Nuclear ground-state spins and magnetic moments of ${}^{27}\mathrm{Mg}$, ${}^{29}\mathrm{Mg}$, and ${}^{31}\mathrm{Mg}$

The ground-state spins and magnetic moments of neutron-rich ${}^{27}\mathrm{Mg}$, ${}^{29}\mathrm{Mg}$, and ${}^{31}\mathrm{Mg}$ were measured for the first time with laser and β-NMR spectroscopy at ISOLDE/CERN. The hyperfine structure of ${}^{27}\mathrm{Mg}$—observed in fluorescence—confirms previous assignments of the spin $I=1/2$ and reveals the magnetic moment ${\mu }_I({}^{27}\mathrm{Mg})=-0.4107(15){\mu }_N$. The hyperfine structure and nuclear magnetic resonance of optically polarized ${}^{29}\mathrm{Mg}$—observed in the asymmetry of its β decay after implantation in a cubic crystal—give $I=3/2$ and ${\mu }_I({}^{29}\mathrm{Mg})=+0.9780(6){\mu }_N$. For ${}^{31}\mathrm{Mg}$ they yield together $I=1/2$ and ${\mu }_I({}^{31}\mathrm{Mg})=-0.88355(15){\mu }_N$, where the negative magnetic moment provides evidence for a positive parity. The results for ${}^{27}\mathrm{Mg}$ and ${}^{29}\mathrm{Mg}$ agree well with shell-model calculations confined only to the $\mathit{sd}$ model space, whereas the ground state of ${}^{31}\mathrm{Mg}$ involves large contributions from neutrons in the $\mathit{pf}$ shell, which places this nucleus inside the “island of inversion.”

Figure 1

Collinear laser spectroscopy and β-NMR setup.

Figure 2

Adiabatic decoupling of the nuclear and electronic spins in a magnetic field for the example of ${}^{29}\mathrm{Mg}$ ($I=3/2,{\mu }_I>0$).

Figure 3

Hyperfine structure of the $D_1$ transition in ${}^{27}\mathrm{Mg}$.

Figure 4

Measured hyperfine structure (left) and simulations (right) for the $D_2$ transition in ${}^{29}\mathrm{Mg}$ ($I=3/2,{\mu }_I>0$). The simulated spectra are given on a frequency scale that corresponds to the voltage scale in the real spectra. The experimental baseline is different from zero because of an instrumental asymmetry offset.

Figure 5

Larmor resonance of ${}^{29}\mathrm{Mg}$ in MgO.

Figure 6

Measured hyperfine structure (left) and its simulations (right) for the $D_2$ transition in ${}^{31}\mathrm{Mg}$ ($I=1/2,{\mu }_I<0,a_{\beta }=-1$). The simulated spectra are given on a frequency scale that corresponds to the voltage scale in the real spectra. The experimental baseline is different from zero because of an instrumental asymmetry offset.

Figure 7

Theoretical and experimental magnetic moments of $N=15$ isotones with even $Z$. Theoretical values based on our calculations using USD [24] and USDB [25] residual interactions and the ANTOINE code [26]. Experimental values are from Refs. [16, 41, 42] and this work.

Figure 8

Theoretical and experimental magnetic moments of even-$Z$, odd-$N$ nuclei with one unpaired neutron in the $d_{3/2}$ shell ($N=17$ or 19) from Refs. [16, 41, 43, 44] and our measurements.

Figure 9

Measured and predicted excitation energies and $g$ factors for the ground state and lowest excited states in ${}^{29}\mathrm{Mg}$. Experimental results are from Ref. [45] and our measurements. Theoretical values from our own calculations and Ref. [37].

Figure 10

Measured and predicted excitation energies, spins, parities, and $g$ factors for the ground state and lowest excited states in ${}^{31}\mathrm{Mg}$. For the $\mathit{pf}$-shell calculations intruder $1/2^{-}$ states are also shown. For the SDPF.NR interaction only levels up to 500 keV are shown. Experimental results are from Refs. [46, 47] and our measurements. Theoretical results are from the present calculations and Refs. [10, 32, 36, 37].