  While the shell model Monte Carlo approach has been successful in the
microscopic calculation of nuclear state densities, it has been difficult to
calculate accurately state densities of odd-even heavy nuclei. This is because
the projection on an odd number of particles in the shell model Monte Carlo
method leads to a sign problem at low temperatures, making it impractical to
extract the ground-state energy in direct Monte Carlo calculations. We show
that the ground-state energy can be extracted to a good precision by using
level counting data at low excitation energies and the neutron resonance data
at the neutron threshold energy. This allows us to extend recent applications
of the shell-model Monte Carlo method in even-even rare-earth nuclei to the
odd-even isotopic chains of $^{149-155}$Sm and $^{143-149}$Nd. We calculate the
state densities of the odd-even samarium and neodymium isotopes and find close
agreement with the state densities extracted from experimental data.
