Abstract
Dirac fermions interacting with a cylindrically symmetric quantum dot potential created in single and bilayer graphene are not confined but form quasibound states. The broadening of these quasibound states (i.e., the inverse of their lifetimes) decreases (increases) with the orbital momentum of the electron in the case of graphene (bilayer). Quasibound states with energy below (above) the barrier height are dominantly electronlike (holelike). 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.
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