Systematic description of nuclear electric quadrupole moments

The nuclear electric quadrupole moment (NQM) is one of the fundamental bulk properties of the nucleus with which nuclear deformations can be investigated. The number of measured NQMs is significantly less than that of known masses, and there is still no global NQM formula for all bound nuclei. In this paper, we propose an analytical formula, which includes the shell corrections and which is the function of the charge number, mass number, spin, charge radius, and nuclear deformation, for calculating the NQMs of all bound nuclei. Our calculated NQMs of 524 nuclei in their ground states are reasonable compared to the experimental data based on the nuclear deformation parameters derived from the Weizsäcker-Skyrme (WS) nuclear mass models. Smaller rms deviations between the calculated NQMs and experimental data indicate that the deformation parameters predicted from the WS mass models are reasonable. In addition, 161 unmeasured NQMs with known spins are also predicted with the proposed formula.