The response of many-fermion system in the framework of spectral function and momentum distribution

According to Benhar et al. (BFF), there are significant differences between the two alternative definitions of the incoherent dynamical response function of many-fermion system, i.e., (i) the spectral function and (ii) the momentum distribution function within the impulse approximation (IA). The aim of present article is to look into details of these differences. The coherent and incoherent response functions are calculated and it is shown that at a larger momentum transfer, the coherent part is negligible. By using the impulse approximation, we discuss the condition that both (i) the spectral function and (ii) momentum distribution reproduce identical response functions. In agreement with BFF, we show that the ambiguities arise as a result of two different implementations of IA assumptions which lead to the above alternative formalisms. Finally we present a few examples for the non-interacting and interacting nuclear matter and light nuclei, and we calculate the corresponding nuclear structure factors.