Abstract. The influence of the unpaired nucleon on the location and nature of phase transitions in odd-mass nuclei is an intersting issue. To study this, one needs to find adequate definition/choice of the control and order parameters, empirical signatures of the phase transition, and possible candidates for critical point nuclei. We present the evolution of the level structures determined by unique parity orbitals in odd-mass nuclei between Zn and Am, by correlations between excitation energies and ratios of such energies in both odd-mass nuclei and their even-even core nuclei. Clear evidence for a critical phase transition between the decoupling and strong coupling limits is found for nuclei in the mass 160 region around neutron number 90, which is closely correlated with the known critical shape phase transition in their even-even core nuclei from vibrator to rotor (the X(5) critical point). This abrupt change of structure is corroborated by a corresponding non-monotonic behavior of the differential variation of the two-neutron separation energy.

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