Determination of the mean excitation energy of water from proton beam ranges

The stopping powers of protons in water are important quantities in proton therapy since they determine absorbed doses to water. These stopping powers were provided by the ICRU in report 49 using the stopping power formula with a mean excitation energy (I  -value) of water of 75±3eV. After the ICRU work was completed, new values of 80±280±2, 81.8, and 77 eV were reported. The difference in the I-values between 75 and 80 eV results in 0.8–1.2% differences in the stopping power in the energy range of 10–250 MeV, which implies the same impact on absorbed doses. It is therefore important to verify the I-value. We have determined the I-value from the proton beam ranges in water. The ranges were determined from the depth dose curves of mono-energetic beams (Bragg curve) measured in a water phantom. The proton energies at the synchrotron were determined with good accuracy. The I  -value was determined to be 78.4±1.0eV, so that the ranges calculated from the stopping power formula for the proton energies at the synchrotron agreed with the measured ranges. The uncertainty came from the ambiguity in the range determination from the Bragg curves, the water-equivalent thicknesses of the devices in the beam line, and the displacement error of the detector in the water phantom.