  We consider a system consisting of an atom in the approximation of a harmonic
oscillator of frequency $\bar{\omega}$, coupled to the scalar potential inside
a spherical reflecting cavity of radius R. We use {\it dressed} states
introduced in a previous publication [Andion, Malbouisson and Matos Neto, J.
Phys. A34, 3735 (2001)], which allow a non-perturbative unified description of
the atom radiation process, in both cases, of a finite or an arbitrarily large
cavity. We perform a study of the energy distribution in a small cavity, with
the initial condition that the atom is in the first excited state and we
conclude for the quasi-stability of the excited atom. For instance, for a
frequency $\bar{\omega}$ of the order $\bar{\omega}\sim 4.00\times 10^{14}/s$
(in the visible red), starting from the initial condition that the atom is in
the first excited level, we find that for a cavity with diameter $2R\sim
1.0\times 10^{-6}m$, the probability that the atom be at any time still in the
first excited level, will be of the order of 97%. For a typical microwave
frequency $\bar{\omega}\sim 2,00\times 10^{10}/s$ we find stability in the
first excited state also of the order of 97% for a cavity radius $R\sim
1.4\times 10^{-2}m$.
