Level structures of 110,111,112,113Rh from measurements on 252Cf

Level schemes of $^{111}\mathrm{Rh}$ and $^{113}\mathrm{Rh}$ are proposed from the analysis of $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ coincidence data from a $^{252}\mathrm{Cf}$ spontaneous fission source with Gammasphere. These schemes have the highest excitation energies and spins yet established in these nuclei, as well as weakly populated bands not reported in earlier fission-$\ensuremath{\gamma}$ work. From these data, information on shapes is inferred. By analogy with lighter $Z=45$ odd-even isotopes, tentative spins and parities are assigned to members of several rotational bands. In this region triaxial nuclear shapes are known to occur, and we carried out calculations for $^{111}\mathrm{Rh}$ and $^{113}\mathrm{Rh}$ with the triaxial-rotor-plus-particle model. The $7∕{2}^{+}\ensuremath{\pi}{g}_{9∕2}$ bands of both nuclei, as well as lighter isotopes studied by others, show similar signature splitting. Our model calculations give a reasonable fit to the signature splitting, collective sidebands, and transition probabilities at near-maximum triaxiality with $\ensuremath{\gamma}\ensuremath{\approx}28\ifmmode^\circ\else\textdegree\fi{}$. For the $K=1∕{2}^{+}[431]$ band, experiment and model calculations do not fit well, which is accounted for by greater prolate deformation of the $K=1∕{2}^{+}$ band, a case of shape coexistence. Our data on $^{110,112}\mathrm{Rh}$ show no backbending and thus support the idea of the band crossing in the ground band of the odd-A neighbors being due to alignment of an ${h}_{11∕2}$ neutron pair. In $^{111,113}\mathrm{Rh}$ above the band crossing (spins $\ensuremath{\approx}21∕2\ensuremath{\hbar}$) the ground band appears to split, with two similar branches. We consider the possibility that chiral doubling may be involved, but there are not enough levels to determine that.