementioned paper only the orbital exchange interaction is consideredassuming that all electrons have the same spin orientation. Then, themany-particle wave function is a complex Slater determinant of thesingle-particle wave-packets. In the present work the previous formalism isextended to study many-particle wave functions where the electrons havedifferent spin orientations.The main difficulty to treat N different electronspin orientations with time-dependent wave-packets is that one must study allthe possible N!N! products of permutations among spin states. To overcome thiscomputationally inaccessible problem, in this article the total wave functionis treated as a separated product of two many-particle wave functions, thefirst with spin up and the second with spin down. In order to numericallyjustify this approximation, the Bohm velocity in different antisymmetric totalwave-function scenarios is computed. The computational results confirms theaccurate validity of our approximation under a large number of cases.

Towards the explicit computation of Bohm velocities associated to N-electron wave-functions with arbitrary spin-orientations