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The van der Waals and Casimir-Polder interaction of different atoms withgraphene is investigated using the Dirac model which assumes that the energy ofquasiparticles is linear with respect to the momentum. The obtained results forthe van der Waals coefficients of hydrogen atoms and molecules and atoms ofmetastable He${}^{\ast}$ and Na as a function of separation are compared withrespective results found using the hydrodynamic model of graphene. It is shownthat, regardless of the value of the gap parameter, the Dirac model leads tomuch smaller values of the van der Waals coefficients than the hydrodynamicmodel. The experiment on quantum reflection of metastable He${}^{\ast}$ and Naatoms on graphene is proposed which is capable to discriminate between the twomodels of the electronic structure of graphene. In this respect the parametersof the phenomenological potential for both these atoms interacting withgraphene described by different models are determined.

Comparison of the hydrodynamic and Dirac models of the dispersion interaction between graphene and H, He${}^{\ast}$, or Na atoms