  Dirac fermions interacting with a cylindrically symmetric quantum dot
potential created in single and bilayer graphene are not confined but form
quasi-bound states. The broadening of these quasi-bound states (i. e. the
inverse of their lifetimes) decreases (increases) with the orbital momentum of
the electron in the case of graphene (bilayer). Quasi-bound states with energy
below (above) the barrier height are dominantly electron(hole)-like. A
remarkable decrease of the energy level broadening is predicted for electron
energies close to the barrier height, which are a consequence of the total
internal reflection of the electronic wave at the dot edge.
