Dispersion C3 coefficients for the alkali-metal atoms interacting with a graphene layer and with a carbon nanotube

We evaluate separation dependent van der Waal dispersion ($C_3$) coefficients for the interactions of the Li, Na, K and Rb alkali atoms with a graphene layer and with a single walled carbon nanotube (CNT) using the hydrodynamic and Dirac models. The results from both the models are evaluated using accurate values of the dynamic polarizabilities of the above atoms. Accountability of these accurate values of dynamical polarizabilities of the alkali atoms in determination of the above $C_3$ coefficients are accentuated by comparing them with the coefficients evaluated using the dynamic dipole polarizabilities estimated from the single oscillator approximation which are typically employed in the earlier calculations. For practical description of the atom-surface interaction potentials the radial dependent $C_3$ coefficients are given for a wide range of separation distances between the ground states of the considered atoms and the wall surfaces and also for different values of nanotube radii. The coefficients for the graphene layer are fit to a logistic function dependent on the separation distance. For CNT, we have carried out a paraboloid kind of fit dependent on both the separation distances and radii of the CNT. These fitted functions,with the list of fitting parameters, can be used to extrapolate the interaction potentials between the considered alkali atoms and the graphene layer or CNT surface conveniently at the given level of accuracy.