Quadrupole Moment of $^{37}$K*

The electric quadrupole coupling constant of the ground state of $^{37}$K($I^{\pi}$ = 3/2$^+$, $T_{1/2}$ = 1.22 s) in a tetragonal KH$_2$PO$_4$ single crystal was measured to be $|eqQ/h| = 2.99 \pm 0.07$ MHz. The experiment was performed at NSCL using a newly-developed $\beta$-ray detecting nuclear quadrupole resonance system. The electric quadrupole moment of $^{37}$K was determined to be $|Q(^{37}{\rm K})| = 10.6 \pm 0.4$ $e$ fm$^2$, where the known electric quadrupole coupling constant of stable $^{39}$K in the KH$_2$PO$_4$ crystal [1] was used as a reference. The present experimental result is consistent with but more precise than the previous value (11 $\pm$ 4 $e$ fm$^2$) measured by laser spectroscopy [2]. The present result is larger than that predicted by shell-model calculations in the $sd$ or the $sd$ and $fp$ model spaces. Evaluation of effective charges in this region of the chart of nuclides will be presented as one means to reconcile the discrepancy between experiment and theory. [1] J. Seliger, V. Zagar, Phys. Rev. B 49, 14918 (1994). [2] J. A. Behr et al., Phys. Rev. Lett. 79, 375 (1997).