  At low temperatures and 3He concentrations below 6.6 %, there is experimental
evidence about the existence in liquid helium mixtures, of stable vortices with
3He-rich cores. When the system is either supersaturated or submitted to a
tensile strength, vortices lose stability becoming metastable and eventually
completely unstable, so that their cores freely expand. Within a density
functional approach, we have determined the pressure-3He concentration curve
along which this instability appears at zero temperature.
