Magnetic Moment of $^{57}$Cu and shell breaking of the $^{56}$Ni core

The nuclear magnetic moment of the ground state of $^{57}$Cu was deduced for the first time. Together with a known magnetic moment of the mirror partner, $^{57}$Ni, the spin expectation value, which is a contribution of nucleon spins to the magnetic moment, was extracted from the isoscaler part of magnetic moments. In the $sd$ shell, a systematic trend of the spin expectation value of isospin $T$ = 1/2 mirror nuclei has been observed. On the other hand, in the $fp$ shell, only a few mirror magnetic moments are known and therefore it is essential to measure more magnetic moments to explore the evolution of shell structure. Because $^{57}$Cu consists of the closed-shell $^{56}$Ni core plus one proton, the single-particle contribution is expected to be strong and any deviation from the shell model is a direct proof of shell breaking at $^{56}$Ni, which has been suggested [1] based on a systematic deviation between magnetic moments of odd-mass Cu isotopes and theoretical shell-model predictions. \\ From the resonance frequency, the magnetic moment was derived as $|\mu(^{57}{\rm Cu})| = (2.00 \pm 0.05) \mu_{\rm N}$ [2]. The $A$ = 57, $T$ = 1/2 spin expectation value was extracted as $\langle\Sigma\sigma_z\rangle = -0.78 \pm 0.13$. The small $\mu(^{57}$Cu) results in a large deviation and opposite sign from the shell-model calculations [3,4]. Considering the systematic behavior of the spin expectation value of $T$ = 1/2 nuclei in the $sd$ shell, the present result indicates a significant shell breaking at $^{56}$Ni with the neutron number $N$ = 28.\\ \noindent [1] V. V. Golovko {\it et al}., Phys. Rev. {\bf C 70}, 014312 (2004).\\ \noindent [2] K. Minamisono {\it et al}., Phys. Rev. Lett. {\bf 96}, 102501 (2006).\\ \noindent [3] D. R. Semon {\it et al}., Phys. Rev. {\bf C 53}, 96 (1996).\\ \noindent [4] M. Honma {\it et al}., Phys. Rev. {\bf C 69}, 034335 (2004).