In the course of investigations of thermal neutron detection based on mixtures of $^{10}$BF$_3$ with other gases, knowledge was required of the photoabsorption cross sections of $^{10}$BF$_3$ for wavelengths between 135 and 205 nm. Large discrepancies in the values reported in existing literature led to the absolute measurements reported in this communication. The measurements were made at the SURF III synchrotron radiation facility at the National Institute of Standards and Technology. The measured absorption cross sections vary from 10$^{-20}$ cm$^2$ at 135 nm to less than 10$^{-21}$ cm$^2$ in the region from 165 to 205 nm. Three previously unreported absorption features with resolvable structure were found in the regions 135 to 145 nm, 150 to 165 nm and 190 to 205 nm. Quantum mechanical calculations, using the TD-B3LYP/aug-cc-pVDZ variant of time-dependent density functional theory implemented in Gaussian 09, suggest that the observed absorption features arise from symmetry-changing adiabatic transitions.
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