Shell-structure fingerprints of tensor interaction

TL;DR

This paper investigates how tensor interactions influence nuclear binding energies and shell structure, revealing tensorial magic numbers and their evolution with neutron excess using Skyrme functional analysis.

Contribution

It introduces the concept of tensorial magic numbers in nuclear binding energies and analyzes their behavior under different nuclear configurations and neutron excess.

Findings

Tensor contribution exhibits shell-like topological features.

Tensorial magic numbers are identified at N(Z)=14, 32, 56, 90.

These magic numbers shift with increasing neutron excess.

Abstract

We address consequences of strong tensor and weak spin-orbit terms in the local energy density functional, resulting from fits to the $f_{5/2} - f_{7/2}$ splittings in $^{40}$Ca, $^{48}$Ca, and $^{56}$Ni. In this study, we focus on nuclear binding energies. In particular, we show that the tensor contribution to the binding energies exhibits interesting topological features closely resembling that of the shell-correction. We demonstrate that in the extreme single-particle scenario at spherical shape, the tensor contribution shows tensorial magic numbers equal to $N(Z)$=14, 32, 56, and 90, and that this structure is smeared out due to configuration mixing caused by pairing correlations and migration of proton/neutron sub-shells with neutron/proton shell filling. Based on a specific Skyrme-type functional SLy4$_T$, we show that the proton tensorial magic numbers shift with increasing neutron excess to $Z$=14, 28, and 50.