Tunnelling through the self-potential of a Nielsen-Olesen vortex

We calculate the self-potential of a test charge in the presence of a Nielsen-Olesen vortex. The self-potential arises from the non-trivial spatial geometry of the vortex, which has the form of a snub-nosed cone. A potential barrier of about 107 GeV is found. By solving the Dirac equation in the presence of this potential we calculate the tunnelling through the barrier. Whilst the barrier is very large, it is also narrow, resulting in a very small suppression of the fermion wave function. The implications for string catalysis of baryon decay are discussed. (orig.)