Superluminal Tunneling of a Relativistic Half-Integer Spin Particle through a Potential Barrier

This paper investigates the problem of a relativistic Dirac half-integer spin free particle tunneling through a rectangular quantum-mechanical barrier. If the energy difference between the barrier and the particle is positive, and the barrier width is large enough, there is proof that the tunneling is always superluminal. For antiparticle states, the tunneling may be either subluminal or superluminal instead, depending on the barrier width. These results derive from studying the tunneling time in terms of phase time. For particle states these are always negatives while for antiparticle states they are always positives, whatever the height and width of the barrier. The scattering also leads to an anomalous distortion of the Dirac spinor that tends to disappear as the particle velocity approaches the speed of light. Moreover, the phase time tends to zero, increasing the potential barrier both for particle and antiparticle states. This agrees with the interpretation of quantum tunneling that the Heisenberg uncertainty principle provides. This study’s results are innovative with respect to those available in the literature. Moreover, they show that the superluminal behaviour of particles occurs in those processes with high-energy confinement.