On Fermi's model for the scattering of a slow neutron from a bound proton

We consider a model Hamiltonian, introduced by Fermi in 1936, describing a two-particle system made of a neutron and a harmonically bound proton, where the neutron-proton interaction has the form of a $\delta$-potential. For such Hamiltonian we prove the Limiting Absorption Principle and describe the stationary scattering theory. Finally, we derive Fermi's formula for the scattering cross-section valid in the Born approximation.