Shape polarization in the tin isotopes near $N=60$ from precision $g$-factor measurements on short-lived $11/2^{-}$ isomers

Abstract

The $g$ factors of $11/2^{-}$ isomers in semimagic ${}^{109}$Sn and ${}^{111}$Sn (isomeric lifetimes $\ddot{I}„=2.9(3)$ ns and $\ddot{I}„=14.4(7)$ ns, respectively) were measured by an extension of the Time Differential Perturbed Angular Distribution technique, which uses \LaBr detectors and the hyperfine fields of a gadolinium host to achieve precise measurements in a new regime of short-lived isomers. The results, $g(11/2^{-};{}^{109}\text{Sn})=-0.186(8)$ and $g(11/2^{-};{}^{111}\text{Sn})=-0.214(4)$, are significantly lower in magnitude than those of the $11/2^{-}$ isomers in the heavier isotopes and depart from the value expected for a near pure neutron $h_{11/2}$ configuration. Broken-symmetry density functional theory calculations applied to the sequence of $11/2^{-}$ states reproduce the magnitude and location of this deviation. The $g(11/2^{-})$ values are affected by shape core polarization; the odd $0h_{11/2}$ neutron couples to $J^{\ddot{I}}€=2^{+},4^{+},6^{+}...$ configurations in the weakly-deformed effective core, causing a decrease in the $g$-factor magnitudes.

8 pages, 7 figures. Accepted in Physics Letters B