A glimpse into an effective world

Our contribution aims to celebrate the immeasurable contribution that Tom Kuo has provided to the understanding of the structure of atomic nuclei, and also of the infinite nuclear matter, in terms of the fundamental principles governing the realistic nuclear potential. The authors want to testify Tom Kuo's heritage and impact on their approach to the study of nuclear systems by reviewing some recent findings on the role of the two-body component of shell-model effective $\beta$-decay operators. The focus is spotted on the so-called Pauli-blocking effect, that plays a non-negligible role in nuclei characterized by a large number of valence nucleons.