  In this paper we use the formalism of S.Weinberg in order to construct a
mathematical model based on the weak decay of hadrons and nuclei. In particular
we consider a model which generalizes the weak decay of the nucleus of the
cobalt. We associate with this model a Hamiltonian with cutoffs in a Fock
space. The Hamiltonian is self-adjoint and has an unique ground state. By using
the commutator theory we get a limiting absorption principle from which we
deduce that the spectrum of the Hamiltonian is absolutely continuous above the
energy of the ground state and below the first threshold.
