  We derive scaling laws for the spin decoherence of neutral atoms trapped near
conducting and superconducting plane surfaces. A new result for thin films
sheds light on the measurement of Y.J. Lin, I. Teper, C. Chin, and V.
Vuleti\'{c} [Phys. Rev. Lett. \textbf{92}, 050404 (2004)]. Our calculation is
based on a quantum-theoretical treatment of electromagnetic radiation near
metallic bodies [P.K. Rekdal, S. Scheel, P.L. Knight, and E.A. Hinds, Phys.
Rev. A \textbf{70}, 013811 (2004)]. We show that there is a critical
atom-surface distance that maximizes the spin relaxation rate and we show how
this depends on the skin depth and thickness of the metal surface. In the light
of this impedance-matching effect we discuss the spin relaxation to be expected
above a thin superconducting niobium layer.
