Testing the predictive power of realistic shell model calculations via lifetime measurement of the 11/2+ state in Sb131

Abstract

The lifetime of the $11/{2}_{1}^{+}$ state in the $^{131}\mathrm{Sb}$ nucleus was measured at the LOHENGRIN spectrometer of the Institut Laue-Langevin via neutron-induced fission of $^{235}\mathrm{U}$ using $\ensuremath{\gamma}$-ray fast-timing techniques. The obtained value of ${T}_{1/2}=3\phantom{\rule{0.16em}{0ex}}$(2) ps, at the edge of the sensitivity of the experimental method, is the first result for the $11/{2}_{1}^{+}$ state half-life in neutron-rich Sb isotopes. The corresponding quadrupole reduced transition probability to the ground state is $B(E2)=1.{4}_{\ensuremath{-}0.6}^{+1.5}$W.u., indicating a noncollective nature of this state. Realistic shell-model calculations performed in a large valence space reproduce well the experimental value and point to a dominant ${2}^{+}(^{130}\mathrm{Sn})\ensuremath{\bigotimes}\ensuremath{\pi}{\mathrm{g}}_{7/2}$ configuration for the $11/{2}_{1}^{+}$ state, as expected in a weak-coupling scenario. At the same time, the sum of the quadrupole strength of the multiplet states is predicted to exceed the one of the $^{130}\mathrm{Sn}$ core as a consequence of the equal contribution of the proton and the proton-neutron quadrupole matrix elements, pointing to possible development of collectivity already in the close neighborhood of $^{132}\mathrm{Sn}$.