Spectroscopy of ThF$^{\mathrm{+}}$ in aim of a new eEDM measurement with trapped molecular ions

A measurement of the electric dipole moment of the electron (eEDM) can constrain beyond-standard-model physics. Our group at JILA has measured the eEDM to a precision of 1.3e-28 e cm [1]. While a second generation experiment with technological and measurement scheme improvements is underway, we are developing a third generation experiment aimed at increasing the sensitivity to the eEDM with several key improvements: (i) a new molecular ion species, ThF$^{\mathrm{+}}$, which has an eEDM-sensitive ground state and an effective electric field of 38 GV/cm [2], and (ii) a new trap structure allowing for continuous measurement. The first step in designing this experiment is understanding the energy structure of our molecule. In this talk we discuss recent ThF$^{\mathrm{+}}$ spectroscopic results and their implications on the upcoming third generation measurement. [1] Cairncross, W. B. et. Al. Phys. Rev. Lett. 119, 15 (2017), 153001. [2] Skripnikov, L. V., and A. V. Titov. Phys. Rev. A 91.4 (2015): 042504.