Measurement of the spin and magnetic moment of $^{31}$Mg: Evidence for a strongly deformed intruder ground state

Unambiguous values of the spin and magnetic moment of $^{31}$Mg are obtained by combining the results of a hyperfine-structure measurement and a $\beta$-NMR measurement, both performed with an optically polarized ion beam. With a measured nuclear $\textit{g}$-factor and spin $\scriptstyle\textrm{I}$= 1/2, the magnetic moment $\mu(^{31}\!$Mg)=-0.88355(15)$\mu\scriptstyle_\textrm{N}$ is deduced. A revised level scheme of $^{31}$Mg( Z=12, N=19 ) with ground state spin/parity $\scriptstyle\textrm{I}$$^{\pi}$= 1/2$^{+}$ is presented, revealing the coexistence of 1p-1h and 2p-2h intruder states below 500keV. Advanced shell-model calculations and the Nilsson model suggest that the $\scriptstyle\textrm{I}$$^{\pi}$= 1/2$^{+}$ ground state is a strongly prolate deformed intruder state. This result plays a key role for the understanding of nuclear structure changes due to the disappearance of the N=20 shell gap in neutron-rich nuclei.