Measurement of the Spin and Magnetic Moment of ${}^{31}\mathrm{M}\mathrm{g}$: Evidence for a Strongly Deformed Intruder Ground State

Unambiguous values of the spin and magnetic moment of ${}^{31}\mathrm{M}\mathrm{g}$ 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 $g$ factor and spin $I=1/2$, the magnetic moment $\mu ({}^{31}\mathrm{M}\mathrm{g})=-0.88355(15){\mu }_N$ is deduced. A revised level scheme of ${}^{31}\mathrm{M}\mathrm{g}$ ($Z=12$, $N=19$) with ground state spin/parity $I^{\pi }=1/2^{+}$ is presented, revealing the coexistence of 1p-1h and 2p-2h intruder states below 500 keV. Advanced shell-model calculations and the Nilsson model suggest that the $I^{\pi }=1/2^{+}$ 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.

Figure 1

(a),(b) Hyperfine structure (HFS) spectra of ${\sigma }^{+}/{\sigma }^{-}$ optically polarized ${}^{31}\mathrm{M}\mathrm{g}^{+}$ ions, observed via the asymmetry in the nuclear $\beta$ decay after implantation into MgO. (c) Hyperfine structure in the transition $3s{}^{2}S_{1/2}\to 3p{}^{2}P_{3/2}$ ($D_2$ line) assuming a nuclear spin $I=1/2$. (d)–(f) Simulated spectra assuming $I=1/2$ or $I=3/2$, using the absolute $g$ factor measured by NMR. The allowed transitions are labeled by the total angular momenta $F$ of the ground- and excited-state hyperfine levels.

Figure 2

Typical $\beta$ NMR for ${}^{31}\mathrm{M}\mathrm{g}$ implanted in MgO.

Figure 3

Partial experimental level scheme of ${}^{31}\mathrm{M}\mathrm{g}$, with new spin/parity assignments, compared to various shell-model calculations (see text for details). The magnetic moments of theoretical levels are mentioned on the right (units ${\mu }_N$).