  The nonperturbative expressions for the free energy and force of interaction
between a ground-state atom and a real-material surface at any temperature are
presented. The transition to the Matsubara representation is performed,
whereupon the comparison is made with the commonly used perturbative results
based on the standard Lifshitz theory. It is shown that the Lifshitz formulas
for the free energy and force of an atom-surface interaction follow from the
nonperturbative ones in the lowest order of the small parameter. Numerical
computations of the free energy and force for the atoms of He${}^{\ast}$ and Na
interacting with a surface of an Au plate have been performed using the
frequency-dependent dielectric permittivity of Au and highly accurate dynamic
atomic polarizabilities in the framework of both the nonperturbative and
perturbative theories. According to our results, the maximum deviations between
the two theories are reached at the shortest atom-surface separations of about
1nm. Simple analytic expressions for the atom-surface free energy are derived
in the classical limit and for an ideal-metal plane. In the lowest order of the
small parameter, they are foundX// in agreement with the perturbative ones
following from the standard Lifshitz theory. Possible applications of the
obtained results in the theory of van der Waals adsorption are discussed.
