Mean excitation energy of liquid water
In plain words
How quickly a charged particle slows down in water depends on one material constant, the average energy needed to excite a water molecule. Its uncertainty alone produces millimetre-scale uncertainty in where a proton beam stops in water.
Precise statement
Determine the mean excitation energy $I$ of liquid water, which enters the Bethe stopping-power formula, to an uncertainty below 1 eV; the ICRU 90 recommendation is $I = 78 \pm 2\,\mathrm{eV}$, and published experimental and dielectric-response values spread over several eV around it. An answer is a value with uncertainty consistent between direct range or stopping-power measurements and optical-data calculations.
What would settle it
Precision range measurements of monoenergetic protons and ions in liquid water at 1 to 250 MeV combined with an evaluation of the optical oscillator strength of liquid water.