Collective properties of the odd-mass I nuclei:I123,125,127

The high-spin states of ${}_{}{}^{123,125,127}{}_{}{}^{}\mathrm{I}$ have been investigated 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. In-beam measurements of $\gamma$-ray excitations, $\gamma -\gamma$ coincidences, $\gamma$-ray angular distributions, and pulsed beam-$\gamma$ timing were performed with Ge detectors to determine level energies, decay schemes, $\gamma$-ray multipolarities, $J^{\pi }$ assignments, and lifetime information. A similar study of the ${}_{}{}^{117,119,121}{}_{}{}^{}\mathrm{I}$ isotopes is reported in the following paper. Two collective features have been identified in these odd-mass I nuclei. Systematic $\Delta J=1\mathrm{}$ bands built on low-lying ${\frac{9}{2}}^{+}$ proton-hole (4p-1h) states were observed. The ${\frac{9}{2}}^{+}$ bandheads, that involve the excitation of a $1g_{\frac{9}{2}}$ proton across the $Z=50\mathrm{}$ shell, drop to very low energies near the middle of the neutron shell. The properties of the ${\frac{9}{2}}^{+}$ proton-hole states for all of the odd-mass I isotopes are presented and related to the systematic information for the proton-hole states in the entire $Z>\mathrm{}50\mathrm{}$ transition region. Systematic $\Delta J=2\mathrm{}$ bands built on ${\frac{11}{2}}^{-}$ ($1h_{\frac{11}{2}}$ quasiproton) states, on ${\frac{7}{2}}^{+}$ ($1g_{\frac{7}{2}}$ quasiproton) states, and on ${\frac{5}{2}}^{+}$ ($2d_{\frac{5}{2}}$ quasiproton) states were also observed. The $\Delta J=2\mathrm{}$ band spacings generally follow the spacings of the Te-core ground-state bands with the exception of the ${\frac{11}{2}}^{-}$