Fine and hyperfine structure of $^{\mathrm{173}}$YbF

$^{\mathrm{174}}$YbF has been used for some time in attempts to determine the electrostatic T,P violating electron electric dipole moment (eEDM). It was recently pointed out [1] that $^{\mathrm{173}}$YbF may be an avenue for determining an EDM induced by the magnetic quadrupole moment (MQM). As in the eEDM case, here the molecular properties of $^{\mathrm{173}}$YbF are experimentally advantageous. We report a detailed analysis of the fine and hyperfine structure in the $X^{\mathrm{2}}\Sigma^{\mathrm{+}}$ state from a combined analysis of rotational and optical transitions. Numerous hyperfine components in the $N=$4-5 and $N=$3-4 rotational transitions were recorded using a separated field pump/probe microwave optical double residence technique. Fourier transform microwave spectroscopy was used to record five features of the $N=$0-1 rotational transition. This rotational data was combined with precisely measured (0,0) A$^{\mathrm{2}}\Pi _{\mathrm{1/2}}-X^{\mathrm{2}}\Sigma^{\mathrm{+}}$ optical transitions of a cold molecular beam sample. Resulting fine and hyperfine parameters will be discussed and compared with recent theory [2]. 1. V.V. Flambaum, et al., arXiv:1810.02477v2 [hep-ph] (10 Dec 2018) 2. P. Schwerdtfeger, et al., Mol. Phys. \textbf{114}, 1110 (2016)