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By inferring the dynamic permittivity of different material media from theobservations and calculating dynamic electric dipole polarizabilties of the Lithrough Cs alkali atoms, precise values of $C_3$ coefficients were estimated inPhys. Rev. A {\bf 89}, 022511 (2014) and Phys. Lett. A {\bf 380}, 3366 (2016).Since significant contribution towards the long range van der Waals potentialis given by the quadrupole polarization effects, we have estimated the $C_5$coefficients in this work arising from the quadrupole polarization effects ofall the alkali atoms interacting with metal (Au), semiconductor (Si) and fourdielectric materials (SiO$_2$, SiN$_x$, YAG and sapphire). The required dynamicelectric quadrupole (E2) polarizabilities are evaluated by calculating E2matrix elements of a large number of transitions in the alkali atoms byemploying a relativistic coupled-cluster method. Our finding shows thatcontributions from the $C_5$ coefficients to the atom-wall interactionpotentials are pronounced at short distances (1$-$10 nm). The $C_3$coefficients of Fr atom interacting with the above material media are alsoreported. These results can be useful in understanding the interactions ofalkali atoms trapped in different material bodies during the high-precisionmeasurements.

Accurate estimate of $C_5$ dispersion coefficients of the alkali atoms interacting with different material media