Collective properties of the odd-mass I nuclei:I117,119,121

The high-spin states of ${}_{}{}^{117,119,121}{}_{}{}^{}\mathrm{I}$ have been investigated by in-beam $\gamma$-ray spectroscopy via the ${}_{}{}^A{}_{}{}^{}\mathrm{Sn}({}_{}{}^6{}_{}{}^{}\mathrm{Li}, 3n){}_{}{}^{A+3\mathrm{}}{}_{}{}^{}\mathrm{I}$ reactions to study the collective properties of the odd-mass I isotopes. A similar study of ${}_{}{}^{123,125,127}{}_{}{}^{}\mathrm{I}$ is reported in the preceding paper. Two collective features have been observed: $\Delta J=1\mathrm{}$ bands built on low-lying ${\frac{9}{2}}^{+}$ proton-hole states and $\Delta J=2\mathrm{}$ bands built on ${\frac{11}{2}}^{-}$, ${\frac{7}{2}}^{+}$ and ${\frac{5}{2}}^{+}$ quasiproton states. The $\Delta J=2\mathrm{}$ energy spacings for the ${\frac{11}{2}}^{-}$ bands decrease significantly relative to those for the ground-state bands of the Te core nuclei as $A$ decreases, but not for the ${\frac{7}{2}}^{+}$ and ${\frac{5}{2}}^{+}$ $\Delta J=2\mathrm{}$ bands. This unexpected decrease can be explained in a generalized seniority scheme. The systematic properties of the $\Delta J=2\mathrm{}$ bands for all of the odd-mass I isotopes are summarized. These collective properties are examined in terms of both the microscopic and phenomenological approaches. Pulsed-beam-$\gamma$ measurements yielded mean lifetimes of $\tau =17.5\mathrm{}\pm 1.0, 41.5\pm 1.5, 13.5\pm 0.5$ ns for the ${\frac{9}{2}}^{+}$ proton-hole states in ${}_{}{}^{117,119,121}{}_{}{}^{}\mathrm{I}$, respectively. These values imply hindrances of ∼ ${10}^4$ relative to $M1\mathrm{}$ Weisskopf estimates for the transitions to the ${\frac{7}{2}}^{+}$...