A glimpse into an effective world

TL;DR

The paper investigates how to model beta decay in a shell-model framework starting from realistic nuclear potentials. It develops a consistent set of effective Hamiltonians and decay operators, $H_{\rm eff}$ and $\Theta_{\rm eff}$, derived from the CD-Bonn potential renormalized by $V_{low-k}$ via a $\hat{Q}$ box folded-diagram approach. Focusing on $^{100}$Mo with 22 valence nucleons, it shows that the two-body component of the GT decay operator is essential to capture Pauli-blocking effects and to reconcile calculated $M^{2\nu}$ values with experiment, reducing quenching relative to one-body results. The findings support a non-universal GT quenching picture, emphasize the importance of induced many-body operators in large model spaces, and extend Kuo's legacy of connecting realistic nuclear forces to observable nuclear structure. Together, the work demonstrates a practical path to include induced many-body operators in large-scale shell-model calculations.

Abstract

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 $β$-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.

Figures (2)

• Figure 1: Two-body second-order diagrams included in the perturbative expansion of the $\hat{\Theta}$ box. The asterisk indicates the bare operator $\Theta$, $\lambda$ is the rank of the decay operator.
• Figure 2: Running sums of the $^{100}$Mo $\sum {\rm B(GT^-)}$ strengths as a function of the excitation energy $E_x$ up to 3 MeV.