Quadrupole Moments of Neutron-Deficient ${}^{20,21}$Na

Abstract

The electric-quadrupole coupling constant of the ground states of the proton drip line nucleus ${}^{20}$Na($I^{\ddot{I}}€$ = 2${}^{+}$, $T_{1/2}$ = 447.9 ms) and the neutron-deficient nucleus ${}^{21}$Na($I^{\ddot{I}}€$ = 3/2${}^{+}$, $T_{1/2}$ = 22.49 s) in a hexagonal ZnO single crystal were precisely measured to be $|eqQ/h|=690\pm 12$ kHz and 939 $\pm$ 14 kHz, respectively, using the multi-frequency ${\hat{I}}^2$-ray detecting nuclear magnetic resonance technique under presence of an electric-quadrupole interaction. A electric-quadrupole coupling constant of ${}^{27}$Na in the ZnO crystal was also measured to be $|eqQ/h|=48.4\pm 3.8$ kHz. The electric-quadrupole moments were extracted as $|Q{(}^{20}$Na)$|$ = 10.3 $\pm$ 0.8 $e$ fm${}^2$ and $|Q{(}^{21}$Na)$|$ = 14.0 $\pm$ 1.1 $e$ fm${}^2$, using the electric-coupling constant of ${}^{27}$Na and the known quadrupole moment of this nucleus as references. The present results are well explained by shell-model calculations in the full $sd$-shell model space.

Accepted for publication in Physics Letters B