Scaling features of the nuclear electromagnetic response functions unveil aspects of nuclear dynamics that are crucial for interpretating neutrino- and electron-scattering data. In the large momentum-transfer regime, the nucleon-density response function defines a universal scaling function, which is independent of the nature of the probe. In this work, we analyze the nucleon-density response function of $^{12}$C, neglecting collective excitations. We employ particle and hole spectral functions obtained within two distinct many-body methods, both widely used to describe electroweak reactions in nuclei. We show that the two approaches provide compatible nucleon-density scaling functions that for large momentum transfers satisfy first-kind scaling. Both methods yield scaling functions characterized by an asymmetric shape, although less pronounced than that of experimental scaling functions. This asymmetry, only mildly affected by final state interactions, is mostly due to nucleon-nucleon correlations, encoded in the continuum component of the hole SF.
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