Magnetism of an Excited Self-Conjugate Nucleus: Precise Measurement of the $g$ Factor of the $2_1^{+}$ State in ${}^{24}\mathrm{Mg}$

A precise measurement of the $g$ factor of the first-excited state in the self-conjugate ($N=Z$) nucleus ${}^{24}\mathrm{Mg}$ is performed by a new time-differential recoil-in-vacuum method based on the hyperfine field of hydrogenlike ions. Theory predicts that the $g$ factors of such states, in which protons and neutrons occupy the same orbits, should depart from 0.5 by a few percent due to configuration mixing and meson-exchange effects. The experimental result, $g=0.538\pm 0.013$, is in excellent agreement with recent shell-model calculations and shows a departure from 0.5 by almost 3 standard deviations, thus achieving, for the first time, the precision and accuracy needed to test theory. Proof of the new method opens the way for wide applications including measurements of the magnetism of excited states of exotic nuclei produced as radioactive beams.

Figure 1

Sketch of experiment. The “stopper” of the traditional plunger technique is replaced by a thin foil that resets the electron configuration of H-like ions. The particle detector, with segmentation around the beam axis, is located downstream of the $\gamma$-ray detectors.

Figure 2

Random-subtracted $\gamma$-ray spectrum collected at $80\mu \mathrm{m}$ plunger separation, showing the ${}^{24}\mathrm{Mg}$ $2^{+}\to 0^{+}$ 1368-keV photopeak. Data for all $\gamma$-ray detectors in coincidence with one particle detector segment are shown.

Figure 3

$R(T)$ ratio data, Eq. (2), and fits based on detailed modeling of the experiment [9]. The distance is the separation of target and reset foils ($22.4\mu \mathrm{m}=1\mathrm{ps}$ flight time). The frequency of the oscillation determines the $g$ factor.

Figure 4

Present result (open red circle) and previous results (filled green circles) [6, 17, 18, 19] compared to shell-model calculations with USDA (dashed brown line) and USDB (solid blue line) calculations.