The nuclear magnetic moment of the ground state of $^{55}$Ni ($I^{pi}=3/2^{-}, T_{1/2}=204$ ms) has been deduced to be $|mu$^{55}Ni)$|=(0.976 pm 0.026)$ $mu_N$ using the $beta$-NMR technique. Results of a shell model calculation in the full textit{fp
} shell model space with the GXPF1 interaction reproduce the experimental value. Together with the known magnetic moment of the mirror partner $^{55}$Co, the isoscalar spin expectation value was extracted as $<sum sigma_z >=0.91 pm 0.07$. The $<sum sigma_z>$ shows a similar trend as that established in the textit{sd} shell. The present theoretical interpretations of both $mu(^{55}$Ni) and $<sum sigma_z>$ for the $T=1/2$, A=55 mirror partners support the softness of the $^{56}$Ni core.
Progress in the measurement of the ground state magnetic moments of mirror nuclei at NSCL is presented. The systematic trend of the spin expectation value $<s>$ and the linear behavior of $gamma_p$ versus $gamma_n$, both extracted from the magnetic m
oments of mirror partners, are updated to include all available data.
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 Z
nO 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.
A beta-ray detecting nuclear quadrupole resonance system has been developed at NSCL/MSU to measure ground-state electric quadrupole moments of short-lived nuclei produced as fast rare isotope beams. This system enables quick and sequential applicatio
n of multiple transition frequencies over a wide range. Fast switching between variable capacitors in resonance circuits ensures sufficient power delivery to the coil in the beta-ray detecting nuclear magnetic resonance technique. The fast switching technique enhances detection efficiency of resonance signals and is especially useful when the polarization and/or production rate of the nucleus of interest are small and when the nuclear spin is large.
