  A 2-level spin-system of cold sodium atoms is proposed. Both the cases that
the system has arrived at thermo-equilibrium and is in the early stage of
evolution have been studied. This system is inert to the magnetic field $B$ in
general but very sensitive in a narrow domain around $B=B_0$, where $B_0$ can
be predicted and is tunable. A characteristic constant $\gamma=0.278466$
dedicated to various 2-level systems is found, and leads to a upper limit for
the internal energy $U$ of the whole system so that $U\leq\gamma k_B T$. This
limit is considerably lower than the energy assigned to the spatial motion of
only a single particle. Under thermo-equilibrium, the populations of
spin-components measured at distinct $T$ converge to a fixed value when
$B=B_0$. The period and amplitude of population oscillation are found to be
seriously affected by the special sensitivity against $B$. Rich messages on the
dynamic parameters could be obtained via experimental measurements of these
systems.
