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

TL;DR

This study precisely measured the quadrupole moments of neutron-deficient $^{20}$Na and $^{21}$Na nuclei using nuclear magnetic resonance techniques, providing data that align with shell-model predictions.

Contribution

First precise measurement of quadrupole moments of $^{20}$Na and $^{21}$Na, confirming shell-model calculations in the full $sd$-shell space.

Findings

Measured quadrupole moments: $^{20}$Na = 10.3 e fm$^2$, $^{21}$Na = 14.0 e fm$^2$

Results agree with shell-model calculations

Provided new data on electric-quadrupole interactions in these nuclei

Abstract

The electric-quadrupole coupling constant of the ground states of the proton drip line nucleus $^{20}$Na($I^{\pi}$ = 2$^{+}$, $T_{1/2}$ = 447.9 ms) and the neutron-deficient nucleus $^{21}$Na($I^{\pi}$ = 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 $\beta$-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.