  Supersymmetric extensions of the standard model exhibiting bilinear R-parity
violation can generate naturally the observed neutrino mass spectrum as well
mixings. One interesting feature of these scenarios is that the lightest
supersymmetric particle (LSP) is unstable, with several of its decay properties
predicted in terms of neutrino mixing angles. A smoking gun of this model in
colliders is the presence of displaced vertices due to LSP decays in large
parts of the parameter space. In this work we focus on the simplest model of
this type that comes from minimal supergravity with universal R-parity
conserving soft breaking of supersymmetry (RmSUGRA). We evaluate the
potentiality of the Fermilab Tevatron to probe the RmSUGRA parameters through
the analysis of events possessing two displaced vertices stemming from LSP
decays. We show that requiring two displaced vertices in the events leads to a
reach in m_{1/2} twice the one in the usual multilepton signals in a large
fraction of the parameter space.
