We start from the spinning electron model by Barut and Zanghi, which h
as been recently translated into the Clifford algebra language. We ''c
omplete'' such a translation, first of ah, by expressing in the Cliffo
rd formalism a particular Barut-Zanghi (BZ) solution, which refers (at
the classical limit) to an ''internal'' helical motion with a time-li
ke speed (and is here shown to originate from the superposition of pos
itive and negative frequency solutions of the Dirac equation). Then, w
e show how to construct solutions of the Dirac equation describing hel
ical motions with light-like speed, which meet very well the standard
interpretation of the velocity operator in the Dirac equation theory (
and agree with the solution proposed by Hestenes, on the basis - howev
er - of ad-hoc assumptions that are unnecessary in the present approac
h). The above results appear to support the conjecture that the zitter
bewegung motion (a helical motion, at the classical limit) is responsi
ble for the electron spin.