We evaluate the damage function Dia(T) giving the "Global Damage" of type a produced in a cascade initiated by a recoil atom of type i of (recoil) energy T. Global Damage of type a may indicate, for example, the number of vacancies of atoms of type j, ionization produced in the cascade, energy dissipated by electronic heating, and energy dissipated by nuclear heating.

We establish an integral equation of the "importance, or adjoint" type for Dia(T) and solve it numerically. To start directly from an equation for Dia(T) is for our purpose much easier and faster than (1) to construct the flux of moving atoms by solving the Boltzmann equation (e.g., by the Monte Carlo method) and then (2) to evaluate the damage by keeping track of all particle histories and collecting the information at damage events.

The total damage of Type α due to a neutron spectrum ϕ(E) is then given by Dα(ϕ)=∑i∫dE∫dTϕ(E)∑i(T∕E)Diα(T)=∫ϕ(E)=∑α(E)dE where Σ i (T/E) = neutron-reaction cross section for producing recoil atoms of type ⁱ with recoil energy ^T, and Σ α (E) = macroscopic damage cross section (for damage type α) for the material under investigation.

In a first application we evaluate this macroscopic damage cross section (for vacancy production) for ⁵⁶Fe in the energy range from 7.0 to 40.0 MeV. Fe was taken to be in a homogeneous amorphous phase of density of 7.8 g/cm³.