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PURPOSE: This paper considers the kinematic physical characteristics of ionic beams for maximum relative bio-effectiveness (RBE). METHODS: RBE studies, based on heterogenous cell survival studies at different laboratories and linear energy transfer (LET) conditions for proton, helium, carbon, neon and argon ions have been further analysed to determine the LETU values where RBE is maximal and the LET-RBE relationship has a turnover point. The SRIM stopping power software and other classical equations are used to determine the particle velocities, kinetic energies and their effective ionic charges at LETU. RESULTS: The estimated mean LETU values increase with atomic number (Z). Each LETU has a unique relativistic velocity, =v/c, the velocity v expressed as a fraction of the speed of light, c), and which is non-linearly proportional to Z. For ions helium and heavier ions, these velocities indicate that the effective charge Z* is around 0.99 of the full Z value at each LETU, with remarkably stable velocities of 3-4 nm.fs-1 per nucleon, or around 6-8 nm.fs-1 per unit Z. For Z=1, (protons and deuterium) some values fall outside these ranges but the result depends on the mix of proton and deuterium used in experiments. An alternative index of A/Z2 (A is the atomic mass number), suggests an average velocity of around 15 nm.fs-1 for each particle at LETU. These distances, traversed in the time of the radiochemical process initiation, are all within the dimensions of the nucleosome. Curve fitting of the data set provides a predictive equation for LETU for any ion, as LETU=30.4+108.4⁄0.61 (1-Exp[-0.61(Z-1)]) when normalised to protons. These data can be extended to heavier ions such as silicon and Iron and give values that are consistent with experimental data. CONCLUSIONS: Each ion probably has a unique LETU value. Kinematic studies show maximum bio-effectiveness occurs at particle velocities where electron stripping remains at around 99% and where the velocity per nucleon is around 3-4 nm.fs-1.

Original publication




Journal article


Phys Med Biol

Publication Date



LET, RBE, radiobiology