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

TL;DR

This paper rigorously analyzes Fermi's 1936 model of neutron-proton scattering, proving key mathematical principles and deriving the scattering cross-section formula within the Born approximation.

Contribution

It provides a rigorous mathematical foundation for Fermi's model, including the Limiting Absorption Principle and the derivation of Fermi's scattering formula.

Findings

Proved the Limiting Absorption Principle for the model

Described the stationary scattering theory for the system

Derived Fermi's formula for the scattering cross-section

Abstract

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.