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

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.