  The shell model Monte Carlo (SMMC) method is a powerful method for
calculating exactly (up to statistical errors) thermal observables and
statistical properties of atomic nuclei. However, its application has been
limited by a sign problem at low temperatures that arises from the projection
onto odd particle number even for good-sign interactions. Here, we develop a
technique - the partition function extrapolation method (PFEM) - to extract the
ground-state energy of an odd-mass nucleus from the excitation partition
function calculated at temperatures at which this sign problem is moderate. We
validate the PFEM in heavy even-mass nuclei and systematically calculate
ground-state energies for isotopic chains of heavy odd-mass nuclei. The PFEM
can be extended to other finite-size quantum many-body systems.
