Mass radius and D-term of atomic nuclei in relativistic mean field theory

TL;DR

This study uses relativistic mean field theory to analyze nuclear radii and the D-term across various isotopes, revealing shell structure effects on nuclear mechanical properties.

Contribution

It provides the first detailed analysis of how nuclear shell structure influences mechanical properties like the D-term and radii in atomic nuclei.

Findings

D-term exhibits non-monotonic behavior with neutron number.

Characteristic kinks in radii at magic and sub-magic numbers.

Strong sensitivity of mechanical properties to shell structure.

Abstract

Based on relativistic mean field theory for atomic nuclei, we compute the mass radius and other radii associated with the energy momentum tensor for dozens of spin-0 nuclei across the nuclear chart. We also compute the D-term of these nuclei, the forward limit of the gravitational form factor $D(t=0)=D$. The dependence on the neutron number $N$ is systematically studied for calcium (Ca), nickel (Ni), zirconium (Zr), tin (Sn) and lead (Pb) isotopes. Remarkably, $|D|$ does not monotonically increase with $N$. Instead, it exhibits local maxima and minima when $N$ equals a magic number and even a sub-magic number. This results in characteristic kinks in the mass, scalar, tensor and shear radii of these isotopes. Our work for the first time elucidates the strong sensitivity of the various mechanical properties of nuclei to the nuclear shell structure.