We have found the complete energy spectrum and the corresponding eigenfunctions of the recently proposed Dirac oscillator. We found the electromagnetic potential associated with its interaction term.This exactly soluble problem has a hidden supersymmetry, responsible for the special properties of its energy spectrum. We calculate the related superpotential and~e discuss the implications of this supersymmetry on the stability of the Dirac sea.PACS numbers: 11.10. Qr, 11.30.Pb, 12.40. gq In a recent work, Moshinsky and Szczepaniak' introduced a very interesting potential in the Dirac equation. Following the original Dirac procedure they introduce a system whose Dirac Hamiltonian is linear in both p and r; consequently, its nonrelativistic approximation is quadratic in r as in the case of the harmonic oscillator. This property is in fact the origin of the name Dirac oscillator. The system is then, excepting for a strong spinorbit coupling term, the square root of the harmonic oscillator in the same sense as the Dirac equation is the square root of the Klein-Gordon equation. The Hamiltonian of the system is obtained by introducing in a nonminimal way the external potential with the substitution i(rilir/rlt) =Hiir= [a (p imrupr)-+mpl lir.(2)The interaction introduced by Eq. (1) has been shown to correspond to an anomalous magnetic interaction. In fact, if we select a frame-dependent vectorthen the interaction term in Eq.(2) can be put in the form imcoa r =cr"'x"u, ;(4) consequently, Eq.(2) can be written in the manifestly covariant form [y"p"-m+ (ke/4m )cr"'F", l @=0, with (s) F""= (u "x"u'x"), p p i mrupr, where m is the mass of the particle and co is the oscillator frequency. We follow the usual conventions concerning the Dirac matrices. The Dirac equation for the system is then (11'i c =1) Dirac oscillator. The electromagnetic potential can be cast in the form (7) but, taking advantage of the gauge invariance of the electromagnetic interaction and selecting the gauge l= -, ' x (u x), we can write Eq. (7) in the equivalent forms For either selection the electromagnetic field takes the form E=mror and 8 0, expressions which are, of course, frame dependent. In this way we have shown that the interaction occurs as if it were produced by an infinite sphere carrying a uniform charge-density distribution, resulting in a linearly growing electric field. The interaction term introduced by Eq. (1) is interesting in its own right, but also has applications in quantum chromodynamics (QCD). For example, if we think of the construction of quark-confinement models, the linearly growing interaction characteristic of the system can be regarded as an effective chromoelectric field, at least if we think that the color-field lines are constrained to strings of constant volume instead of constrained to constant cross section, as is usually supposed. Also, it can be useful for estimating the quark masses.These considerations make the Dirac oscillator important to QCD models, as we will discuss in a forthcoming paper. Moshinsky and Sz...