Effect of tensor force on lowering of 5/2$^{-}$ level in heavier Cu isotopes

TL;DR

This paper investigates how the tensor component of the nucleon-nucleon interaction influences shell evolution, specifically the inversion of energy levels in heavier Cu isotopes, using an analytical approach within the shell model.

Contribution

The study introduces an analytical method to incorporate tensor force TBMEs into the shell model for the extit{pfg} space, where traditional spin-tensor decomposition is not applicable.

Findings

Tensor force inclusion improves agreement with experimental level inversion.

Analytical tensor TBMEs effectively modify the effective interaction.

Tensor force is crucial for accurate shell evolution modeling.

Abstract

The inversion of 3/2$^{-}$ and 5/2$^{-}$ levels in heavier Cu isotopes is one of the most visible example of shell-evolution, caused by the strong monopole attraction between the nucleons occupying the orbitals $\pi 0f_{5/2}$ and $\nu 0g_{9/2}$. The tensor part of the nucleon-nucleon interaction is expected to be the driving force behind this monopole migration. In shell model framework, usually spin-tensor decomposition is used to get the information of individual force components to the shell evolution, however, in the present scenario, this method can not apply on \textit{pfg} model space due to the missing spin-orbit partners $ 0f_{7/2}$ and $ 0g_{7/2}$. Therefore, we have analytically obtained the tensor force two-body matrix elements (TBMEs) for this model space using Yukawa potential, and subtract it from effective interaction jj44b \cite{}. The interaction without tensor part, named as jj44a, have been used for calculation of Ni, Zn, Ge and Cu isotopes with various physics viewpoints. In most of the cases, the theoretical results are in good agreement with the experiment only when tensor force is included to the interaction jj44a.