  We derive the spontaneous and thermal spin-flip rates for a neutral two-level
ultra-cold atom that is coupled to a magnetic field. We apply this theory to an
atom in the vicinity of a 2-layer cylindrical absorbing dielectric body
surrounded by an unbounded homogeneous medium. An analytical expression is
obtained for the spontaneous and thermal spin-flip rate in this particular
geometry. The corresponding lifetime is then computed numerically. We compare
these theoretical lifetimes to those measured by Jones et al. [M.P.A. Jones,
C.J. Vale, D. Sahagun, B.V. Hall, and E.A. Hinds, Phys. Rev. Lett. {\bf 91},
080401 (2003)]. We investigate how the lifetime depends on the materials (skin
depths) of the cylindrical body. We also show how scaling of the dimensions of
the cylindrical body affects the lifetime when (i) the distance from the wire
to the atom is fixed and (ii) when the distance from the wire to the atom is
scaled.
