  We introduce a spin model which exhibits the main properties of a Kerr medium
to describe an intensity dependent coupling between a two-level atom and the
radiation field. We select a unitary irreducible representation of the su(2)
Lie algebra such that the number of excitations of the field is bounded from
above. We analyze the behavior of both the atomic and the field quantum
properties and its dependence on the maximal number of excitations.
