Magnetic Dipole Moment of the Doubly-Closed-Shell Plus One Proton Nucleus ${}^{49}\mathrm{Sc}$

The nucleus ${}^{49}\mathrm{Sc}$, having a single $f_{7/2}$ proton outside doubly magic ${}^{48}\mathrm{Ca}$ ($Z=20$, $N=28$), is one of the very few isotopes which makes possible testing of the fundamental theory of nuclear magnetism. The magnetic moment has been measured by online $\beta$ NMR of nuclei oriented at milli-Kelvin temperatures to be $(+)5.616(25){\mu }_N$. The result is discussed in terms of a detailed theory of the structure of the magnetic moment operator, showing excellent agreement with calculated departure from the $f_{7/2}$ Schmidt limit extreme single-particle value. The measurement completes the sequence of moments of Sc isotopes with even numbers of $f_{7/2}$ neutrons: the first such isotopic chain between two major shells for which a full set of moment measurements exists. The result further completes the isotonic sequence of ground-state moments of nuclei with an odd number of $f_{7/2}$ protons coupled to a closed subshell of $f_{7/2}$ neutrons. Comparison with a recent shell-model calculation of the latter sequence is made.

Figure 1

Production of the sample of almost pure ${}^{49}\mathrm{Sc}$ activity following the beam cutoff. Upper: Decrease of 3084 keV ${}^{49}\mathrm{Ca}$ $\gamma$ counts. Center: Combined ${}^{49}\mathrm{Ca}+{}^{49}\mathrm{Sc}$ $\beta$ asymmetry showing change from a negative few $\%$ to a positive $\sim 15\%$ effect. Lower: Anisotropy in the ${}^{60}\mathrm{Co}$ $\gamma$ transition at 1173 keV showing a drop in implant foil temperature.

Figure 2

Upper: Resonance of ${}^{49}\mathrm{Sc}$ $\beta$ activity in Fe. Black (circular) data are from the wide (1 MHz) step search and red (triangular) data from the narrow (0.5 MHz) step search. Horizontal bars—FM width. Vertical bars—statistical error. Lower: Anisotropy of the 1173 keV transition in ${}^{60}\mathrm{Co}$ showing constancy of temperature during the resonance search.

Figure 3

Measured magnetic moments (left) of odd-$A$ Sc $\pi (f_{7/2}{)}^1$ isotopes with additional pairs of $7/2^{-}$ neutrons and (right) of isotones with $\pi (f_{7/2}{)}^n$, $n$ odd, and closed neutron shell $N=28$. Also shown are the $\pi (f_{7/2})$ Schmidt limit and calculations by Honma et al. [11] (triangles).