  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.
