  The Casimir-Polder interaction of an atom with a metallic wall is
investigated in the framework of the Lifshitz theory. It is demonstrated that
in some temperature (separation) region the Casimir-Polder entropy takes
negative values and goes to zero when the temperature vanishes. This result is
obtained both for an ideal metal wall and for real metal walls. Simple
analytical representations for the Casimir-Polder free energy and force are
also obtained. These results are used to make a comparison between the
phenomenological potential used in the theoretical description of quantum
reflection and exact atom-wall interaction energy, as given by the Lifshitz
theory. Computations are performed for the atom of metastable He${}^{\ast}$
interacting with metal (Au) and dielectric (Si) walls. It is shown that the
relative differences between the exact and phenomenological interaction
energies are smaller in the case of a metallic wall. This is explained by the
effect of negative entropy which occurs only for a metal wall. More accurate
atom-wall interaction energies computed here can be used for the interpretation
of measurement data in the experiments on quantum reflection.
