Simple correlations between electric quadrupole moments of atomic nuclei

Abstract

Measurements of nonyrast electric quadrupole moments (i.e., diagonal $E2$ matrix elements) of atomic nuclei are becoming widely available from multiple-step Coulomb excitation. It is shown that, where quadrupole-moment data exist, $\ensuremath{\langle}{2}_{1}^{+}||E2||{2}_{1}^{+}\ensuremath{\rangle}+\ensuremath{\langle}{2}_{2}^{+}||E2||{2}_{2}^{+}\ensuremath{\rangle}\ensuremath{\approx}0$ is observed across a wide range of masses, deformations, and first ${2}^{+}$ energies. Nearly all of these quadrupole-moment data, particularly $\ensuremath{\langle}{2}_{2}^{+}||E2||{2}_{2}^{+}\ensuremath{\rangle}$, are from the past two decades with half of the data from the past decade. In addition, $\ensuremath{\langle}{4}_{1}^{+}||E2||{4}_{1}^{+}\ensuremath{\rangle}+\ensuremath{\langle}{4}_{2}^{+}||E2||{4}_{2}^{+}\ensuremath{\rangle}+\ensuremath{\langle}{4}_{3}^{+}||E2||{4}_{3}^{+}\ensuremath{\rangle}\ensuremath{\approx}0$ is observed within two standard deviations for three of the four existing measurements. Despite many and varying complexities in the structure details of the individual nuclei, the correlations in the quadrupole moments appear simple.