Renormalization persistency of tensor force in nuclei

TL;DR

This paper demonstrates that the tensor component of effective nuclear interactions remains largely unchanged through renormalization procedures, a property termed 'Renormalization Persistency', with significant implications for nuclear structure modeling.

Contribution

It introduces and provides evidence for the 'Renormalization Persistency' of the tensor force in nuclear effective interactions, a novel insight into the stability of tensor contributions after renormalization.

Findings

Tensor-force contribution to the monopole term is nearly unchanged after renormalization.

Renormalization persistency is observed primarily in the tensor force, not in the central force.

This property holds across different renormalization methods and shell-model spaces.

Abstract

In this work we analyze the tensor-force component of effective interactions appropriate for nuclear shell-model studies, with particular emphasis on the monopole term of the interactions. Standard nucleon-nucleon ($NN$) interactions such as AV8' and $\chi$N$^3$LO are tailored to shell-model studies by employing $V_{low k}$ techniques to handle the short-range repulsion of the $NN$ interactions and by applying many-body perturbation theory to incorporate in-medium effects. We show, via numerical studies of effective interactions for the $sd$ and $pf$ shells, that the tensor-force contribution to the monopole term of the effective interaction is barely changed by these renormalization procedures, resulting in almost the same monopole term as the one of the bare $NN$ interactions. We propose to call this feature {\it Renormalization Persistency} of the tensor force, as it is a remarkable property of the renormalization and should have many interesting consequences in nuclear systems. For higher multipole terms, this feature is maintained to a somewhat smaller extent. We present general intuitive explanations for the renormalization persistency of the tensor force, as well as analyses of core-polarization terms in perturbation theory. The central force does not exhibit a similar renormalization persistency.