In this work, we study the differential scattering cross-section (DSCS) in the first-order Born approximation. It is not difficult to show that the DSCS can be simplified in terms of the system response function. Also, the system response function has this property to be written in terms of the spectral function and the momentum distribution function in the impulse approximation (IA) scheme. Therefore, the DSCS in the IA scheme can be formulated in terms of the spectral function and the momentum distribution function. On the other hand, the DSCS for an electron off the [Formula: see text] and [Formula: see text] nuclei is calculated in the harmonic oscillator shell model. The obtained results are compared with the experimental data, too. The most important result derived from this study is that the calculated DSCS in terms of the spectral function has a high agreement with the experimental data at the low-energy transfer, while the obtained DSCS in terms of the momentum distribution function does not. Therefore, we conclude that the response of a many-fermion system to a probe particle in IA must be written in terms of the spectral function for getting accurate theoretical results in the field of collision. This is another important result of our study.
Addendum: Calculation of momentum distribution function of a non-thermal fermionic dark matter
