Ambiguities in the implementation of the impulse approximation for the response of many-fermion systems

Within the impulse approximation the response of a many body system at large momentum tranfer can be written in a simple and transparent form, allowing to directly relate the inclusive scattering cross section to the properties of the target ground state. Although the physics assumptions underlying impulse approximation are well defined, their implementation involves ambiguities that may cause significant differences in the calculated responses. We show that, while minimal use of the impulse approximation assumptions naturally leads to write the response in terms of the target spectral function, the widely used alternative definition in terms of the momentum distribution involves a more extended use of the same assumtpions. The difference between the responses resulting from the two procedures is illustrated by two examples.