Nuclear Magnetic Moment of the ${}^{57}\mathrm{Cu}$ Ground State

The nuclear magnetic moment of the ground state of ${}^{57}\mathrm{Cu}(I^{\pi }=3/2^{-},T_{1/2}=196.3\mathrm{ms})$ has been measured to be $|\mu ({}^{57}\mathrm{Cu})|=(2.00\pm 0.05){\mu }_N$ using the $\beta$-NMR technique. Together with the known magnetic moment of the mirror partner ${}^{57}\mathrm{Ni}$, the spin expectation value was extracted as $⟨\Sigma {\sigma }_z⟩=-0.78\pm 0.13$. This is the heaviest isospin $T=1/2$ mirror pair above the ${}^{40}\mathrm{Ca}$ region for which both ground state magnetic moments have been determined. The discrepancy between the present results and shell-model calculations in the full $fp$ shell giving $\mu ({}^{57}\mathrm{Cu})\sim 2.4{\mu }_N$ and $⟨\Sigma {\sigma }_z⟩\sim 0.5$ implies significant shell breaking at ${}^{56}\mathrm{Ni}$ with the neutron number $N=28$.

Figure 1

Asymmetry change ($1+2AP$) of ${}^{57}\mathrm{Cu}$ in the NaCl as a function of $H_0$ is shown in (a). In (b), the NMR data taken at 0.2 T with $\mathrm{FM}=\pm 50\mathrm{kHz}$ are shown. In (c), the data taken at 0.15 T with $\mathrm{FM}=\pm 25\mathrm{kHz}$ are shown. The hatched areas in (b) and (c) are base lines obtained from weighted sum of all the data except the resonance point.

Figure 2

Magnetic moments of odd-mass Cu isotopes. The solid circle is the present result and solid squares are the experimental data. The dashed line and open squares are the theoretical calculation from 4, the open circle from 10, and the open-inverse triangle from 6. The open triangles are predictions based on the systematics [5].

Figure 3

Spin expectation value of known $T=1/2$ pair in the $fpg$ shell. The solid circles are the experimental data, open square is from 10 and the open circle from 6. The Schmidt values are indicated by the solid lines.