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Using accurate dynamic polarizabilities of Li, Na, K and, Rb atoms, wescrutinize the thermal Casimir-Polder interactions of these atoms with a singlelayered graphene. Considering the modified Lifshitz theory for materialinteractions, we reanalyze the dispersion coefficients ($C_3$s) of the aboveatoms with graphene as functions of separation distance, gap parameter andtemperature among which some of them were earlier studied by estimating dynamicpolarizabilities of the above atoms from the single oscillator modelapproximation. All these $C_3$ coefficients have been evaluated in theframework of the Dirac model. The interactions are described for a wide rangeof distances and temperatures to demonstrate the changes in behavior with thevarying conditions of the system and also sensitivities in the interactions areanalyzed by calculating them for different values of the gap parameter. Fromthese analyses, we find a suitable value of the gap parameter for which thetrue nature of the interactions in graphene can be surmised more accurately.

Emending thermal dispersion interactions of Li, Na, K and Rb alkali metal-atoms with graphene in the Dirac model