  We analyze the scattering sector of the Hamiltonians for both gapless and
gapped graphene in the presence of a charge impurity using the 2D Dirac
equation, which is applicable in the long wavelength limit. We show that for
certain range of the system parameters, the combined effect of the short range
interactions due to the charge impurity can be modelled using a single real
parameter appearing in the boundary conditions. The phase shifts and the
scattering matrix depend explicitly on this parameter. We argue that this
parameter for graphene can be fixed empirically, through measurements of
observables that depend on the scattering data.
