Abstract
We extend an effective field theory developed to describe rotational bands in even-even nuclei to the odd-mass case. This organizes Bohr and Mottelson's treatment of a particle coupled to a rotor as a model-independent expansion in powers of the angular velocity of the overall system. We carry out this expansion up to fourth order in the angular velocity and present results for $^{99}\mathrm{Tc}$, $^{159}\mathrm{Dy}$, $^{167,169}\mathrm{Er}$, $^{167,169}\mathrm{Tm}$, $^{183}\mathrm{W}$, $^{235}\mathrm{U},$ and $^{239}\mathrm{Pu}$. In each case, the accuracy and breakdown scale of the effective field theory can be understood based on the single-particle and vibrational energy scales in that nucleus.
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