Quadrupole Moments of Odd-Neutron Nuclei; Spin and Moments of 14-YearCd113m

The nuclear spin and hfs in the $\mathrm{}\left(5s5p\right)\mathrm{}{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ state of 14-year ${\mathrm{Cd}}^{113m}$ have been measured by the optical double-resonance technique. The isotope was produced by the reaction ${\mathrm{Cd}}^{112}(n, \gamma ){\mathrm{Cd}}^{113m}$. After irradiation, the ${\mathrm{Cd}}^{113m}$ was separated from the ${\mathrm{Cd}}^{112}$ with an electromagnetic mass separator. The nuclear spin $I$, and the hfs separations are: $I=\frac{11}{2}$; $\nu (\frac{13}{2}-\frac{11}{2})=4310.572\mathrm{}\left(5\right)\mathrm{}$ Mc/sec; $\nu (\frac{11}{2}-\frac{9}{2})=3949.625\mathrm{}\left(7\right)\mathrm{}$ Mc/sec. The hfs coupling constants, corrected to second order for interaction with the ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ states, are: $A\left(113m\right)=-686.0425\mathrm{}\left(8\right)\mathrm{}$ Mc/sec; $B\left(113m\right)=+169.047\mathrm{}\left(9\right)\mathrm{}$ Mc/sec. If we neglect nuclear structure and quadrupole shielding effects, the nuclear moments are: $\mu \mathrm{}\left(113m\right)=-1.08885\mathrm{}\left(13\right)\mathrm{}{\mu }_N$; $Q\left(113m\right)=-0.79\mathrm{}\left(10\right)\mathrm{}$ b. The ratio of the ${\mathrm{Cd}}^{113m}$ and ${\mathrm{Cd}}^{109}$ quadrupole moments is $\frac{Q\left(113m\right)\mathrm{}}{Q\left(109\right)\mathrm{}}=-1.02371\mathrm{}\left(4\right)\mathrm{}$; this result is independent of the shielding corrections. The spin and magnetic moment are consistent with a ${\left(2\mathrm{}{d}_{\frac{5}{2}}\right)}^6{\left(1\mathrm{}{g}_{\frac{7}{2}}\right)}^8{\left(1\mathrm{}{h}_{\frac{11}{2}}\right)}^1$ neutron assignment with some configuration mixing. We compare the observed quadrupole moments in cadmium and other spherical odd-neutron nuclei (A$189<A<\mathrm{}210\mathrm{}$) with predictions of the shell model, including configuration mixing, and with the quasiparticle model of Kisslinger and Sorensen. In addition, we show that the semiempirical formula $Q=-\left[\frac{\mathrm{}(2j+1-2N)\mathrm{}}{\mathrm{}(2j+2)\mathrm{}}\right]Q_0\mathrm{}\left(Z\right)\mathrm{}$ accurately predicts the quadrupole-moment ratios for the isotopes of several elements. We find that $Q_0\mathrm{}\left(Z\right)\mathrm{}$ exhibits strongly oscillatory dependence on the nuclear charge $Z$ with minima near the magic proton numbers. We suggest that $Q_0\mathrm{}\left(Z\right)\mathrm{}$ may be interpreted in terms of the quadrupolar polarizability of the proton core.